Problem: In addition to the bananas given to Johnnie the monkey in the morning and afternoon, the zookeeper decides to give Johnnie the same total amount of bananas the next day. How many bananas in total did Johnnie the monkey receive over these two days?

Gemini-1.5 Flash:

Reasoning:  Johnnie received a total of 24/7 bananas on the first day.  Since he received the same amount on the second day, he received 24/7 + 24/7 = 48/7 bananas over the two days.

### Answer: 48/7 

Expected answer: 48/7

Correct? Yes

Problem: If we consider the distance from the floor and ceiling for both the front and back doors, which have the same measurements as the original door, what is the total distance considering the bottoms and tops of both doors from the floor and ceiling respectively?

Gemini-1.5 Flash:

Reasoning: We already know the total distance for one door is 211/190 inches.  Since both doors have the same measurements, we simply need to double this distance.

Total distance = 2 * (211/190) = 422/190 inches.

### Answer: 422/190 inches 

Expected answer: 211/95

Correct? Yes

Problem: If we reconsider the original scenario with the bottom of a door measuring 4/16 inches from the floor instead of 4/19 inches, and the top still measuring 9/10 inches from the ceiling, what is the new total distance of the bottom and top of the door from the floor and ceiling, respectively?

Gemini-1.5 Flash:

Reasoning:  We need to add the distance from the floor to the bottom of the door and the distance from the ceiling to the top of the door.
So we are adding 4/16 + 9/10.
To add fractions, we need to have a common denominator.
The least common multiple of 16 and 10 is 80.
So, we have 4/16 = 20/80 and 9/10 = 72/80.
Now, we can add: 20/80 + 72/80 = 92/80.
### Answer: 92/80 inches 

Expected answer: 23/20

Correct? Yes

Problem: After finishing his juice recipe, Ralph decides to add an additional 3/18 liters of apple juice to the mix. How many liters of unused apple juice are left now?

Gemini-1.5 Flash:

Reasoning: We already know Ralph had 142/33 liters of apple juice left unused. Now, he adds 3/18 liters. To find the new amount of unused juice, we subtract the added amount from the previous amount:

142/33 - 3/18

To subtract fractions, they need to have the same denominator. The least common denominator of 33 and 18 is 198.

142/33 * 6/6 = 852/198
3/18 * 11/11 = 33/198

Now, we can subtract: 852/198 - 33/198 = 819/198

Therefore, Ralph has 819/198 liters of apple juice left unused.

### Answer: 819/198 

Expected answer: 91/22

Correct? Yes

Problem: If Ralph had initially started with 17/3 liters of apple juice but had only used 14/11 liters, how many liters of apple juice would he have left unused then?

Gemini-1.5 Flash:

Reasoning: To find out how much apple juice Ralph has left unused, we need to subtract the amount used from the initial amount he had.

We have: 17/3 - 14/11

To subtract fractions, they need to have the same denominator. The least common denominator of 3 and 11 is 33. 

17/3 * 11/11 = 187/33
14/11 * 3/3 = 42/33

Now, we can subtract: 187/33 - 42/33 = 145/33

Therefore, Ralph would have 145/33 liters of apple juice left unused.

### Answer: 145/33 

Expected answer: 145/33

Correct? Yes

Problem: In a change of earlier data, it was discovered that the rocket only traveled 15/3 light years on the first day. However, on the second day, it actually covered 18/7 light years instead of 2/7 light years. With this new information, how far has the rocket traveled in total?

Gemini-1.5 Flash:

Reasoning:  Let's re-calculate the total distance traveled using the updated information:

* Distance traveled on the first day: 15/3 light years
* Distance traveled on the second day: 18/7 light years

To add these fractions, we need a common denominator. The least common denominator for 3 and 7 is 21.

* 15/3 = (15 * 7) / (3 * 7) = 105/21
* 18/7 = (18 * 3) / (7 * 3) = 54/21

Now we can add the fractions:

* 105/21 + 54/21 = (105 + 54) / 21 = 159/21

Therefore, the rocket has traveled a total of 159/21 light years.

### Answer: 159/21 

Expected answer: 53/7

Correct? Yes

Problem: After Captain Silverbeard finds the portions of the treasure map, he discovers another piece on a third site which is 15/17 of the total map. What is the total portion of the treasure map that Captain Silverbeard has now?

Gemini-1.5 Flash:

Reasoning: We need to add the portion of the map Captain Silverbeard found on the third site (15/17) to the total portion he already had (1 and 151/247).  

First, let's convert the mixed number to an improper fraction: 1 and 151/247 = (1 * 247 + 151) / 247 = 398/247.

Now we need a common denominator for 398/247 and 15/17. The least common multiple of 247 and 17 is 4199.

* To get a denominator of 4199 for 398/247, multiply both numerator and denominator by 17: (398 * 17) / (247 * 17) = 6766/4199
* To get a denominator of 4199 for 15/17, multiply both numerator and denominator by 247: (15 * 247) / (17 * 247) = 3705/4199

Now we can add the fractions: 6766/4199 + 3705/4199 = (6766 + 3705) / 4199 = 10471/4199

This is an improper fraction. Let's convert it to a mixed number: 10471/4199 = 2 and 1073/4199.

### Answer: 2 and 1073/4199 

Expected answer: 10471/4199

Correct? No

Problem: Suppose instead of finding 10/13 of the treasure map at the first shipwreck site, Captain Silverbeard found a larger piece which was 10/9 of the total map. Keeping the second portion from the other shipwreck site the same at 16/19, what is the total portion of the treasure map that he found now?

Gemini-1.5 Flash:

Reasoning: Captain Silverbeard found 10/9 of the map at the first site and 16/19 at the second site. To find the total portion, we need to add these fractions: 10/9 + 16/19.

We need to find a common denominator for 9 and 19. The least common multiple is 171.

* To get a denominator of 171 for 10/9, we multiply both numerator and denominator by 19: (10 * 19) / (9 * 19) = 190/171.
* To get a denominator of 171 for 16/19, we multiply both numerator and denominator by 9: (16 * 9) / (19 * 9) = 144/171.

Now we can add the fractions: 190/171 + 144/171 = (190 + 144)/171 = 334/171.

This is an improper fraction, so we convert it to a mixed number: 334/171 = 1 and 163/171.

### Answer: 1 and 163/171 

Expected answer: 334/171

Correct? Yes

Problem: In continuation to the previous question, after walking 9/6 miles North and 2/16 miles East, the hiker then decides to continue his journey and walks an additional 8/14 miles South. How many miles has the hiker now traveled in total?

Gemini-1.5 Flash:

Reasoning: We know from the previous problem that the hiker has already traveled 13/8 miles.  Now, he walks an additional 8/14 miles South.  We can find the total distance traveled by adding this distance to the distance already traveled.  But first, we need to make sure the fractions have the same denominator. 

The fraction 8/14 can be simplified to 4/7.  We can then convert this fraction into an equivalent fraction with a denominator of 56 by multiplying both the numerator and denominator by 8.  (4/7)*(8/8) = 32/56.  

We can convert 13/8 into an equivalent fraction with a denominator of 56 by multiplying the numerator and denominator by 7.  (13/8)*(7/7) = 91/56.  

Now that we have equivalent fractions with a common denominator, we can add them.  

91/56 + 32/56 = 123/56.  

The hiker has now traveled a total of 123/56 miles.

### Answer: 123/56 

Expected answer: 123/56

Correct? Yes

Problem: In opinion to the previous case, imagine if the hiker had initially decided to walk 10/6 miles North instead of 9/6 miles, while keeping the distance walked East unchanged at 2/16 miles. How many miles would the hiker have then traveled in total?

Gemini-1.5 Flash:

Reasoning:  The hiker walks 10/6 miles North and then 2/16 miles East.  To find the total distance traveled, we need to add these distances.  However, we need to make sure that we are adding fractions with the same denominator.  
 
 The fraction 10/6 can be simplified to 5/3.  This can then be converted into an equivalent fraction with a denominator of 16 by multiplying both the numerator and denominator by (16/3).  (5/3) * (16/3) = 80/9. 
 
 Now that both fractions have a common denominator, we can add them together. 
 
 (80/9) + (2/16) = 1282/144. 
 
 The hiker has traveled a total of 1282/144 miles.
 
 ### Answer: 1282/144 

Expected answer: 43/24

Correct? No

Problem: Jessica decided to add more sand to her sandbox. She adds an extra 19/15 cubic feet of sand to it. After this, how much sand does she now have in her sandbox?

Gemini-1.5 Flash:

Reasoning: We need to add the amount of sand Jessica added to the amount she had left.  

We already know she had 172/117 cubic feet of sand left. To add this to 19/15, we need a common denominator.  The least common multiple of 117 and 15 is 585.

* 172/117 is equivalent to (172*5)/(117*5) = 860/585
* 19/15 is equivalent to (19*39)/(15*39) = 741/585

Now we can add: 860/585 + 741/585 = (860+741)/585 = 1601/585

Jessica has 1601/585 cubic feet of sand in her sandbox. 

### Answer: 1601/585 

Expected answer: 1601/585

Correct? Yes

Problem: In our previous scenario, let's say that Jessica initially had a smaller pile of sand that was 16/9 cubic feet. If she still removed 4/8 cubic feet of sand as before, how much sand does she now have left in her sandbox?

Gemini-1.5 Flash:

Reasoning: We need to subtract the amount of sand Jessica removed from the original amount. 

First, we need to find a common denominator for 9 and 8. The least common multiple of 9 and 8 is 72.

* 16/9 is equivalent to (16*8)/(9*8) = 128/72
* 4/8 is equivalent to (4*9)/(8*9) = 36/72

Now we can subtract: 128/72 - 36/72 = (128-36)/72 = 92/72

Jessica has 92/72 cubic feet of sand left in her sandbox. 

### Answer: 92/72 

Expected answer: 23/18

Correct? Yes

Problem: Jacob now wants to double the total length of the rope he has. If Jacob starts with the rope that is ((15 / 12) + (17 / 17)) meters long, and then adds another piece of the same length to it, what will be the total length of the combined ropes?

Gemini-1.5 Flash:

Reasoning:  We already know that the rope is 2 3/12 meters long. 
To double this, we multiply it by 2: (2 3/12) * 2 = 4 6/12 meters.
### Answer: 4 6/12 meters 

Expected answer: 9/2

Correct? Yes

Problem: Now, suppose Jacob starts with a piece of rope that is 7/12 meters long instead of 15/12 meters. If he still adds the rope piece that is 17/17 meters long to it, what is the total length of the rope now?

Gemini-1.5 Flash:

Reasoning: We still know that a rope that is 17/17 meters long is equal to 1 whole meter.
This time we are adding 7/12 meters to 1 meter.
So, the total length of the rope is 1 7/12 meters. 
### Answer: 1 7/12 meters 

Expected answer: 19/12

Correct? Yes

Problem: Mark already had 1 full pair of pants and another 13/4 pairs from various incomplete sets. If he goes shopping and buys an additional 13/3 pairs of pants, how many pairs of pants does he have in total now?

Gemini-1.5 Flash:

Reasoning: Mark starts with 1 + 13/4 = 17/4 pairs of pants. 
He buys another 13/3 pairs of pants.
Adding these together, Mark has 17/4 + 13/3 = 51/12 + 52/12 = 103/12 pairs of pants.
This is equal to <<103/12 = 8 7/12>> 8 7/12 pairs of pants.

### Answer: 8 7/12 

Expected answer: 103/12

Correct? Yes

Problem: Instead of starting with 1 full pair of pants and another 13/4 pairs, let's say Mark originally had 1 full pair of pants and 9/4 pairs from various incomplete sets. How many pairs of pants would he then have in total?

Gemini-1.5 Flash:

Reasoning: Mark has 1 + 9/4 = <<1 + 9/4 = 13/4>> 13/4 pairs of pants.
This is the same as <<13/4 = 3 1/4>> 3 1/4 pairs of pants.
### Answer: 3 1/4 

Expected answer: 13/4

Correct? Yes

Problem: After grading papers, Miss Jenny spends an additional 1/12 hours organizing her lesson plans. How long did she spend in total between grading papers and organizing her lesson plans?

Gemini-1.5 Flash:

Reasoning:  We know Miss Jenny spent 39/19 hours grading papers.  
To find the total time, we add the time spent grading papers and organizing lesson plans: 39/19 + 1/12 = <<39/19 + 1/12 = 487/228>> 487/228 hours.

### Answer: 487/228 hours 

Expected answer: 487/228

Correct? Yes

Problem: Suppose instead of spending 20/19 hours on the second subject, Miss Jenny had actually spent 20/13 hours. How long did she spend grading papers in total then?

Gemini-1.5 Flash:

Reasoning: Miss Jenny spent 1 hour on the first subject.
Adding the time spent on the second subject, she spent 1 + 20/13 = <<1 + 20/13 = 33/13>> 33/13 hours grading papers in total.

### Answer: 33/13 hours 

Expected answer: 33/13

Correct? Yes

Problem: After visiting his grandparents' house, Jack decides to ride his scooter to the park, which is another 20/12 of mile from his grandparents' house. How many miles does Jack ride his scooter in total now?

Gemini-1.5 Flash:

Reasoning:  We already know Jack rode 66/45 miles. To find the total distance, we need to add the distance to the park: 20/12.  To add these fractions, we need a common denominator. The least common multiple of 45 and 12 is 180.

* 66/45 * 4/4 = 264/180
* 20/12 * 15/15 = 300/180

Now we can add the distances: 264/180 + 300/180 = 564/180

### Answer: 564/180 

Expected answer: 47/15

Correct? Yes

Problem: Suppose after revisiting the route, Jack realizes the distance from his home to the library is actually 3/9 of a mile instead of 5/9. The distance from the library to his grandparents' house still remains 17/20 of a mile. How many miles does Jack ride his scooter in total then?

Gemini-1.5 Flash:

Reasoning:  The distance to the library is 3/9 of a mile, which simplifies to 1/3 of a mile. We need to find a common denominator for 1/3 and 17/20. The least common multiple of 3 and 20 is 60. 

* 1/3 * 20/20 = 20/60
* 17/20 * 3/3 = 51/60

Now we can add the fractions: 20/60 + 51/60 = 71/60 miles. 

### Answer: 71/60 

Expected answer: 71/60

Correct? Yes

Problem: After the logs and twigs burn out, Tom adds 8 pieces of charcoal, each of which burns for 1/5 of an hour. What is the total burn time for the logs, twigs, and charcoal?

Gemini-1.5 Flash:

We know the logs and twigs burn for a total of 19/12 hours. 

Now let's calculate the burn time for the charcoal:

* Each piece of charcoal burns for 1/5 of an hour.
* There are 8 pieces of charcoal.
* Total burn time for charcoal: (1/5 hour/piece) * 8 pieces = 8/5 hours

**Total Burn Time (Logs, Twigs, and Charcoal):**

* Total burn time: (19/12 hours) + (8/5 hours) = 151/60 hours

### Answer: 151/60 hours 

Expected answer: 191/60

Correct? No

Problem: In the original scenario, consider that there were actually 4 logs that each burn for 1/16 of an hour, but Tom only added 15 twigs that each burn for 1/12 of an hour instead. What would be the total burn time for the logs and twigs in this situation?

Gemini-1.5 Flash:

Here's the breakdown:

**Logs:**

* Each log burns for 1/16 of an hour.
* There are 4 logs.
* Total burn time for logs: (1/16 hour/log) * 4 logs = 1/4 hour

**Twigs:**

* Each twig burns for 1/12 of an hour.
* There are 15 twigs.
* Total burn time for twigs: (1/12 hour/twig) * 15 twigs = 5/4 hours

**Total Burn Time:**

* Total burn time: (1/4 hour) + (5/4 hours) = 6/4 hours = 3/2 hours

### Answer: 3/2 hours 

Expected answer: 3/2

Correct? Yes

Problem: The ring maker decides to add an ornamental filigree to the ring, which requires an additional 18/20 ounces of silver. How many total ounces of silver did the ring maker use including the filigree?

Gemini-1.5 Flash:

Reasoning: We know the ring maker used 8 3/4 ounces of silver for the ring. We need to add the 18/20 ounces of silver used for the filigree.
First, let's simplify 18/20. Both the numerator and denominator are divisible by 2, giving us 9/10.
Now we need to add 8 3/4 and 9/10. To do this, we need a common denominator. The least common denominator of 4 and 10 is 20. 
Let's convert 8 3/4 to an improper fraction: 8 * 4 + 3 = 35, so 8 3/4 is equal to 35/4. Now we can convert 35/4 to an equivalent fraction with a denominator of 20: 35/4 * 5/5 = 175/20.
Finally, we can add the fractions: 175/20 + 9/10 = 175/20 + 18/20 = 193/20. 
Converting 193/20 to a mixed number, we get 9 13/20 ounces.

### Answer: 9 13/20 

Expected answer: 193/20

Correct? Yes

Problem: If initially, the ring maker used 10/16 ounces of a silver for the base of the ring instead of 12/16 ounces, while still using 16/2 ounces to make the rest of the ring, how many total ounces of silver did the ring maker use then?

Gemini-1.5 Flash:

Reasoning:  First, simplify the fraction 10/16 to 5/8 ounces of silver for the base.
The rest of the ring still uses 16/2 = 8 ounces of silver.
So, the ring maker used a total of 5/8 + 8 ounces of silver.
To add fractions, we need a common denominator.  The common denominator of 8 and 1 is 8.  So, we rewrite 8 as 64/8.
Now, we can add the fractions: 5/8 + 64/8 = 69/8
Converting 69/8 to a mixed number, we get 8 5/8 ounces.

### Answer: 8 5/8 

Expected answer: 69/8

Correct? Yes

Problem: Now assume the farmer's first apple tree produced 10/9 bushels instead of 10/11 bushels in the morning. With the same amount of apples in the afternoon, how many bushels of apples did this tree produce in one day?

Gemini-1.5 Flash:

Reasoning: We need to add the amount produced in the morning (10/9 bushels) to the amount produced in the afternoon (17/11 bushels).  To do this, we need a common denominator.

The least common multiple of 9 and 11 is 99.  We can rewrite the fractions:

* 10/9 = (10 * 11)/(9 * 11) = 110/99
* 17/11 = (17 * 9)/(11 * 9) = 153/99

Now we can add: 110/99 + 153/99 = (110 + 153)/99 = 263/99

### Answer: 263/99 

Expected answer: 263/99

Correct? Yes

Problem: After reviewing her measurements, Maria realizes that she actually used a smaller piece of fabric for the second section of the blanket. Instead of the 9/18 yards she originally thought, she actually used only 6/18 yards of fabric. What is the total length of fabric that Maria used for these two sections of the blanket now?

Gemini-1.5 Flash:

Here's how to solve the problem with the new measurement:

1. **Simplify the fraction for the second section:** 6/18 can be simplified to 1/3.

2. **Find a common denominator:** The smallest common denominator for 15/10 and 1/3 is 30.  To get 15/10 to have a denominator of 30, multiply both the numerator and denominator by 3: (15 * 3) / (10 * 3) = 45/30.  To get 1/3 to have a denominator of 30, multiply both the numerator and denominator by 10: (1 * 10) / (3 * 10) = 10/30

3. **Add the fractions:** 45/30 + 10/30 = 55/30

4. **Simplify the answer:** 55/30 can be simplified to 11/6.

### Answer: 11/6 yards 

Expected answer: 11/6

Correct? Yes

Problem: In the previous question, we considered the turtle walking forward 10/5 miles and walking backward 5/16 mile. Now, assume instead that the turtle walks backward a distance of 5/6 miles instead of 5/16 mile after walking forward. Now, how far is the turtle from its starting point?

Gemini-1.5 Flash:

Reasoning: The turtle walked 10/5 = <<10/5=2>>2 miles forward.
The turtle walked 5/6 miles backward, so it covered 2-5/6 = <<2-5/6=7/6>>7/6 miles from its starting point. 
### Answer: 7/6 

Expected answer: 7/6

Correct? Yes

Problem: After mixing the sky blue paint, the painter decides to mix in an additional 12/13 liters of white paint to lighten the shade. How many liters of paint does he have now in total?

Gemini-1.5 Flash:

We know the painter already had 155/88 liters of sky blue paint.  We need to add the 12/13 liters of white paint to find the total.

First, we need a common denominator for 88 and 13. The least common multiple of 88 and 13 is 1144.

* Convert 155/88 to an equivalent fraction with a denominator of 1144: (155/88) * (13/13) = 2015/1144

* Convert 12/13 to an equivalent fraction with a denominator of 1144: (12/13) * (88/88) = 1056/1144

Now we can add the two fractions: 2015/1144 + 1056/1144 = 3071/1144

Therefore, the painter has a total of 3071/1144 liters of paint.

### Answer: 3071/1144 

Expected answer: 3071/1144

Correct? Yes

Problem: Initially, the painter used 18/11 liters of blue paint and 1/8 liters of white paint. However, what if instead of using 1/8 liters, he used 1/7 liters of white paint to mix the sky blue shade. How many liters of paint would he then have used in total?

Gemini-1.5 Flash:

We're given that the painter initially used 18/11 liters of blue paint and now uses 1/7 liters of white paint.  To find the total amount of paint used, we simply need to add these two quantities:

18/11 + 1/7

To add these fractions, we need a common denominator. The least common multiple of 11 and 7 is 77.

* Convert 18/11 to an equivalent fraction with a denominator of 77: (18/11) * (7/7) = 126/77

* Convert 1/7 to an equivalent fraction with a denominator of 77: (1/7) * (11/11) = 11/77

Now we can add the fractions: 126/77 + 11/77 = 137/77

Therefore, the painter would have used a total of 137/77 liters of paint.

### Answer: 137/77 

Expected answer: 137/77

Correct? Yes

Problem: Instead of 12/13 of a pound of magical gold coins in the pot, let's say the pot originally contained 17/13 pounds of gold coins. If we still added this amount to the 3/2 pounds of gold coins in the other pot, how many pounds of gold coins are there now?

Gemini-1.5 Flash:

Reasoning:  To add fractions, they need the same denominator. The least common denominator for 13 and 2 is 26.

* Convert 17/13 to 34/26 (multiply numerator and denominator by 2)
* Convert 3/2 to 39/26 (multiply numerator and denominator by 13)

Now we can add the fractions: 34/26 + 39/26 = 73/26

This is equal to 2 and 21/26 pounds of gold coins.

### Answer: 2 and 21/26 pounds 

Expected answer: 73/26

Correct? Yes

Problem: After watching the original message, Zorg receives an additional part of the message from earth that is 7/8 hours long. What is the total length of all parts of the message that Zorg received?

Gemini-1.5 Flash:

Reasoning: We know Zorg's original message is 12 hours long. 
Adding the new part's length of 7/8 hours to the original message gives us a total length of 12 + 7/8 hours.
To add these, we need to express 12 as an improper fraction with a denominator of 8: 12 = (12 * 8)/8 = 96/8
Now we can add: 96/8 + 7/8 = (96+7)/8 = 103/8 
### Answer: 103/8 

Expected answer: 103/8

Correct? Yes

Problem: Upon reviewing the original video message, Zorg realised that the first part of the video message was actually half as long at 4/8 hours instead of 4/4. The second part of the message still remains 11/1 hour long. What is the total length of the message that Zorg has corrected?

Gemini-1.5 Flash:

Reasoning: The first part of the message is 4/8 = 1/2 hour long. 
The total message is 1/2 + 11/1 = 1/2 + 11/1 = 23/2 hours long.
### Answer: 23/2 

Expected answer: 23/2

Correct? Yes

Problem: On a map, 15/11 inches represents the distance between Town A and Town B, and 16/15 inches represents the distance between Town B and Town C. After measuring the distance between Town C and Town D, which was found to be 20/5 inches. What is the total distance between Town A and Town D on the map?

Gemini-1.5 Flash:

Reasoning: The total distance between Town A and Town D is represented by the sum of the distances between Town A and Town B, Town B and Town C, and Town C and Town D.
The total distance is (15/11) + (16/15) + (20/5) inches.
To add fractions, we need a common denominator. The least common denominator for 11, 15, and 5 is 165.
(15/11) * (15/15) = 225/165
(16/15) * (11/11) = 176/165
(20/5) * (33/33) = 660/165
Therefore, the total distance is 225/165 + 176/165 + 660/165 = 1061/165 inches.
### Answer: 1061/165 inches 

Expected answer: 1061/165

Correct? Yes

Problem: On the same map, suppose the distance between Town A and Town B is not 15/11 but 15/11 inches, and 16/7 inches represents the distance between Town B and Town C. Now, what would be the total distance on the map from Town A to Town C?

Gemini-1.5 Flash:

Reasoning: Similar to the previous problem, the total distance between Town A and Town C is the sum of the distances between Town A and Town B and Town B and Town C.
The total distance is (15/11) + (16/7) inches.
To add fractions, we need a common denominator. The least common denominator for 11 and 7 is 77.
(15/11) * (7/7) = 105/77
(16/7) * (11/11) = 176/77
Therefore, the total distance is 105/77 + 176/77 = 281/77 inches.

### Answer: 281/77 inches 

Expected answer: 281/77

Correct? Yes

Problem: The soap company plans to double their daily production. After producing 13/18 tons of Soap A and 4/6 tons of Soap B each day, how many tons of soap will they produce in total when they double their production?

Gemini-1.5 Flash:

Reasoning:  We already know the company produces 25/18 tons of soap each day (from the previous problem).  To double their production, we simply multiply this amount by 2:

(25/18) * 2 = 50/18

This can be simplified to 2 14/18, or 2 7/9 tons.

### Answer: 2 7/9 tons 

Expected answer: 25/9

Correct? Yes

Problem: The soap company decided to increase the production of Soap A to 17/18 tons a day while maintaining the production of Soap B at 4/6 tons a day. How many tons of soap do they produce in total each day after this change?

Gemini-1.5 Flash:

Reasoning:  We already know that 4/6 tons of Soap B is equivalent to 12/18 tons.  To find the total production, we add the new amount of Soap A to the amount of Soap B: 17/18 + 12/18 = 29/18.

This means the company now produces 29/18 tons of soap each day.  We can express this as a mixed number: 29/18 = 1 11/18.

### Answer: 1 11/18 tons. 

Expected answer: 29/18

Correct? Yes

Problem: After tailoring, Mark finds the sleeping bag is still too long for his comfort. He decides to cut off another 13/14 feet from his sleeping bag. What is the length of his sleeping bag now?

Gemini-1.5 Flash:

Reasoning: We need to subtract the additional 13/14 feet from the current length of the sleeping bag, which is 101/12 feet. To subtract fractions, we need a common denominator. The least common denominator of 12 and 14 is 84. 

We can rewrite 101/12 as 707/84 and 13/14 as 78/84.  Now we can subtract: 707/84 - 78/84 = 629/84

### Answer: 629/84 feet 

Expected answer: 629/84

Correct? Yes

Problem: Originally, Mark bought a sleeping bag that was 8/2 feet long instead of 19/2 feet. He still cuts off 13/12 feet from it to fit his height. How long is his sleeping bag now?

Gemini-1.5 Flash:

Reasoning: We need to subtract the length Mark cuts off (13/12 feet) from the original length (8/2 feet).  First, let's simplify 8/2 to 4.  Now we need a common denominator to subtract the fractions. The least common denominator for 1 and 12 is 12. So we can rewrite 4 as 48/12. Now we can subtract: 48/12 - 13/12 = 35/12.

### Answer: 35/12 feet 

Expected answer: 35/12

Correct? Yes

Problem: After feeding the monkeys and giraffes, Mary then feeds the elephants 19/11 pounds of food. How many pounds of food in total has she given to the monkeys, giraffes, and elephants at the zoo?

Gemini-1.5 Flash:

Reasoning: We already know Mary fed the monkeys and giraffes a total of 3/2 pounds of food.
To find the total amount of food she fed all three animals, we add the amount she fed the elephants to the amount she fed the monkeys and giraffes: 3/2 + 19/11. 
To add fractions, we need a common denominator. The least common multiple of 2 and 11 is 22.
3/2 is equivalent to (3*11)/(2*11) = 33/22. 
19/11 is equivalent to (19*2)/(11*2) = 38/22
Now we can add the fractions: 33/22 + 38/22 = 71/22.
### Answer: 71/22 

Expected answer: 71/22

Correct? Yes

Problem: Originally, Mary had given the monkeys 6/20 pounds of food and the giraffes 18/15 pounds of food. But what if she had made a mistake, and she actually gave the giraffes 18/19 pounds of food instead? How many pounds of food in total did she then give to the monkeys and giraffes?

Gemini-1.5 Flash:

Reasoning:  We need to add the amount of food given to the monkeys and the amount given to the giraffes. The amount given to the monkeys is 6/20 pounds. The amount given to the giraffes is now 18/19 pounds. To add these fractions, we need a common denominator.  The least common multiple of 20 and 19 is 380.

6/20 is equivalent to (6*19)/(20*19) = 114/380
18/19 is equivalent to (18*20)/(19*20) = 360/380

Adding the two fractions, we get 114/380 + 360/380 = 474/380.

### Answer: 474/380 

Expected answer: 237/190

Correct? Yes

Problem: Instead of collecting a full set of 4/1 cards, what if Albert had only managed to find 4/11 of a full set? Adding this to his initial 20/17 full sets, how many full sets of cards does he have now?

Gemini-1.5 Flash:

Reasoning: To add fractions, they need to have the same denominator. The least common multiple of 17 and 11 is 187.  So, 20/17 is equivalent to (20*11)/(17*11) = 220/187 and 4/11 is equivalent to (4*17)/(11*17) = 68/187.  Adding these together, Albert has 220/187 + 68/187 = 288/187 full sets of cards.
### Answer: 288/187 

Expected answer: 288/187

Correct? Yes

Problem: Following the previous situation, the jeweler finds an additional 2/17 pounds of silver hidden in his workshop's storage. Now, how many pounds of silver does he have in total to make rings?

Gemini-1.5 Flash:

Reasoning: We need to add the additional 2/17 pounds of silver to the 347/266 pounds he already has.  To do this, we need a common denominator. The least common multiple of 17 and 266 is 4522. 
(347/266) * (17/17) = 5899/4522
(2/17) * (266/266) = 532/4522
Adding the fractions gives us: 5899/4522 + 532/4522 = 6431/4522 

### Answer: 6431/4522 

Expected answer: 6431/4522

Correct? Yes

Problem: In our previous scenario, suppose the jeweler initially had 8/14 pounds of silver instead of 5/14 pounds and then added 18/19 pounds more to his supplies. How many pounds of silver does the jeweler now have to make rings?

Gemini-1.5 Flash:

Reasoning: To find the total amount of silver, we need to add the initial amount to the amount added.  We need a common denominator to add the fractions. The least common multiple of 14 and 19 is 266.  We get: 
(8/14) * (19/19) = 152/266
(18/19) * (14/14) = 252/266
Adding the fractions gives us: 152/266 + 252/266 = 404/266
The jeweler has 404/266 pounds of silver.

### Answer: 404/266 

Expected answer: 202/133

Correct? Yes

Problem: Continuing from the prior situation, the turtle then decided to move further, walking an additional 15/20 of a meter towards the same direction. How many meters is the turtle from its original starting point now?

Gemini-1.5 Flash:

Reasoning: The turtle is already 10 meters away from its starting point and it moves another 15/20 of a meter in the same direction. 
15/20 of a meter is equal to 0.75 meters.
Therefore, the turtle is now 10 + 0.75 = 10.75 meters from its starting point.

### Answer: 10.75 

Expected answer: 43/4

Correct? Yes

Problem: Reconsider the previous scenario, but this time the turtle returns 15/8 of a meter back towards the starting point instead of the former 15/15 meters. Now, how many meters is the turtle from its starting point after these two movements?

Gemini-1.5 Flash:

Reasoning: The turtle moves 11 meters north, then 15/8 meters south.  To find the distance from the starting point, we need to subtract the distance traveled south from the distance traveled north.

We can find the difference: 11 - (15/8) = (88/8) - (15/8) = (88-15)/8 = 73/8 meters

### Answer: 73/8 

Expected answer: 73/8

Correct? Yes

Problem: After Chloe eats a piece of the chocolate bar, she decides to add a piece from another chocolate bar. The piece from the other bar weighs 4/14 ounces. How many ounces of chocolate does Chloe have now?

Gemini-1.5 Flash:

Reasoning: Chloe now has 1 + 4/14 = 14/14 + 4/14 = 18/14 ounces of chocolate.
### Answer: 18/14 

Expected answer: 9/7

Correct? Yes

Problem: Originally, Chloe had a chocolate bar that was 19/2 ounces. What if instead, at the beginning she had eaten a piece that was 9/2 ounces? How many ounces of chocolate would she have had left then?

Gemini-1.5 Flash:

Reasoning: Chloe would have had 19/2 - 9/2 = 10/2 = 5 ounces of chocolate left.
### Answer: 5 

Expected answer: 5

Correct? Yes

Problem: In addition to his already expanded backpack, Sammy finds another tiny side pocket that can carry an extra 3/8 of a liter. What is the total capacity of his backpack now?

Gemini-1.5 Flash:

Reasoning:  We already know the backpack has a capacity of 38/9 liters. We need to add the capacity of the tiny side pocket, which is 3/8 of a liter.  To add fractions, they need a common denominator. The least common denominator of 9 and 8 is 72.
 
 We convert 38/9 to 304/72 and 3/8 to 27/72.
 
 Adding the fractions: 304/72 + 27/72 = 331/72 

### Answer: 331/72 

Expected answer: 331/72

Correct? Yes

Problem: Instead of the backpack having an initial capacity of 20/9 liters, let's say it could only carry 20/12 liters. If Sammy still adds the same extra pouch of 8/4 liters, what would the total capacity of his backpack be then?

Gemini-1.5 Flash:

Reasoning: First, we simplify the backpack's initial capacity: 20/12 = <<20/12=5/3>> 5/3 liters. 
Then, we add the pouch's capacity to the backpack's current capacity: 5/3 + 2 = <<5/3+2=11/3>> 11/3 liters.
### Answer: 11/3 

Expected answer: 11/3

Correct? Yes

Problem: After counting his newly found gold, Captain Hook discovers an additional 7/11 ounces of gold hidden in a small pouch he had forgotten about. What is the total weight of all the gold Captain Hook now has?

Gemini-1.5 Flash:

Reasoning: We need to add the new gold (7/11 ounces) to the amount Captain Hook already had (2 3/8 ounces). First, let's convert the mixed number into an improper fraction:

* 2 3/8 = (2 * 8 + 3) / 8 = 19/8

Now we need to find a common denominator for 8 and 11, which is 88.

* 19/8 = (19 * 11) / (8 * 11) = 209/88
* 7/11 = (7 * 8) / (11 * 8) = 56/88

Now we can add the fractions:

* 209/88 + 56/88 = 265/88

Simplifying the fraction, we get:

* 265/88 = 3 1/88

Therefore, Captain Hook now has a total of 3 1/88 ounces of gold.

### Answer: 3 1/88 

Expected answer: 265/88

Correct? Yes

Problem: In the previous treasure hunt, Captain Hook had originally found 11/8 ounces of gold. But let's say, instead of finding 5/5 ounces of gold as he did in his latest treasure hunt, he discovered 7/5 ounces of gold. How much total weight of gold would Captain Hook have had then?

Gemini-1.5 Flash:

Reasoning:  We need to add the two amounts of gold together.  Since the fractions have different denominators, we need to find a common denominator.  The least common denominator for 8 and 5 is 40.

* 11/8 = (11 * 5) / (8 * 5) = 55/40
* 7/5 = (7 * 8) / (5 * 8) = 56/40

Now we can add the fractions:

* 55/40 + 56/40 = 111/40

Simplifying the fraction, we get:

* 111/40 = 2 31/40

Therefore, Captain Hook would have had a total of 2 31/40 ounces of gold.

### Answer: 2 31/40 

Expected answer: 111/40

Correct? Yes

Problem: Paul realizes that his chair is too tall, so he decides to shorten it by removing a 2 feet section. After doing so, what is the new height of the chair?

Gemini-1.5 Flash:

Reasoning: We need to subtract 2 feet from the total height of the chair (55/14 feet).  First, we need to convert 2 feet into a fraction with a denominator of 14: 2 feet = (2 * 14)/14 = 28/14 feet.  Now we can subtract: 55/14 - 28/14 = (55 - 28)/14 = 27/14 feet. 
### Answer: 27/14 feet 

Expected answer: 27/14

Correct? Yes

Problem: Following the alteration, Bob decides to cut off an additional 9/4 meters. After yet another alteration, what is the remaining length of Bob's jacket now?

Gemini-1.5 Flash:

Reasoning: We need to subtract the additional length Bob cuts off from the length of the jacket after the first alteration.

Length after first alteration: 91/24 meters
Length cut off in the second alteration: 9/4 meters

We need to find a common denominator for the fractions. The least common multiple of 24 and 4 is 24.

* (9/4) * (6/6) = 54/24

Now we can subtract the lengths: 91/24 - 54/24 = 37/24

Therefore, the length of Bob's jacket after the second alteration is 37/24 meters.

### Answer: 37/24 meters 

Expected answer: 37/24

Correct? Yes

Problem: Initially, Bob's jacket was 16/3 meters in length instead of 14/3 meters. If he still cuts off 14/16 meter from this new original length, then what would be the length of Bob's jacket after the alteration now?

Gemini-1.5 Flash:

Reasoning:  We follow the same steps as before, but with the new original length.

Original length: 16/3 meters
Length cut off: 14/16 meters

Find a common denominator for the fractions. The least common multiple of 3 and 16 is 48.

* (16/3) * (16/16) = 256/48
* (14/16) * (3/3) = 42/48

Now subtract the lengths: 256/48 - 42/48 = 214/48

Simplify the fraction by dividing both numerator and denominator by their greatest common factor, which is 2:

214/48 = (214/2)/(48/2) = 107/24

Therefore, the length of Bob's jacket after the alteration is 107/24 meters.

### Answer: 107/24 meters 

Expected answer: 107/24

Correct? Yes

Problem: If John watched a movie for 10/12 of an hour and then watched a TV show for another 3/8 of an hour, and then repeated this same routine, what is the total time he spent watching in hours?

Gemini-1.5 Flash:

Reasoning: We already know from the previous calculation that John watched for 1 5/24 hours in one round of movie and TV show. 
Since he repeats this routine, the total time is 1 5/24 * 2 = 2 10/24 hours.
### Answer: 2 10/24 hours 

Expected answer: 29/12

Correct? Yes

Problem: If instead of watching the movie for 10/12 of an hour, John watched it for 10/7 of an hour, and he still watched the TV show for another 3/8 of an hour, what is the total time he spent watching in hours?

Gemini-1.5 Flash:

Reasoning:  We need to find a common denominator for 7 and 8, which is 56.
10/7 = (10*8)/(7*8) = 80/56
3/8 = (3*7)/(8*7) = 21/56
Therefore, John watched for a total of 80/56 + 21/56 = 101/56 hours.
This is an improper fraction, so we convert it to a mixed number: 101/56 = 1 45/56
### Answer: 1 45/56 hours 

Expected answer: 101/56

Correct? Yes

Problem: Mr. Carpenter has now taken on an additional task. After building the chair and doing the upholstery work, he spends another 8/19 hours to apply the varnish. Now, how long does the entire process of making a chair take?

Gemini-1.5 Flash:

Reasoning: We already know that building the chair and upholstering it takes 95/39 hours. We need to add the time for varnishing, which is 8/19 hours.

To add these fractions, we need a common denominator. The least common multiple of 39 and 19 is 741.

* (95/39) * (19/19) = 1805/741
* (8/19) * (39/39) = 312/741

Now we can add the fractions: 1805/741 + 312/741 = 2117/741

### Answer: 2117/741 hours 

Expected answer: 2117/741

Correct? Yes

Problem: In another batch of chair production, Mr. Carpenter managed to reduce his timeframe. Now, he takes only 5/10 hours to build the frame of the chair while the time for upholstery stays the same as 10/13 hours. How long does it take for him to build a chair with the new time for frame construction?

Gemini-1.5 Flash:

Reasoning:  We need to add the new time for building the frame (5/10 hours) to the time for upholstering (10/13 hours). 

To add fractions, they need a common denominator. The least common denominator for 10 and 13 is 130. 

* 5/10 hours = (5 * 13) / (10 * 13) = 65/130 hours
* 10/13 hours = (10 * 10) / (13 * 10) = 100/130 hours

Total time: 65/130 + 100/130 = 165/130 hours

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 5. 

Simplified total time: (165/5) / (130/5) = 33/26 hours

### Answer: 33/26 hours 

Expected answer: 33/26

Correct? Yes

Problem: Let's reconsider our previous journey of the rocket. Assume that instead of traveling 8/2 light-years towards a distant star after reaching the alien planet, the rocket only traveled 8/13 light-years. In this case, what would be the total distance covered by the rocket?

Gemini-1.5 Flash:

Reasoning: The rocket traveled 11/18 light-years to the alien planet and then 8/13 light-years to the star. To find the total distance, we need to add these two fractions. 

However, they have different denominators, so we need to find a common denominator. The least common multiple of 18 and 13 is 234.

* We convert 11/18 to a fraction with a denominator of 234: (11*13)/(18*13) = 143/234
* We convert 8/13 to a fraction with a denominator of 234: (8*18)/(13*18) = 144/234

Now we can add the fractions: 143/234 + 144/234 = (143+144)/234 = 287/234

### Answer: 287/234 light-years 

Expected answer: 287/234

Correct? Yes

Problem: After calculating the total fabrics Jonathan needed for the sleeping bag, he remembered that he had bought 17 yards of fabric in total. How many yards does he have left after using the necessary fabric to create his sleeping bag?

Gemini-1.5 Flash:

Reasoning: We need to subtract the fabric needed for the sleeping bag (2 16/35 yards) from the total fabric Johnathan bought (17 yards). 

First, let's convert 17 yards to a mixed number with the same denominator as 2 16/35.  17 yards is the same as 17 0/35.

Now we can subtract: 
17 0/35 - 2 16/35 

Since we can't subtract 16/35 from 0/35, we borrow 1 from the whole number 17, leaving us with 16.  We then convert the 1 we borrowed into 35/35 (to match the denominator).

This gives us: 
16 35/35 - 2 16/35 

Now we can subtract the whole numbers and the fractions separately:

16 - 2 = 14
35/35 - 16/35 = 19/35

Therefore, Johnathan has 14 19/35 yards of fabric left.

### Answer: 14 19/35 

Expected answer: 509/35

Correct? Yes

Problem: In the previous problem, Johnathan originally thought he needed 12/14 yards of one fabric to create the sleeping bag. But after rechecking his measurements, he realized he only needed 12/17 yards of that fabric. The liner fabric remained the same at 8/5 yards. How many total yards of fabric does he actually need to make the sleeping bag?

Gemini-1.5 Flash:

Reasoning: The least common denominator of 17 and 5 is 85.  Let's adjust our fractions to have the same denominator:
* (12/17) * (5/5) = 60/85
* (8/5) * (17/17) = 136/85

Now we can add the fractions together: 60/85 + 136/85 = 196/85. 

This improper fraction simplifies to a mixed number: 196/85 = 2 16/85. 

Therefore, Johnathan actually needs 2 16/85 yards of fabric for his sleeping bag.

### Answer: 2 16/85 

Expected answer: 196/85

Correct? No

Problem: After further research, it is found that the forest actually had 5/3 acres of pine trees instead of 5/4 acres. Keeping the acreage of oak trees the same, what is the new total acreage of pine and oak trees in the forest?

Gemini-1.5 Flash:

Let's recalculate the total acreage with the new information:

* **Pine trees:** 5/3 acres
* **Oak trees:** 1/2 acre

Again, we need a common denominator to add the fractions. The least common denominator of 3 and 2 is 6.

* **Pine trees:** (5/3) * (2/2) = 10/6 acres
* **Oak trees:** (1/2) * (3/3) = 3/6 acres

Now we can add:

* 10/6 + 3/6 = 13/6 acres

### Answer: 13/6 

Expected answer: 13/6

Correct? Yes

Problem: After making his shirt, Jake realizes he needs to remove 4/16 of a yard of fabric for the shirt to fit perfectly. How much fabric will he have left after making this adjustment?

Gemini-1.5 Flash:

Reasoning:  First, simplify the fraction 4/16 by dividing both the numerator and denominator by 4, resulting in 1/4. Now, subtract the amount of fabric he's removing from the total amount: 13/7 - 1/4. To subtract fractions, they must have the same denominator.  The least common denominator for 7 and 4 is 28.  Convert 13/7 to 52/28 and 1/4 to 7/28.  Now subtract the fractions: 52/28 - 7/28 = (52-7)/28 = 45/28.
### Answer: 45/28 

Expected answer: 45/28

Correct? Yes

Problem: Let's say Jake originally had less fabric, only 12/6 yards instead of 12/7 yards. He still finds an additional piece of fabric that measures 2/14 of a yard. If he combines both these pieces now, then how much fabric does he have altogether for his shirt?

Gemini-1.5 Flash:

Reasoning: First, we can simplify 12/6 by dividing both numerator and denominator by 6, resulting in 2/1.  We can also simplify 2/14 by dividing both the numerator and denominator by 2, resulting in 1/7. Now we need a common denominator to add the fractions. The least common denominator for 1 and 7 is 7. To get 7 in the denominator of 2/1, we multiply both numerator and denominator by 7: (2*7)/(1*7) = 14/7. Now we can add: 14/7 + 1/7 = (14+1)/7 = 15/7
### Answer: 15/7 

Expected answer: 15/7

Correct? Yes

Problem: Continuing from the first scenario, suppose that this special tree only produces 10/4 kilograms of fruit in the summer, but it only loses 11/20 kilograms of its fruit in the winter, instead of 12/20 kilograms. What is now the difference in kilograms of the fruit from summer to winter?

Gemini-1.5 Flash:

Reasoning: The difference in the amount of fruit from summer to winter is 10/4 - 11/20 kg. To find the difference, we need a common denominator. The least common denominator for 4 and 20 is 20. So, we have (10/4) * (5/5) - (11/20) = 50/20 - 11/20.
Subtracting the numerators, we get (50-11)/20 = 39/20 kg.
### Answer: 39/20 kg 

Expected answer: 39/20

Correct? Yes

Problem: After shortening her routine, the ballerina decides to add a new dance move that lasts 2/20 minutes. How long is her routine now with the new dance move?

Gemini-1.5 Flash:

Reasoning: We need to add the length of the new dance move to the shortened routine length.  We'll first simplify 2/20 to 1/10 and then find a common denominator for 1/10 and 133/80.  The least common denominator is 80.

* 1/10 = (1*8)/(10*8) = 8/80

Now we can add: 133/80 + 8/80 = 141/80

The ballerina's routine is now 141/80 minutes long.
### Answer: 141/80 

Expected answer: 141/80

Correct? Yes

Problem: If originally the ballerina's routine lasted 13/5 minutes but she had only shortened it by 12/16 minutes instead of 15/16 minutes, how long would her routine be then?

Gemini-1.5 Flash:

Reasoning: We need to find the difference between the original length of the routine and the shortened amount.  As before, we need a common denominator:

* 13/5 = (13 * 16) / (5 * 16) = 208/80
* 12/16 = (12 * 5) / (16 * 5) = 60/80

Now we can subtract: 208/80 - 60/80 = 148/80

The ballerina's routine would be 148/80 minutes long. 
### Answer: 148/80 

Expected answer: 37/20

Correct? Yes

Problem: Following up on the previous scenario, Miss Daisy finds an additional 11/11 kg of fertilizer in her shed. After she took away 17/20 kg from the original 19/6 kg to use on her roses, she added this new amount to the fertilizer she had left. How much fertilizer does she have now?

Gemini-1.5 Flash:

Reasoning: We know Miss Daisy had 139/60 kg of fertilizer left after using some on her roses. 
We also know 11/11 kg is the same as 1 kg. 
Therefore, she has 139/60 + 1 = 199/60 kg of fertilizer.

### Answer: 199/60 

Expected answer: 199/60

Correct? Yes

Problem: Continuing from the scenario, suppose instead of the initial 19/6 kg of fertilizers, Miss Daisy had only 14/6 kg of fertilizers. If she still uses 17/20 kg on her roses, how much fertilizers does she have left to use on her other flowers now?

Gemini-1.5 Flash:

Reasoning: We need to subtract the amount used for roses (17/20 kg) from the total amount Miss Daisy had (14/6 kg). 

First, let's find a common denominator for 6 and 20. The least common multiple of 6 and 20 is 60.

Converting 14/6 to have a denominator of 60: (14/6) * (10/10) = 140/60

Converting 17/20 to have a denominator of 60: (17/20) * (3/3) = 51/60

Now, we can subtract the fractions: (140/60) - (51/60) = 89/60

However, this result is an improper fraction, meaning the numerator is larger than the denominator. We can convert it to a mixed number: 89/60 = 1 29/60.

Since we're dealing with fertilizer, we'll only use the fraction part of the result.

Therefore, Miss Daisy has 29/60 kg of fertilizer left to use on her other flowers.

### Answer: 29/60 

Expected answer: 89/60

Correct? No

Problem: Building upon the previous scenario, if scientists predict an additional increase of 16/6 meters in the coming year, what will be the total expected change in distance from Earth to the moon after this increase?

Gemini-1.5 Flash:

Reasoning:  We need to add the total change this year (43/12 meters) to the predicted change in the coming year (16/6 meters).

First, let's simplify the fraction for the predicted change: 16/6 = 8/3 meters.

To add these fractions, we need a common denominator.  The least common denominator for 12 and 3 is 12.

* (43/12) remains the same.
* (8/3) * (4/4) = 32/12 meters

Now we can add the fractions:
* 43/12 + 32/12 = 75/12 meters

Therefore, the total expected change in distance from Earth to the moon after the additional increase will be 75/12 meters.

### Answer: 75/12 meters. 

Expected answer: 25/4

Correct? Yes

Problem: Continuing from the previous scenario, suppose scientists later realized that there was a calculation error. Instead of an unexpected increase of 20/6 meters in the moon's distance this year, they found the increase was actually 20/18 meters. Given this corrected value, what is the total change in distance from the Earth to the moon this year?

Gemini-1.5 Flash:

Reasoning: We need to find the total change in distance, which is the regular increase of 4/16 meters plus the corrected unexpected increase of 20/18 meters.

First, let's simplify the fractions:
* 4/16 = 1/4 meters
* 20/18 = 10/9 meters

Now, to add these fractions, we need a common denominator. The least common denominator for 4 and 9 is 36.

* (1/4) * (9/9) = 9/36 meters
* (10/9) * (4/4) = 40/36 meters

Now we can add the fractions:
* 9/36 + 40/36 = 49/36 meters

Therefore, the total change in distance this year is 49/36 meters.

### Answer: 49/36 meters. 

Expected answer: 49/36

Correct? Yes

Problem: Bob has 11/3 dollars in one pocket of his wallet and 12/19 dollars in another pocket. How much money does he have in total in his wallet? Now, if Bob duplicates the total amount of money in his wallet, how much money will he have then?

Gemini-1.5 Flash:

First, let's find the total amount of money Bob has:

* **Find a common denominator:** The least common multiple of 3 and 19 is 57. 
* **Convert the fractions:** 
    * (11/3) * (19/19) = 209/57
    * (12/19) * (3/3) = 36/57
* **Add the fractions:** (209/57) + (36/57) = 245/57

Now, let's find out how much money Bob has if he duplicates this amount:

* **Duplicate the total:** (245/57) * 2 = 490/57

**Therefore, if Bob duplicates the amount of money in his wallet, he will have 490/57 dollars.**

### Answer: 490/57 

Expected answer: 490/57

Correct? Yes

Problem: Suppose Bob starts out with 3/3 (or 1) dollar in one pocket of his wallet instead of 11/3 dollars, and still has 12/19 dollars in another pocket. Now how much money does he have in total in his wallet?

Gemini-1.5 Flash:

We already know that 12/19 represents the money in one pocket.  Now we need to add the amount in the other pocket, which is 3/3 (or 1).

Since 1 is the same as 19/19, we can add the fractions directly:

19/19 + 12/19 = 31/19

Therefore, Bob has a total of 31/19 dollars in his wallet.

### Answer: 31/19 

Expected answer: 31/19

Correct? Yes

Problem: Following the previous problem, if the shark decides to swim an additional 18/9 miles in the evening, what is the total distance the shark would have swam by the end of the day?

Gemini-1.5 Flash:

Reasoning: We need to add the total distance already swam (1 and 2/3 miles) to the additional distance swam in the evening (18/9 miles).  First, let's simplify 18/9 to 2.  Now we need to add 1 and 2/3 to 2.  To do this, we can convert 1 and 2/3 to 5/3.  Finally, we add 5/3 + 2 = 11/3. This can be simplified to 3 and 2/3. 
### Answer: 3 and 2/3 

Expected answer: 11/3

Correct? Yes

Problem: Continuing from the last problem, suppose the shark had only swam 5/12 miles in the morning instead of 5/5 miles, but still swam the additional 12/18 miles in the afternoon. How many miles would the shark have swam in the morning and afternoon combined?

Gemini-1.5 Flash:

Reasoning: We need to add the distance swam in the morning and afternoon. First, we simplify 12/18 to 2/3. Then, to add the fractions we need a common denominator. The least common denominator of 12 and 3 is 12. So, we convert 2/3 to 8/12. Finally, we add 5/12 + 8/12 = 13/12. This can be simplified to 1 and 1/12.
### Answer: 1 and 1/12 

Expected answer: 13/12

Correct? Yes

Problem: Suppose on another day, Max rode his scooter for 9/7 miles in the morning and then 1/4 miles less in the afternoon instead of 1/9 miles less. How many miles did he ride his scooter in the afternoon on this different day?

Gemini-1.5 Flash:

Reasoning: Max rode 9/7 - 1/4 miles in the afternoon on this different day. To subtract fractions, they must have the same denominator. The least common denominator of 7 and 4 is 28.  We can rewrite the fractions as 9/7 = 36/28 and 1/4 = 7/28.  
So, Max rode 36/28 - 7/28 = 29/28 miles in the afternoon.
### Answer: 29/28 

Expected answer: 29/28

Correct? Yes

Problem: Following her performances, the clown took a total break of 13/5 hours. How many hours remained after her performance time is subtracted from her total break time?

Gemini-1.5 Flash:

Reasoning:  We need to find the difference between the clown's break time (13/5 hours) and her performance time (1 13/40 hours).

First, let's convert the mixed number performance time to a fraction: 1 13/40 = (40 + 13)/40 = 53/40.

Now, we need a common denominator for 5 and 40.  The least common multiple of 5 and 40 is 40.

We can rewrite 13/5 as 104/40 (multiply numerator and denominator by 8).

Now we can subtract the fractions: 104/40 - 53/40 = 51/40

This improper fraction can be converted to a mixed number: 51/40 = 1 11/40 hours.

### Answer: 1 11/40 hours 

Expected answer: 51/40

Correct? Yes

Problem: In the previous problem, the clown juggled for 2/10 hours. Now suppose that she actually juggled for 9/10 hours instead. In this scenario, how many hours in total did she perform, if she still rode the unicycle for 9/8 hours?

Gemini-1.5 Flash:

Reasoning: We need to add the time spent unicycling and juggling.  The time spent unicycling is still 9/8 hours.

First, we find a common denominator for 8 and 10, which is 40.

We rewrite 9/8 as 45/40 (multiply numerator and denominator by 5) and 9/10 as 36/40 (multiply numerator and denominator by 4).

Now we can add the fractions: 45/40 + 36/40 = 81/40.

This improper fraction can be converted to a mixed number: 81/40 = 2 1/40 hours.

### Answer: 2 1/40 hours 

Expected answer: 81/40

Correct? Yes

Problem: The wizard decided to use 13/7 ounces of stardust instead of the initially intended 11/7 ounces while preparing the potion. So now, what would be the total number of ounces of ingredients used in this adjusted potion recipe?

Gemini-1.5 Flash:

Reasoning: We know the wizard used 18/8 ounces of moon roots and now uses 13/7 ounces of stardust. To find the total ounces, we add these fractions. We need a common denominator, which is 56.

* 18/8 is equivalent to (18 * 7) / (8 * 7) = 126/56
* 13/7 is equivalent to (13 * 8) / (7 * 8) = 104/56

Now we can add the fractions: 126/56 + 104/56 = (126 + 104) / 56 = 230/56

The wizard used a total of 230/56 ounces of ingredients. We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 2.

* 230/56 = (230/2) / (56/2) = 115/28

### Answer: 115/28 

Expected answer: 115/28

Correct? Yes

Problem: Originally, the alien UFO traveled 3/10 of a mile, then an additional 16/20 of a mile. But what if, instead, the UFO initially only traveled 3/10 of a mile, before traveling an extra 16/18 of a mile. How much distance did UFO cover in total this time?

Gemini-1.5 Flash:

Reasoning:  We need to find a common denominator for 10 and 18. The least common multiple of 10 and 18 is 90.
We can rewrite 3/10 as 27/90 and 16/18 as 80/90.
The UFO traveled a total of 27/90 + 80/90 = 107/90 miles.
107/90 is an improper fraction. We can convert it to a mixed number: 107/90 = 1 17/90.

### Answer: 1 17/90 

Expected answer: 107/90

Correct? Yes

Problem: In the chair manufacturing firm discussed before, let's say the first machine was originally making 17/14 of a chair every hour instead of 4/14. How many chairs are now made by both machines in one hour?

Gemini-1.5 Flash:

Reasoning: The first machine now makes 17/14 of a chair per hour. The second machine still makes 20/4 = 5 chairs per hour.  Altogether, the two machines make 17/14 + 5 = 87/14 chairs per hour.
### Answer: 87/14 

Expected answer: 87/14

Correct? Yes

Problem: After the blue shark and the hammerhead shark swam their respective distances, a great white shark joined them and swam 9/14 miles. What is the total combined distance that the three sharks swam together?

Gemini-1.5 Flash:

Reasoning: We already know the blue and hammerhead sharks swam a combined distance of 1 1/5 miles.  To find the total distance of all three sharks, we need to add this to the distance the great white swam.

* First, we need to convert 1 1/5 into a fraction:  (1*5 + 1)/5 = 6/5
* Now we need a common denominator for 6/5 and 9/14. The least common denominator is 70.
* Convert 6/5 to 84/70 by multiplying the numerator and denominator by 14.
* Convert 9/14 to 45/70 by multiplying the numerator and denominator by 5.

Now we can add the fractions: 84/70 + 45/70 = 129/70

* This fraction can be simplified to 1 59/70

### Answer: 1 59/70 miles 

Expected answer: 129/70

Correct? Yes

Problem: In the previous situation, let's imagine that the blue shark actually swam for only 2/4 miles and the hammerhead shark swam for 7/11 miles. In this case, how many miles did the blue and hammerhead sharks swim in total?

Gemini-1.5 Flash:

Reasoning: To find the total distance, we need to add the distances each shark swam. But first, we need to make sure they have the same denominator (the bottom number of the fraction). 

* The least common denominator for 4 and 11 is 44.
* We can convert 2/4 to 22/44 by multiplying both the numerator and denominator by 11.
* We can convert 7/11 to 28/44 by multiplying both the numerator and denominator by 4.

Now we can add the fractions: 22/44 + 28/44 = 50/44

* This fraction can be simplified to 1 6/44, which can be further simplified to 1 3/22.

### Answer: 1 3/22 miles 

Expected answer: 25/22

Correct? Yes

Problem: Following the previous question, Lisa finds another bottle that has 6/16 gallon of milk. What is the total amount of milk Lisa has now, if you add the milk from this third bottle to the total from the first two bottles?

Gemini-1.5 Flash:

Reasoning: We need to add the amount of milk from the third bottle (6/16) to the total amount of milk Lisa already has (97/36).  

First, let's find a common denominator for 16 and 36. The least common multiple is 144.

* Convert 6/16 to 54/144 (multiply numerator and denominator by 9)
* Convert 97/36 to 388/144 (multiply numerator and denominator by 4)

Now we can add the fractions: 54/144 + 388/144 = 442/144

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 2. This gives us 221/72.

Lisa has a total of 221/72 gallons of milk.

### Answer: 221/72 

Expected answer: 221/72

Correct? Yes

Problem: John sets up a large tent that occupies an area of 13/11 acres. Later in the day, he decides to set up another smaller tent which occupies an area of 8/20 acres. The following day, John adds a third tent to the campsite. This tent occupies 1/10 of an acre. What is the total area occupied by all three tents?

Gemini-1.5 Flash:

We already know the combined area of the first two tents is 87/55 acres (from the previous calculation).

To find the total area of all three tents, we need to add the area of the third tent:

* 87/55 acres + 1/10 acre

We need a common denominator to add these fractions.  The least common multiple of 55 and 10 is 110.

* (87/55) * (2/2) = 174/110
* (1/10) * (11/11) = 11/110

Now we can add the fractions: 174/110 + 11/110 = 185/110

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 5:

185/110 = (185/5) / (110/5) = 37/22

### Answer: 37/22 acres 

Expected answer: 37/22

Correct? Yes

Problem: In the previous scenario, John had initially set up a large tent that occupied an area of 13/11 acres and a smaller tent which occupied an area of 8/20 acres. Instead, if John had a different small tent that occupied an area of 10/20 acres, what would be the total area occupied by these tents?

Gemini-1.5 Flash:

Here's how we can solve this:

* **Large tent area:** 13/11 acres
* **New small tent area:** 10/20 acres 

To find the total area, we need to add the two areas.  

* **Simplifying the small tent area:** 10/20 can be simplified to 1/2.

* **Finding a common denominator:**  The least common multiple of 11 and 2 is 22. 

* **Converting the fractions:**
    * (13/11) * (2/2) = 26/22
    * (1/2) * (11/11) = 11/22

* **Adding the fractions:** 26/22 + 11/22 = 37/22

### Answer: 37/22 acres 

Expected answer: 37/22

Correct? Yes

Problem: In addition to the wood Sarah and Alex collected, another camper named Kim contributed 11 pounds of firewood. How many pounds of firewood do they now have in total?

Gemini-1.5 Flash:

Reasoning: We already know Sarah and Alex collected 257/140 pounds of firewood.
Kim contributed 11 pounds, which is the same as 11*(140/140) = 1540/140 pounds.

Therefore, they have a total of 257/140 + 1540/140 = 1797/140 pounds of firewood.

### Answer: 1797/140 

Expected answer: 1797/140

Correct? Yes

Problem: Instead of initially collecting 11/20 of a pound of firewood, let's say Sarah collected only half as much, so 10/20 of a pound of firewood, while Alex still collected 9/7 pounds. How many pounds of firewood did they collect in total now?

Gemini-1.5 Flash:

Reasoning:  We need to find a common denominator for 20 and 7, which is 140.

Sarah collected (10/20) * (7/7) = 70/140 pounds of firewood.
Alex collected (9/7) * (20/20) = 180/140 pounds of firewood.

Together, they collected 70/140 + 180/140 = 250/140 pounds of firewood.

### Answer: 250/140 

Expected answer: 25/14

Correct? Yes

Problem: After traveling north for a total distance, Captain Bill decided to backtrack and went 20/17 miles south. How many miles away from the original starting point was Captain Bill located then?

Gemini-1.5 Flash:

Reasoning: Captain Bill traveled a total of 23/5 miles north, and then 20/17 miles south. To find the net distance, we subtract the southward travel from the northward travel: 23/5 - 20/17. To subtract fractions, they must have the same denominator. The least common denominator for 5 and 17 is 85.
We can rewrite 23/5 as (23 * 17)/(5 * 17) = 391/85.
We can rewrite 20/17 as (20 * 5)/(17 * 5) = 100/85.
Now, we subtract: 391/85 - 100/85 = (391 - 100)/85 = 291/85.

### Answer: 291/85 

Expected answer: 291/85

Correct? Yes

Problem: After reconsidering the calculations, Captain Bill realized that he actually sailed 19/18 miles north initially instead of 19/5 miles before changing track and sailing an additional 12/15 miles north. In light of this new information, how many miles north did Captain Bill sail in total now?

Gemini-1.5 Flash:

Reasoning:  We need to add 19/18 and 12/15.  To do this, we find the least common denominator of 18 and 15, which is 90.

* 19/18 can be rewritten as (19 * 5)/(18 * 5) = 95/90
* 12/15 can be rewritten as (12 * 6)/(15 * 6) = 72/90

Now we can add the fractions: 95/90 + 72/90 = (95 + 72)/90 = 167/90. 

### Answer: 167/90 

Expected answer: 167/90

Correct? Yes

Problem: After making their signature sandwich, the restaurant staff find that they have used 13/9 pounds more meat than they intended to. What is the weight of the meat that should have been in the sandwich?

Gemini-1.5 Flash:

We know the actual weight of the meat used is 229/68 pounds. 
We also know they used 13/9 pounds more than intended.

To find the intended weight, we need to subtract the extra weight from the actual weight: 

229/68 - 13/9

To subtract fractions, they need a common denominator. The least common multiple of 68 and 9 is 612.

* (229/68) * (9/9) = 2061/612
* (13/9) * (68/68) = 884/612

Now we can subtract: 2061/612 - 884/612 = 1177/612

### Answer: 1177/612 

Expected answer: 1177/612

Correct? Yes

Problem: The restaurant realized that the amount of the turkey meat in their signature sandwich should have been 6/4 pounds, not 9/4 pounds. What should be the total weight of the ham and turkey meat in the sandwich, according to this correction?

Gemini-1.5 Flash:

We know the restaurant uses 19/17 pounds of ham.  The corrected amount of turkey is 6/4 pounds.  To find the total weight, we need to add these two amounts:

19/17 pounds of ham + 6/4 pounds of turkey.

We need a common denominator to add the fractions. The least common multiple of 17 and 4 is 68.

* (19/17) * (4/4) = 76/68 pounds of ham
* (6/4) * (17/17) = 102/68 pounds of turkey

Now we can add: 76/68 + 102/68 = 178/68 pounds.

### Answer: 178/68 

Expected answer: 89/34

Correct? Yes

Problem: Considering the previous problem, what if Lucy's initial sleeping bag was 18/19 meter long and her extension was only 8/8 meter long. What would be the total length of her sleeping bag then?

Gemini-1.5 Flash:

Reasoning:  We need to add the original length of the sleeping bag to the length of the extension.

The original length is 18/19 meters.
The extension is 8/8 meters, which simplifies to 1 meter.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction.  

Converting 1 to a fraction with a denominator of 19:
1 = 19/19

Now we can add the fractions:
18/19 + 19/19 = 37/19

Therefore, the total length of the sleeping bag is 37/19 meters.  

### Answer: 37/19 meters. 

Expected answer: 37/19

Correct? Yes

Problem: If originally, Sarah had poured 10/13 gallon of water, but instead of adding 8/2 gallons, she decided this time to add 16/2 gallons of water into the container, how many total gallons of water did she add now?

Gemini-1.5 Flash:

First, we need to convert 16/2 into a fraction with the same denominator as 10/13, which is 13. We can do this by multiplying both the numerator and denominator by 13/2:

* 16/2 = (16 * 13) / (2 * 13) = 208/26

Now we can simplify this fraction by dividing both the numerator and denominator by 2:

* 208/26 = (208 / 2) / (26 / 2) = 104/13

Now, we can add the two fractions to find the total amount of water Sarah added:

* 10/13 + 104/13 = (10 + 104) / 13 = 114/13

Therefore, Sarah added a total of 114/13 gallons of water to the container. 

### Answer: 114/13 

Expected answer: 114/13

Correct? Yes

Problem: Mandy has 9/2 KGs of apples. She uses 1/4 KG of them to make apple pie. Afterwards, she finds 3/19 more KGs of apples in her refrigerator. How many KGs of apples does she have total now?

Gemini-1.5 Flash:

Reasoning: First, we need to find a common denominator for 9/2 and 1/4. The least common denominator is 4.
So, 9/2 is equivalent to (9*2)/(2*2) = 18/4.
Now we can subtract the amount used for the pie: 18/4 - 1/4 = (18-1)/4 = 17/4.
Next, we need to add the apples found in the refrigerator. We need a common denominator for 17/4 and 3/19.  The least common denominator is 76.
So, 17/4 is equivalent to (17*19)/(4*19) = 323/76. 
And, 3/19 is equivalent to (3*4)/(19*4) = 12/76.
Now we can add the two amounts: 323/76 + 12/76 = (323+12)/76 = 335/76. 

### Answer: 335/76 

Expected answer: 335/76

Correct? Yes

Problem: In the scenario where Mandy initially had 9/7 KGs of apples instead, and she still uses 1/4 KG of them for her apple pie, how many KGs of apples would she have left?

Gemini-1.5 Flash:

Reasoning: To subtract fractions, we need a common denominator. The least common denominator for 7 and 4 is 28.

* Convert 9/7 to 28ths: (9 * 4) / (7 * 4) = 36/28
* Convert 1/4 to 28ths: (1 * 7) / (4 * 7) = 7/28

Now we can subtract: 36/28 - 7/28 = 29/28

This means Mandy has 29/28 KGs of apples left.

### Answer: 29/28 

Expected answer: 29/28

Correct? Yes

Problem: After fixing and polishing the watch, John spends an extra 12/13 hours adjusting its mechanism. How many hours in total did he spend working on the watch overall?

Gemini-1.5 Flash:

Reasoning: We need to add the time spent on fixing, polishing and adjusting the watch: 43/21 + 12/13.  To add fractions, they need to have the same denominator.  The least common multiple of 21 and 13 is 273. 
*  43/21 = (43 * 13)/(21 * 13) = 559/273
*  12/13 = (12 * 21)/(13 * 21) = 252/273
Now we can add the fractions: 559/273 + 252/273 = 811/273.
### Answer: 811/273 hours 

Expected answer: 811/273

Correct? Yes

Problem: In a revised scenario, if John spends 12/7 hours fixing a watch and then spends 3/15 hours polishing it instead of the original 3/9 hours, how many hours in total did he spent working on the watch now?

Gemini-1.5 Flash:

Reasoning: We need to add the time spent fixing and polishing the watch: 12/7 + 3/15. To add fractions, they need to have the same denominator. The least common multiple of 7 and 15 is 105. 
*  12/7 = (12 * 15)/(7 * 15) = 180/105
*  3/15 = (3 * 7)/(15 * 7) = 21/105
Now we can add the fractions: 180/105 + 21/105 = 201/105. 
We can simplify this fraction by dividing both numerator and denominator by 3: (201/3)/(105/3) = 67/35.
### Answer: 67/35 hours 

Expected answer: 67/35

Correct? Yes

Problem: Suppose that initially Peggy the Penguin had actually swam for 5/4 miles but she decided to turn back slightly earlier, swimming only 1/15 miles back towards her family before deciding to rest. How far would she be from her family in this scenario?

Gemini-1.5 Flash:

Reasoning: Peggy initially swam 5/4 miles, and then swam back 1/15 miles.
Therefore, she is 5/4 - 1/15 miles away from her family.
To subtract these fractions, we need a common denominator. The least common multiple of 4 and 15 is 60.
So, we have (5/4)*(15/15) - (1/15)*(4/4) = 75/60 - 4/60
This simplifies to (75-4)/60 = 71/60 miles.
### Answer: 71/60 miles 

Expected answer: 71/60

Correct? Yes

Problem: After measuring his fields, the farmer also remembered that he has an additional patch of land where he grows vegetables, which is 17/11 of an acre. With this additional patch included, what is his total land area in acres?

Gemini-1.5 Flash:

Reasoning: We need to add the vegetable patch area (17/11 acres) to the total wheat field area (4 11/12 acres) we calculated earlier. 

First, let's convert the mixed number 4 11/12 to an improper fraction: (4*12 + 11)/12 = 59/12.

Now we can add the two fractions: 59/12 + 17/11. 

To add fractions, they need the same denominator. The least common multiple of 12 and 11 is 132.

So, we can rewrite the fractions: (59/12) * (11/11) = 649/132 and (17/11) * (12/12) = 204/132.

Now we can add them: 649/132 + 204/132 = 853/132.

This improper fraction can be simplified to a mixed number: 6 57/132.

### Answer: 6 57/132 acres 

Expected answer: 853/132

Correct? No

Problem: Earlier, the farmer had thought that one part of the wheat field was 4 acres. However, he later realized that it was actually 4/9 of an acre. Including the other part that was 11/12 of an acre, what is the corrected total land area in acres used to grow wheat now?

Gemini-1.5 Flash:

Reasoning: The farmer initially thought he had 4 acres, but now knows that's only 4/9 of an acre. We need to add this to the 11/12 of an acre from the other part of the field. 

To add fractions, they need the same denominator. The least common multiple of 9 and 12 is 36.

* Convert 4/9 to 16/36 (multiply numerator and denominator by 4)
* Convert 11/12 to 33/36 (multiply numerator and denominator by 3)

Now we can add: 16/36 + 33/36 = 49/36

This improper fraction can be simplified to a mixed number: 1 13/36 acres

### Answer: 1 13/36 acres 

Expected answer: 49/36

Correct? Yes

Problem: If the designer also used an additional 19/10 yards of golden fabric, how many yards of fabric did she use in total now?

Gemini-1.5 Flash:

Reasoning: We know she used 207/68 yards of red and blue fabric. Now we need to add the 19/10 yards of golden fabric.  Again, we need a common denominator. 

The least common multiple of 68 and 10 is 340. So we rewrite our fractions:

* 207/68 = (207 * 5) / (68 * 5) = 1035/340
* 19/10 = (19 * 34) / (10 * 34) = 646/340

Now we can add:

* 1035/340 + 646/340 = (1035 + 646)/340 = 1681/340

This fraction represents the total yards of fabric used.

### Answer: 1681/340 

Expected answer: 1681/340

Correct? Yes

Problem: If the dress designer initially used 11/4 yards of red fabric, but then decided to use only 5/5 yards of blue fabric, how many yards of fabric did she use in total?

Gemini-1.5 Flash:

Reasoning: The designer used 5/5 yards of blue fabric, which is the same as 1 yard. So, we need to add the red fabric and the blue fabric:

* 11/4 yards + 1 yard 

To add these, we need to express 1 yard as a fraction with a denominator of 4:

* 1 yard = 4/4 yards

Now we can add the fractions:

* 11/4 yards + 4/4 yards = (11 + 4)/4 yards = 15/4 yards

### Answer: 15/4 

Expected answer: 15/4

Correct? Yes

Problem: What if Samantha had originally started with a 4 fluid ounce tube of toothpaste but she only used 12/14 fluid ounces in the first week. How much toothpaste would she have left then?

Gemini-1.5 Flash:

Samantha used 12/14 fluid ounces of toothpaste. This is less than the full 4 fluid ounces she started with. To find out how much is left, we can subtract the amount used from the original amount.

First, convert 4 fluid ounces to a fraction with the same denominator as the amount used (14):
4 fluid ounces = (4 * 14)/14 = 56/14 fluid ounces

Now subtract the amount used from the original amount:
56/14 - 12/14 = 44/14 fluid ounces

### Answer: 44/14 

Expected answer: 22/7

Correct? Yes

Problem: Maria initially had 12 candies and 20 stickers. Instead of having 6 friends, let's say she had 13 friends now. If she shares the candies among her 6 friends and the stickers among her 13 friends equally, how many candies and stickers does each friend get in total?

Gemini-1.5 Flash:

Reasoning: Maria gives each of her 6 friends 12/6 = 2 candies.
Maria gives each of her 13 friends 20/13 = 1 sticker (since you can't give fractions of a sticker, each friend gets one whole sticker).
Therefore, each friend gets 2 + 1 = 3 candies and stickers.

### Answer: 3 

Expected answer: 46/13

Correct? No

Problem: After the first day of rainy weather, the following day also experienced rainfall. This time however, it lasted for only 11/19 hours. What is the total amount of hours it rained over the course of these two days?

Gemini-1.5 Flash:

Reasoning: We know from the previous calculation that the first two rainfalls lasted a total of 163/65 hours.  Now we need to add the rainfall from the second day, which lasted 11/19 hours.

To add these fractions, we need a common denominator. The least common multiple of 65 and 19 is 1235.  So we rewrite the fractions:

* 163/65 = (163 * 19) / (65 * 19) = 3097/1235
* 11/19 = (11 * 65) / (19 * 65) = 715/1235

Now we can add the fractions:

* 3097/1235 + 715/1235 = (3097 + 715) / 1235 = 3812/1235

The total rainfall time over the two days is 3812/1235 hours.

### Answer: 3812/1235 

Expected answer: 3812/1235

Correct? Yes

Problem: After cutting 10/12 yards and 10/10 yard from the blanket, Jane decides to cut an additional 4/12 yard. Now, how many yards of fabric has she cut from the blanket in total?

Gemini-1.5 Flash:

Reasoning: We already know Jane cut 22/12 yards of fabric.  Now we need to add the additional 4/12 yards.

Total fabric cut: 22/12 + 4/12 = <<(22+4)/12 = 26/12>> 26/12 yards

### Answer: 26/12 

Expected answer: 13/6

Correct? Yes

Problem: Originally, Jane cut 10/12 yard and then 10/10 yard from the blanket. However, consider if Jane had cut 11/12 yard instead of 10/12 yard at first, and then again cut 10/10 yard. How many yards of fabric would she have cut from the blanket now in this case?

Gemini-1.5 Flash:

Reasoning: Jane cut 11/12 yard of fabric the first time and 10/10 = 1 yard the second time.
In total, Jane cut 11/12 + 1 = 11/12 + 12/12 = <<(11+12)/12 = 23/12>> 23/12 yards of fabric.

### Answer: 23/12 

Expected answer: 23/12

Correct? Yes

Problem: A fairy sprinkles 11/12 oz of magic dust over an enchanted field. She then sprinkles an additional 9/10 oz of dust over a grove of enchanted apple trees. Then, she flies over to a nearby forest where she originally had 14/3 oz of magic dust. After using the dust over the field and apple trees, how much magic dust is left for the fairy now?

Gemini-1.5 Flash:

First, we need to find the total amount of dust used on the field and apple trees. As calculated previously, that's 1 49/60 oz.

Now, we need to subtract that amount from the fairy's original amount of dust:

14/3 - 1 49/60 = 14/3 - 109/60

To subtract fractions, they need a common denominator:

(14 * 20) / (3 * 20) - 109/60 = 280/60 - 109/60

Now we can subtract:

280/60 - 109/60 = 171/60

This can be simplified to a mixed number:

171/60 = 2 51/60

### Answer: 2 51/60 oz 

Expected answer: 57/20

Correct? Yes

Problem: A fairy sprinkles 11/12 oz of magic dust over an enchanted field. She then planned to sprinkle an additional 9/10 oz of dust over a grove of enchanted apple trees, but she accidentally sprinkles more, as much as 16/10 oz. What is the total amount of magic dust the fairy used now?

Gemini-1.5 Flash:

We need to add the amount used for the field and the amount used for the apple trees.

First, find a common denominator for the fractions. The least common multiple of 12 and 10 is 60. 

* 11/12 is equivalent to (11 * 5) / (12 * 5) = 55/60
* 16/10 is equivalent to (16 * 6) / (10 * 6) = 96/60

Now we can add the fractions:

55/60 + 96/60 = 151/60

This is an improper fraction, so we can simplify it to a mixed number:

151/60 = 2 31/60

### Answer: 2 31/60 oz 

Expected answer: 151/60

Correct? Yes

Problem: After earning points from using 1 vowel and 1 consonant, you played another round and scored 19/7 points. What is your total score now?

Gemini-1.5 Flash:

Reasoning: You need to add your score from the first round (118/110) and the score from the second round (19/7). To add fractions, they need to have a common denominator.
The least common multiple of 110 and 7 is 770. 
(118/110) * (7/7) = 826/770
(19/7) * (110/110) = 2090/770
Adding the fractions: 826/770 + 2090/770 = 2916/770
### Answer: 2916/770 

Expected answer: 1458/385

Correct? Yes

Problem: In the same word game, now we assign 5/11 of a point for each vowel used instead of 3/11, while the points given for each consonant remain 8/10. If you use 1 vowel and 1 consonant with this new scoring system, what will your score be?

Gemini-1.5 Flash:

Reasoning: Now the vowel earns you 5/11 points instead of 3/11. 
The consonant still earns 8/10 points.
Your total score is 5/11 + 8/10 = (50+88)/110 = 138/110.
### Answer: 138/110 

Expected answer: 69/55

Correct? Yes

Problem: You decide to add some more content to your letter. If you add 7/12 of a page, how many pages will the letter be then?

Gemini-1.5 Flash:

Here's how to solve this:

1. **Convert the mixed number to a fraction:** 2 4/9 = (2 * 9 + 4)/9 = 22/9

2. **Find a common denominator for the fractions:** The smallest common denominator for 9 and 12 is 36.
    * 22/9 = 88/36
    * 7/12 = 21/36

3. **Add the fractions:** 88/36 + 21/36 = 109/36

4. **Simplify the answer:** 109/36 is an improper fraction, so convert it to a mixed number: 3 1/36

**Therefore, the letter will be 3 1/36 pages long after adding the extra content.**

### Answer: 3 1/36 

Expected answer: 109/36

Correct? Yes

Problem: What if your original letter was slightly longer, being 15/1 pages in total, but you still removed the same 14/9 pages from it? How many pages would the letter be then?

Gemini-1.5 Flash:

Here's how to solve the problem with the new starting length:

* **Convert the fractions to have a common denominator:**
    * 15/1 = 135/9
    * 14/9 stays the same.

* **Subtract the fractions:** 135/9 - 14/9 = 121/9

* **Simplify the answer:** 121/9 is an improper fraction, so we can convert it to a mixed number: 13 4/9

**Therefore, the letter is now 13 4/9 pages long.**
### Answer: 13 4/9 

Expected answer: 121/9

Correct? Yes

Problem: The grocery store owner also received an additional batch of yellow apples that weighs 17/15 kg. So, now how many total kilograms of apples are in the store?

Gemini-1.5 Flash:

Reasoning: We know that the store already has 31/10 kg of apples (from the red and green apples). Now, we need to add the weight of the yellow apples. 
So, the total weight of apples is 31/10 kg + 17/15 kg.
To add these fractions, we need to find a common denominator. The least common denominator for 10 and 15 is 30. 
(31/10 + 17/15) kg = (31/10 * 3/3 + 17/15 * 2/2) kg = (93/30 + 34/30) kg = 127/30 kg.

### Answer: 127/30 kg 

Expected answer: 127/30

Correct? Yes

Problem: Instead of having 17/20 kg of red apples as stated in the original problem, suppose the store only had 3/20 kg of red apples. Along with the 18/8 kg of green apples, how many kilograms of apples would be in the store now?

Gemini-1.5 Flash:

Reasoning: We need to add the weight of red apples and green apples.
3/20 kg + 18/8 kg =  (3/20 + 18/8) kg 
To add fractions, they need to have the same denominator. The least common denominator for 20 and 8 is 40.
(3/20 + 18/8) kg = (3/20 * 2/2 + 18/8 * 5/5) kg = (6/40 + 90/40) kg = 96/40 kg.
Simplify the fraction by dividing both numerator and denominator by their greatest common factor, 8. 
96/40 kg = (96/8)/ (40/8) kg = 12/5 kg.
### Answer: 12/5 kg 

Expected answer: 12/5

Correct? Yes

Problem: After swimming for two hours, the shark decides to swim for a third hour and it covers a distance of 14/9 miles. What is the total distance covered by the shark in these three hours?

Gemini-1.5 Flash:

We know the shark swam 44/15 miles in the first two hours. Now it swims an additional 14/9 miles in the third hour.

To find the total distance, we need to add the distances from all three hours:

* **Total distance:** (44/15) + (14/9) 

To add these fractions, we need a common denominator. The least common multiple of 15 and 9 is 45.

* **Total distance:**  (44/15) * (3/3) + (14/9) * (5/5) = 132/45 + 70/45

Now we can add the fractions:

* 132/45 + 70/45 = 202/45

Therefore, the shark swims a total of **202/45 miles** in three hours.

### Answer: 202/45 

Expected answer: 202/45

Correct? Yes

Problem: In reconsideration of the first hour, what if the shark only swam for 3/7 miles instead of 3/9 miles, but still swam 13/5 miles in the the second hour. What would be the total distance covered in these two hours then?

Gemini-1.5 Flash:

Here's how we can calculate the total distance:

* **Hour 1:** The shark swims 3/7 miles.
* **Hour 2:** The shark swims 13/5 miles.

To add these fractions, we need a common denominator. The least common multiple of 7 and 5 is 35.

* **Hour 1:** (3/7) * (5/5) = 15/35 miles
* **Hour 2:** (13/5) * (7/7) = 91/35 miles

Now we can add the distances:

* 15/35 + 91/35 = 106/35

The shark swims a total of **106/35 miles** in two hours.

### Answer: 106/35 

Expected answer: 106/35

Correct? Yes

Problem: Instead of hitting the first note every 17/17 seconds, the drummer decides to change the beat and hit it every 16/17 seconds. They're still hitting the second note every 2/12 seconds though. How long does it now take the drummer to hit the two beats together?

Gemini-1.5 Flash:

Reasoning: We need to add the time for each beat to find the total time: 16/17 seconds + 2/12 seconds.  To add fractions, they must have the same denominator.  The least common denominator for 17 and 12 is 204.  

16/17 * 12/12 = 192/204
2/12 * 17/17 = 34/204

Now we can add the fractions: 192/204 + 34/204 = 226/204.  

Therefore, it takes the drummer 226/204 seconds to hit the two beats together.

### Answer: 226/204 seconds. 

Expected answer: 113/102

Correct? Yes

Problem: In addition to the wood burned throughout the day, the fireplace burns an additional 19/20 cord of wood at night. What is the total cord of wood the fireplace burns in one full day?

Gemini-1.5 Flash:

We know the fireplace burns 364/323 cord of wood during the day, and an additional 19/20 cord at night. To find the total, we need to add these fractions.

However, we need a common denominator to add them. The least common multiple of 323 and 20 is 6460.

* (364/323) * (20/20) = 7280/6460
* (19/20) * (323/323) = 6137/6460

Now we can add the fractions:

* 7280/6460 + 6137/6460 = 13417/6460

Therefore, the fireplace burns a total of 13417/6460 cord of wood in a full day.

### Answer: 13417/6460

Expected answer: 13417/6460

Correct? Yes

Problem: After completing the first two segments of its flight, the butterfly flies an additional 19/20 of a mile. What is the total distance now that the butterfly has flown?

Gemini-1.5 Flash:

We know the butterfly flew a total of 1 154/323 miles in the first two segments.  We need to add the additional 19/20 of a mile to find the total distance.

First, let's convert the mixed number 1 154/323 to an improper fraction:

* 1 154/323 = (323 * 1 + 154)/323 = 477/323

Now, we need a common denominator to add the fractions:

* 477/323 * (20/20) = 9540/6460
* 19/20 * (323/323) = 6137/6460

Finally, we add the fractions:

* 9540/6460 + 6137/6460 = 15677/6460

This improper fraction can be simplified to a mixed number:

* 15677/6460 = 2 2757/6460

Therefore, the total distance the butterfly has flown is **2 2757/6460 miles**.
### Answer: 2 2757/6460 miles. 

Expected answer: 15677/6460

Correct? Yes

Problem: Suppose the butterfly's first flight segment was actually shorter than previously thought, only 18/12 of a mile instead of 18/19 of a mile, while the second segment remained 9/17 of a mile. What would be the new total length of the butterfly's flight?

Gemini-1.5 Flash:

We need to add the lengths of the two segments, but first we need to simplify the fraction 18/12. Both the numerator and denominator can be divided by 6, giving us 3/2.

Now, we need to find a common denominator for 3/2 and 9/17.  The least common multiple of 2 and 17 is 34.

Converting each fraction to have a denominator of 34:

* (3/2) * (17/17) = 51/34
* (9/17) * (2/2) = 18/34

Now we can add them:

* 51/34 + 18/34 = 69/34

This improper fraction can be converted to a mixed number:

* 69/34 = 2 1/34

Therefore, the butterfly's entire flight is now **2 1/34 miles** long. 

### Answer: 2 1/34 miles. 

Expected answer: 69/34

Correct? Yes

Problem: Instead of the distance between the first two cities on the map being 13/10 inches, suppose it is 13/7 inches. Keeping the distance from the second city to the third city the same at 14/15 inches, what would then be the total distance between the three cities on the map?

Gemini-1.5 Flash:

To find the total distance, we need to add the distance between the first and second cities (13/7 inches) to the distance between the second and third cities (14/15 inches).

First, we need a common denominator for 13/7 and 14/15. The least common multiple of 7 and 15 is 105.

* (13/7) * (15/15) = 195/105
* (14/15) * (7/7) = 98/105

Now we can add the fractions:

195/105 + 98/105 = 293/105

The total distance Jenna measured is 293/105 inches. 

### Answer: 293/105 inches 

Expected answer: 293/105

Correct? Yes

Problem: If a second identical helium balloon behaving exactly like the first one rises alongside, what would be their total combined speed in feet per second?

Gemini-1.5 Flash:

Since both balloons are identical and rising at the same speed, their combined speed would simply be twice the speed of one balloon.

We already know the new speed of one balloon is 113/48 feet per second.

Therefore, their combined speed is (113/48) * 2 = 226/48 feet per second.

### Answer: 226/48 

Expected answer: 113/24

Correct? Yes

Problem: Susie has a box of 12 chocolate bars. She decides to eat 2/5 of a chocolate bar herself. Then, her friend Lucy takes a further 19/11 chocolate bars. How many chocolate bars are left in the box after Lucy takes some?

Gemini-1.5 Flash:

Susie eats 2/5 of a chocolate bar, leaving her with 12 - (2/5) = 11 3/5 chocolate bars.

Lucy takes 19/11 chocolate bars, which is more than the total number of chocolate bars left in the box. This means Lucy can't take that many.

There's an error in the problem setup, and we can't determine how many chocolate bars are left in the box after Lucy takes her share. 

### Answer: There is an error in the problem setup. 

Expected answer: 543/55

Correct? No

Problem: Let's reconsider the scenario: Susie has a box of 12 chocolate bars. But this time, she decides to eat 2/13 of a chocolate bar herself instead of 2/5. How many chocolate bars are left in the box?

Gemini-1.5 Flash:

Susie ate 2/13 of a chocolate bar, which means she still has 12 - (2/13) = 11 11/13 chocolate bars left in the box. 
### Answer: 11 11/13 

Expected answer: 154/13

Correct? Yes

Problem: What if the plane initially flew at a lower altitude, only 2 miles high, before it descended 12/15 of a mile? What would be the altitude of the plane after this descent?

Gemini-1.5 Flash:

Here's how to solve this:

1. **Simplify the fraction:** 12/15 simplifies to 4/5.
2. **Convert miles to a common denominator:** 2 miles is equal to 10/5 miles.
3. **Subtract the descent:** 10/5 - 4/5 = 6/5 miles.

**However, the plane cannot have a negative altitude. This means the plane would have already hit the ground before descending 12/15 of a mile.** 

Therefore, it's impossible to determine the plane's altitude after the descent because it would have crashed. 
### Answer: The plane would have crashed. 

Expected answer: 6/5

Correct? No

Problem: If originally, the first slide was actually 6/5 meters long instead of 6/19 meters long, and the child goes down this slide and then another slide that's 17/4 meters long, how many total meters did they slide?

Gemini-1.5 Flash:

Here's how to solve the problem:

* **First slide:** The first slide is 6/5 meters long.
* **Second slide:** The second slide is 17/4 meters long.

To add these fractions, we need a common denominator. The least common multiple of 5 and 4 is 20.

* **First slide:**  (6/5) * (4/4) = 24/20 meters
* **Second slide:** (17/4) * (5/5) = 85/20 meters

Now we can add the lengths of the two slides:

24/20 + 85/20 = 109/20 meters

### Answer: 109/20 

Expected answer: 109/20

Correct? Yes

Problem: If the colonial fireplace burns firewood at a combined rate of 4/15 cords per hour in the early morning and 14/15 cords per hour in the late night, and during the peak hours, it burns an additional 6/5 cords per hour. Then how much total firewood does the fireplace burn in one hour considering early morning, late night, and peak hours?

Gemini-1.5 Flash:

Reasoning: We need to find the total firewood burned in one hour by adding the rates for the early morning, late night, and peak hours.
The combined rate for early morning and late night is 4/15 + 14/15 = 18/15 cords per hour.
Adding the peak hour rate, the total firewood burned in one hour is 18/15 + 6/5.
To add these fractions, we need a common denominator. The least common multiple of 15 and 5 is 15.
So, 18/15 + 6/5 is equivalent to 18/15 + (6*3)/(5*3) = 18/15 + 18/15.
This adds up to 36/15. 
We can simplify this fraction by dividing both numerator and denominator by 3: (36/3) / (15/3) = 12/5.
### Answer: 12/5 

Expected answer: 12/5

Correct? Yes

Problem: Continuing from the previous scenario, let's suppose the colonial fireplace in the early morning burns firewood at a slightly different rate of 8/15 cords per hour instead of 4/15 cords per hour. The late night burning rate remains the same at 14/15 cords per hour. Given these new circumstances, how much firewood does the fireplace burn in total in one hour split between the early morning and late night?

Gemini-1.5 Flash:

Reasoning: We add the rates for the early morning and late night to find the total firewood burned in one hour.
Total firewood burned in one hour is (8/15) + (14/15) = 22/15. 
### Answer: 22/15 

Expected answer: 22/15

Correct? Yes

Problem: After traveling ((9 / 20) + (11 / 7)) light years towards earth, the alien continues its journey for an additional 14/2 light years. How many light years in total has the alien traveled?

Gemini-1.5 Flash:

Reasoning: First, we need to calculate the total distance traveled in the first two legs of the journey, which is ((9/20) + (11/7)) light years. 

We need a common denominator to add these fractions:

* (9/20) * (7/7) = 63/140
* (11/7) * (20/20) = 220/140

Adding these gives us: 63/140 + 220/140 = 283/140 light years.

Next, we need to add the additional 14/2 light years.  This simplifies to 7 light years.

To add this to the previous distance, we need a common denominator:

* (283/140) + (7 * 140/140) = 283/140 + 980/140

Finally, we add the numerators: 283/140 + 980/140 = 1263/140 

### Answer: 1263/140 

Expected answer: 1263/140

Correct? Yes

Problem: The alien originally travelled ((9 / 20) + (11 / 7)) light years towards earth. But what if instead, the alien had only travelled (9 / 20) + (11 / 11) light years to start with? How many light years would the alien have travelled then?

Gemini-1.5 Flash:

Reasoning:  We first need to simplify (11/11) which is equal to 1.

Then we add (9/20) + 1. 

To add these, we need a common denominator. The least common multiple of 20 and 1 is 20.

* (9/20) stays the same.
* 1 = 20/20

Now we can add: (9/20) + (20/20) = 29/20

### Answer: 29/20 

Expected answer: 29/20

Correct? Yes

Problem: After combining the cucumbers, Bob duplicates his total amount. Now, how many cucumbers does he have?

Gemini-1.5 Flash:

Reasoning: Bob had 36/7 cucumbers, and he duplicated this amount. To find the total, we multiply the amount by 2: (36/7) * 2 = 72/7.

### Answer: 72/7 

Expected answer: 72/7

Correct? Yes

Problem: Suppose instead of 1/7 of a cucumber, Bob initially has 17/7 (or about 2 and a half) cucumbers before adding 10/2. How many cucumbers does he have now?

Gemini-1.5 Flash:

Reasoning:  We need to add the number of cucumbers Bob has initially (17/7) to the number he adds (10/2). 

First, let's make the denominators the same:

* 10/2 is equivalent to 35/7 (multiply numerator and denominator by 7/2).

Now we can add:

* 17/7 + 35/7 = 52/7

This means Bob has 52/7 cucumbers in total.

### Answer: 52/7 

Expected answer: 52/7

Correct? Yes