Problem: After both Kyle and Lisa's throws, the ball bounced an additional 3/13 yards. Subtract this distance from the total distance the ball traveled when Kyle and Lisa threw it. What is the remaining distance?

Gemini-1.5 Pro:

Reasoning: We need to subtract 3/13 yards from the total distance the ball traveled when Kyle and Lisa threw it, which is 6 11/18 yards.

First, convert the mixed number 6 11/18 to a fraction: 
(6 * 18 + 11) / 18 = 119/18.

Now, find a common denominator for 18 and 13, which is 234.

Convert 119/18 to an equivalent fraction with a denominator of 234:
(119 * 13) / (18 * 13) = 1547/234

Convert 3/13 to an equivalent fraction with a denominator of 234:
(3 * 18) / (13 * 18) = 54/234

Finally, subtract the two fractions:
1547/234 - 54/234 = 1493/234

Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 1: 1493/234

Convert the improper fraction back to a mixed number: 1493/234 = 6 89/234

### Answer: 6 89/234 yards

Expected answer: 1493/234

Correct? Yes

Problem: In their game, suppose that Kyle actually threw the ball for a distance of 15/4 yards, while Lisa still threw the ball for 19/9 yards. How many yards did the ball travel in total now?

Gemini-1.5 Pro:

Reasoning: We need to calculate 15/4 + 19/9.
The fractions have unlike denominators, so we find a common denominator. The least common denominator for 4 and 9 is 36.
Multiply the numerator and denominator of 15/4 by 9/9 to get (15*9)/(4*9) = 135/36.
Multiply the numerator and denominator of 19/9 by 4/4 to get (19*4)/(9*4) = 76/36.
Now we can add the fractions: 135/36 + 76/36 = 211/36.
Convert the improper fraction to a mixed number: 211/36 = 5 31/36
### Answer: 5 31/36 yards 

Expected answer: 211/36

Correct? Yes

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 Pro:

Reasoning:  We know Johnnie received 24/7 bananas over the course of the first day.  Since he receives the same amount on the second day, we need to add the two-day totals together. This can be represented as (24/7) + (24/7).

Since the two fractions already share a common denominator, we simply add the numerators: (24+24)/7 = 48/7 

### Answer: 48/7 bananas 

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 Pro:

Since both the front and back doors have the same measurements, the total distance for both doors is simply double the distance of one door.

We previously found the total distance for one door to be 211/190 inches.

Therefore, the total distance for both doors is (211/190 inches) * 2 = 422/190 inches

This can be simplified to 211/95 inches

### Answer: 211/95 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 Pro:

We will follow the same process as before, but now with the bottom of the door being 4/16 of an inch from the floor.

First, we add the two distances: 4/16 inches + 9/10 inches

Next, we find a common denominator. The least common denominator for 16 and 10 is 80.

We convert each fraction to have a denominator of 80:
(4/16)*(5/5) + (9/10)*(8/8) = 20/80 + 72/80

Finally, we add the two fractions: 20/80 + 72/80 = 92/80

This fraction can be simplified to 23/20

### Answer: 23/20 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 Pro:

Reasoning: First we need to simplify 3/18 by dividing the numerator and denominator by 3: 3/18 = 1/6.
Then we subtract the extra juice from the unused portion: 142/33 - 1/6 = (142*2)/(33*2) - (1*11)/(6*11) = 284/66 - 11/66 = 273/66 liters. 
We can further simplify this fraction by dividing both numerator and denominator by 3: 273/66 = 91/22 liters.
### Answer: 91/22 liters

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 Pro:

Reasoning: Let's calculate the difference: 17/3 - 14/11 = (17*11)/(3*11) - (14*3)/(11*3) = 187/33 - 42/33 = 145/33 liters. 
### Answer: 145/33 liters 

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 Pro:

Reasoning:  We need to add the distances traveled on both days, keeping in mind the updated information.

First, we need a common denominator for our fractions. The least common denominator for 3 and 7 is 21.
We convert 15/3 to a fraction with a denominator of 21: (15/3) * (7/7) = 105/21
We also convert 18/7 to a fraction with a denominator of 21: (18/7) * (3/3) = 54/21

Now, we add the two distances: 105/21 + 54/21 = 159/21.

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 3: (159/3) / (21/3) = 53/7. 

Therefore, the rocket has traveled 53/7 light years in total.
### Answer: 53/7 light years

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 Pro:

Reasoning: Captain Silverbeard already has 398/247 of the map.  We need to add 15/17 to this fraction. First, we need to find a common denominator.  The least common multiple of 17 and 247 is 4199.

398/247 is equivalent to (398 * 17) / (247 * 17) = 6766 / 4199
15/17 is equivalent to (15 * 247) / (17 * 247) = 3705 / 4199

Adding these two fractions, we get (6766 + 3705) / 4199 = 10471 / 4199 of the treasure map. This fraction is improper (the numerator is larger than the denominator), meaning Captain Silverbeard has more than one complete map. 

### Answer: 10471/4199 

Expected answer: 10471/4199

Correct? Yes

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 Pro:

Reasoning: Similar to the previous problem, we need to find a common denominator to add 10/9 and 16/19. The least common denominator for 9 and 19 is their product, 171.

10/9 is equivalent to (10 * 19)/(9 * 19) = 190/171
16/19 is equivalent to (16 * 9)/(19 * 9) = 144/171

Adding these two fractions, we get (190 + 144)/171 = 334/171 of the treasure map.

### Answer: 334/171 

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 Pro:

Reasoning: First, we need to figure out the total distance the hiker traveled North and South. We can do this by subtracting the distance traveled South from the distance traveled North: 9/6 miles - 8/14 miles = 39/42 miles.

Simplifying this, we find that the hiker traveled a net distance of 13/14 miles North. 

Next, we add the distance traveled East to the total distance traveled North to find the total distance traveled: 13/14 miles + 2/16 miles = 57/56 miles

Simplifying this, we get 1 1/56 miles

### Answer: 1 1/56 miles

Expected answer: 123/56

Correct? No

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 Pro:

Reasoning:  We need to add the distance the hiker walked North to the distance the hiker walked East.  First, simplify 2/16 to 1/8.  10/6 + 1/8 = 43/24 miles.
Simplifying the fraction, we get 1 19/24 miles. 
### Answer: 1 19/24 miles.  

Expected answer: 43/24

Correct? Yes

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 Pro:

Reasoning: First, we need to find a common denominator between the amount of sand Jessica started with and the amount she added. The least common denominator between 15 and 117 is 585. We get this by noticing that 585/117 = 5 and 585/15 = 39. Therefore, we will multiply the numerator and denominator of the first fraction by 5 and the numerator and denominator of the second fraction by 39. This gives us (172*5)/(117*5) + (19*39)/(15*39) = 860/585 + 741/585.
Now that both fractions share a common denominator, we can add them together to get 860/585 + 741/585 = 1601/585 cubic feet.
### Answer: 1601/585 cubic feet 

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 Pro:

Reasoning: First, we need to find a common denominator for our two fractions. The least common denominator for 9 and 8 is 72. We can see that 72/9 = 8 and 72/8 = 9, so we will multiply the numerator and denominator of the first fraction by 8, and the numerator and denominator of the second fraction by 9. This gives us (16*8)/(9*8) - (4*9)/(8*9) = 128/72 - 36/72.
Now, we can subtract the two fractions: 128/72 - 36/72 = 92/72
This can be simplified to 23/18.
### Answer: 23/18 cubic feet 

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 Pro:

Reasoning: We know from the previous problem that (15/12 + 17/17) meters is equal to 27/12 meters.
Doubling a number is the same as adding it to itself, so the total length of the combined ropes will be 27/12 + 27/12 = <<27/12+27/12=54/12>>54/12 meters.
### Answer: 54/12 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 Pro:

Reasoning: 17/17 = <<17/17=1>>1, so Jacob is adding 1 meter of rope.
7/12 + 1 = <<7/12+1=19/12>> 19/12 meters. 
### Answer: 19/12 meters. 

Expected answer: 19/12

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 Pro:

Reasoning: We need to add the time Miss Jenny spent grading papers (39/19 hours) and the time organizing her lesson plans (1/12 hours).
To add these fractions, we need a common denominator: the least common multiple of 19 and 12 is 228.
We can rewrite 39/19 as (39 * 12)/(19 * 12) = 468/228 and 1/12 as (1 * 19)/(12 * 19) = 19/228. 
Therefore, Miss Jenny spent a total of 468/228 + 19/228 = 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 Pro:

Reasoning: 8/8 hours is equal to 1 hour.
Miss Jenny spent 1 + 20/13 = <<1+20/13=33/13>>33/13 hours grading papers.
### Answer: 33/13 hours 

Expected answer: 33/13

Correct? Yes

Problem: Let's now consider this scenario: the cloud was initially at a height of 12/3 kms, then later it ascended by 7/12 kms instead of the previous 15/12 kms. What would be the resultant height of the cloud from the ground in this case?

Gemini-1.5 Pro:

Reasoning: Similar to the previous scenario, the final height is the sum of the initial height and the ascension height.
Resultant height = 12/3 + 7/12 =  <<12/3+7/12=55/12>>55/12 kms
### Answer: 55/12 kms 

Expected answer: 55/12

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 Pro:

Reasoning: The charcoal burns for a total of (1/5) * 8 = 8/5 hours. 
Converting 8/5 hours to a mixed number, we get 1 3/5 hours. 
Adding this to the previous burn time, the total burn time is 1 7/12 + 1 3/5 = 3 11/60 hours.
### Answer: 3 11/60 hours.

Expected answer: 191/60

Correct? Yes

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 Pro:

Reasoning: The logs burn for a total of (1/16) * 4 = 1/4 of an hour.
The twigs burn for a total of (1/12) * 15 = 5/4 of an hour, which is equal to 1 and 1/4 hours.
Adding the log and twig burn times, we get 1/4 + 1 1/4 = 1 1/2 hours. 
### Answer: 1 1/2 hours. 

Expected answer: 3/2

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 Pro:

Reasoning: We need to add the new morning yield (10/9 bushels) to the afternoon yield (17/11 bushels). To add fractions, we need a common denominator:

* The least common denominator for 9 and 11 is 99.
* Convert 10/9 to 110/99 (multiply numerator and denominator by 11).
* Convert 17/11 to 153/99 (multiply numerator and denominator by 9).
* Now we can add: 110/99 + 153/99 = 263/99 bushels

### Answer: 263/99 bushels 

Expected answer: 263/99

Correct? Yes

Problem: If Sam's binoculars instead increased his range of sight by 4/14 of a mile, while Joe's binoculars still increase his range of sight by exactly 1 mile, how much would their combined range increase be when they use the binoculars one after the other?

Gemini-1.5 Pro:

Reasoning: We need to sum the range increase Sam gets with the range increase Joe gets, which is 4/14 + 1.
To sum these numbers, we need to express 1 as a fraction with denominator 14, which is 14/14.
So the combined range increase is 4/14 + 14/14 = (4+14)/14 = 18/14 miles. 
We can simplify this fraction by dividing the numerator and denominator by 2, giving us a combined range increase of 9/7 miles.
### Answer: 9/7 miles. 

Expected answer: 9/7

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 Pro:

Reasoning: Maria used 15/10 yards for the first section, which is equivalent to 3/2 yards.
She used 6/18 yards for the second section, which is equivalent to 1/3 yards.
The total length of fabric used is 3/2 + 1/3 = 9/6 + 2/6 = 11/6 yards.
### Answer: 11/6 yards 

Expected answer: 11/6

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 Pro:

Reasoning: The painter started with 155/88 liters of paint and then added 12/13 liters. So, we need to add the fractions 155/88 and 12/13. 
First, we need to find a common denominator. The least common denominator for 88 and 13 is 1144. 
So 155/88 is equivalent to 155/88 * 13/13 = 2015/1144, and 12/13 is equivalent to 12/13 * 88/88 = 1056/1144. 
Therefore 155/88 + 12/13 = 2015/1144 + 1056/1144 = 3071/1144.

### Answer: 3071/1144 liters 

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 Pro:

Reasoning: We need to add the amount of blue paint (18/11 liters) and the new amount of white paint (1/7 liters).

To add these fractions, they need a common denominator. The least common denominator for 11 and 7 is 77.

*  18/11 is equivalent to (18/11) * (7/7) = 126/77
*  1/7 is equivalent to (1/7) * (11/11) = 11/77

Therefore, the total paint used is 126/77 + 11/77 = 137/77 liters.

### Answer: 137/77 liters

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 Pro:

Reasoning: We need to add the fractions 17/13 and 3/2. To add fractions, we need a common denominator. The least common denominator for 13 and 2 is 26.

(17/13)*(2/2) = 34/26
(3/2)*(13/13) = 39/26

34/26 + 39/26 = 73/26 pounds of gold.

### Answer: 73/26 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 Pro:

Reasoning: We know from before that the first two parts of the message totaled to 12 hours.
The total length of all the parts of the message is 12 + 7/8 = 12 7/8 hours. 
### Answer: 12 7/8 hours 

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 Pro:

Reasoning: 4/8 hours is equal to 1/2 hour, which is 30 minutes.
11/1 hours is equal to 11 hours.
The total length of the corrected message is 30 minutes + 11 hours = 11 hours and 30 minutes. 
### Answer: 11 hours and 30 minutes 

Expected answer: 23/2

Correct? No

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 Pro:

Reasoning: First we need to find the total amount of soap currently produced: (13/18)+(4/6).
First, find a common denominator: (4/6)*(3/3) = 12/18
The problem is now (13/18)+(12/18) = 25/18
Doubling production means they will make (25/18)*2 = 25/9 tons of soap.
### Answer: 25/9 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 Pro:

Reasoning: We need to find (17/18)+(4/6).
First, find a common denominator: (4/6)*(3/3) = 12/18
The problem is now (17/18)+(12/18).
(17/18)+(12/18) = 29/18
### Answer: 29/18 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 Pro:

Reasoning: Mark's sleeping bag is currently 101/12 feet long, and he wants to cut off another 13/14 feet.  To do this, we need to subtract 13/14 from 101/12. First, find a common denominator for 12 and 14, which is 84.

Convert 101/12 and 13/14 to fractions with a denominator of 84:
(101/12) * (7/7) = 707/84
(13/14) * (6/6) = 78/84

Now we can subtract:
(707/84) - (78/84) = 629/84 feet

### 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 Pro:

Reasoning: First, we need to simplify 8/2, which is equal to 4.  We need to figure out how much 4 feet is in terms of twelfths to subtract 13/12 from it. 

Since there are twelve inches in a foot, then 4 feet is the same as 4*12 = <<4*12=48>> 48 inches. This means 4 is equal to 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 Pro:

Reasoning: In total, Mary fed the monkeys and giraffes 1 1/2 pounds of food. 1 1/2 is equal to 3/2.  To add 3/2 and 19/11, we need a common denominator. The least common denominator is 22. 3/2 is equal to 33/22, and 19/11 is equal to 38/22. 33/22 plus 38/22 is equal to 71/22. Simplifying this improper fraction, we get 3 5/22. 
### Answer: 3 5/22 pounds  

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 Pro:

Reasoning: 6/20 pounds is equal to 3/10 pounds. To add this to 18/19 pounds, we must find a common denominator. The least common denominator is 190. 3/10 is equivalent to 57/190, and 18/19 is equivalent to 180/190. 180/190 + 57/190 = 237/190. This improper fraction can be written as the mixed number 1 47/190.
### Answer: 1 47/190 pounds 

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 Pro:

Reasoning:  We need to add the two fractions, 20/17 + 4/11. To do this, we find a common denominator:
* The least common denominator for 17 and 11 is 187 (17 * 11).
* We rewrite 20/17 as 220/187  ((20*11)/(17*11)).
* We rewrite 4/11 as 68/187 ((4*17)/(11*17)). 

Now we can add the fractions: 220/187 + 68/187 = 288/187. 
### 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 Pro:

Reasoning: We need to add the newly found silver (2/17 pounds) to the previous amount (347/266 pounds).

First, find a common denominator for 17 and 266:
* The least common denominator for 17 and 266 is 4522.
* Convert 347/266 to 6246/4522.
* Convert 2/17 to 532/4522.
* Add the two fractions: 6246/4522 + 532/4522 = 6778/4522

The jeweler now has 6778/4522 pounds of silver. This fraction can be simplified to 3389/2261

### Answer: 3389/2261 pounds. 

Expected answer: 6431/4522

Correct? No

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 Pro:

Reasoning: We will follow similar steps as before, but start with 8/14 instead of 5/14.

1. **Common Denominator:** The least common denominator for 14 and 19 is still 266.
2. **Convert Fractions:**
   *  Convert 8/14 to 152/266.
   *  18/19 is still 252/266.
3. **Add the Fractions:** 152/266 + 252/266 = 404/266

The jeweler now has 404/266 pounds of silver. This can be simplified to 202/133.

### Answer: 202/133 pounds. 

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 Pro:

Reasoning: 15/20 of a meter is equivalent to 0.75 meters.
Since the turtle moved back towards the starting point initially and is now moving in the same direction as the initial 11 meters, we add this distance to its current distance from the starting point: 10 meters + 0.75 meters = 10.75 meters.
### Answer: 10.75 meters 

Expected answer: 43/4

Correct? No

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 Pro:

Reasoning: The turtle moves back 15/8 meters, which is more than 1 meter but less than 2 meters. 
To find the remaining distance, subtract the backward movement from the initial northward movement: 11 - 15/8 = 88/8 - 15/8 = 73/8 meters.
### Answer: 73/8 meters 

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 Pro:

Reasoning: Chloe started with 1 ounce of chocolate and then added 4/14 ounces. She now has 1 + 4/14 ounces. 
We can rewrite 1 as 14/14. So Chloe has 14/14 + 4/14 = 18/14 ounces of chocolate.
### Answer: 18/14 ounces 

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 Pro:

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

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 Pro:

Reasoning: We need to add the tiny side pocket's capacity to his backpack's current capacity: 38/9 + 3/8.
To add these fractions, we need a common denominator: the least common multiple of 9 and 8 is 72.
Therefore: 38/9 + 3/8 = (38*8)/72 + (3*9)/72 = 304/72 + 27/72 = 331/72.
### Answer: 331/72 liters. 

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 Pro:

Reasoning: First, we simplify 8/4 liters to 2 liters. 
Then, we need to make the denominator the same for both fractions: 20/12 liters + 2 liters = 20/12 liters + 24/12 liters
Finally, we add the numerators: 20/12 + 24/12 = 44/12 liters.
### Answer: 44/12 liters. 

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 Pro:

Reasoning: We need to add the weight of the newly found gold (7/11 ounces) to his existing total (19/8 ounces).
To add fractions, they must have a common denominator. The least common denominator for 8 and 11 is 88.
Converting 19/8 to a fraction with a denominator of 88: (19/8)*(11/11) = 209/88
Converting 7/11 to a fraction with a denominator of 88: (7/11)*(8/8) = 56/88
Adding the two fractions: 209/88 + 56/88 = 265/88 ounces 
### Answer: 265/88 ounces 

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 Pro:

Reasoning: We need to add the original amount of gold Captain Hook had (11/8 ounces) to the amount he found on his latest treasure hunt (7/5 ounces).

To add fractions, they must have a common denominator. The least common denominator for 8 and 5 is 40.

*  11/8 is equivalent to 55/40 
*  7/5 is equivalent to 56/40

Adding those together, we get 55/40 + 56/40 = 111/40 ounces of gold.

### Answer: 111/40 ounces 

Expected answer: 111/40

Correct? Yes

Problem: Following up on the previous problem, if Jake found an additional 11/5 of a dollar on the street, how much money does he have in his wallet now?

Gemini-1.5 Pro:

Reasoning: We need to add 11/5 dollars to Jake's current amount of 67/30 dollars.  First, we find a common denominator for 5 and 30, which is 30. So, 11/5 is equivalent to 66/30.  Adding this to his previous amount: 67/30 + 66/30 = 133/30 dollars. 
### Answer: 133/30 dollars

Expected answer: 133/30

Correct? Yes

Problem: Following up on the original scenario, if Jake initially had 9/8 of a dollar instead of 9/10 of a dollar, and then received an additional 20/15 of a dollar, how much money does he have in his wallet now?

Gemini-1.5 Pro:

Reasoning: First, we need to find a common denominator for 8 and 15, which is 120. So, 9/8 is equivalent to 135/120, and 20/15 is equivalent to 160/120. Adding these two fractions, we get 135/120 + 160/120 = 295/120. This fraction can be simplified to 59/24, or expressed as a mixed number, 2 11/24.
### Answer: 59/24 dollars or 2 11/24 dollars 

Expected answer: 59/24

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 Pro:

Reasoning: The initial height of the chair was 55/14 feet and Paul shortened it by 2 feet.
First we need to convert 2 to a fraction with a denominator of 14: 2 = 2/1 * 14/14 = 28/14
Now we can subtract the length Paul removed from the initial height: 55/14 - 28/14 = 27/14.
The new height of the chair is 27/14 feet.

### Answer: 27/14 feet. 

Expected answer: 27/14

Correct? Yes

Problem: Following his patrol, Officer Max then begins his shift at the police station which typically lasts 20 hours. How many hours are left in his shift after he finishes his paperwork and neighborhood patrol?

Gemini-1.5 Pro:

Reasoning: Officer Max spends 2/6 + 14/7 = 1/3 + 2 = 7/3 hours on paperwork and patrol. 
Converting this to a mixed number for easier subtraction from his total shift time, we get 7/3 hours = 2 1/3 hours.
This means he has 20 - 2 1/3 = 17 2/3 hours left in his shift. 
### Answer: 17 2/3 hours

Expected answer: 53/3

Correct? Yes

Problem: Now consider a day when Officer Max spends 2/5 part of an hour, instead of 2/6 part of an hour, completing paperwork but still spends 14/7 parts of an hour patrolling the neighborhood. How much time, in parts of an hour, does Officer Max use for these two tasks in this scenario?

Gemini-1.5 Pro:

Reasoning: First, simplify the fraction representing the time Officer Max spends patrolling: 14/7 = 2 hours.
Now, add the time he spends on both tasks: 2/5 + 2 = 2/5 + 10/5 = 12/5 hours.
### Answer: 12/5 

Expected answer: 12/5

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 Pro:

Reasoning: From the previous problem, we know that watching a movie and then a TV show takes 1 and 5/24 hours. Since John repeats this routine, he spends 2 * (1 and 5/24) hours watching. This is equivalent to 2 + (10/24) hours. Simplifying the fraction, we get 2 and 5/12 hours.
### Answer: 2 and 5/12 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 Pro:

Reasoning: To add the fractions, we need a common denominator for 7 and 8, which is 56. So 10/7 of an hour is equivalent to (10/7) * (8/8) = 80/56 hours, and 3/8 of an hour is equivalent to (3/8) * (7/7) = 21/56 hours. The total time spent watching is (80/56) + (21/56) = 101/56 hours. 
Simplifying this improper fraction, we get 1 and 45/56 hours. 
### Answer: 1 and 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 Pro:

Reasoning: We need to add the time spent on varnishing to the time it takes to build and upholster the chair (which we calculated in the previous problem).

Calculation: 95/39 + 8/19 = 95/39 + 16/39 = 111/39 hours

Simplifying the fraction: 111/39 = 37/13 hours 

### Answer: 37/13 hours 

Expected answer: 2117/741

Correct? No

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 Pro:

Reasoning: To find the total time with the reduced frame building time, we need to add the new frame building time to the upholstering time.

Calculation: 5/10 + 10/13 = 1/2 + 10/13 = 13/26 + 20/26 = 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 Pro:

Reasoning: To find the total distance, we need to add the distance traveled to the alien planet and the distance traveled afterwards. 
This gives us 11/18 + 8/13 light-years.
Finding a common denominator of 234, we can rewrite this as 143/234 + 144/234 = 287/234 light-years.
### 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 Pro:

Reasoning: We know Jonathan needs 2 16/35 yards of fabric and has 17 yards total. 
First, convert 17 to a mixed number with a denominator of 35: 16 35/35. 
Then, subtract the amount needed for the sleeping bag: 16 35/35 - 2 16/35 = 14 19/35. 

### Answer: 14 19/35 yards 

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 Pro:

Reasoning: First, we need to find a common denominator for 12/17 and 8/5. The least common denominator is 85. 
Next, we need to convert each fraction to have a denominator of 85: 12/17 = 60/85 and 8/5 = 136/85. 
Finally, we add the two fractions to find the total fabric needed: 60/85 + 136/85 = 196/85 yards.
Simplifying the fraction, we get 2 26/85 yards. 

### Answer: 2 26/85 yards 

Expected answer: 196/85

Correct? Yes

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 Pro:

Reasoning: We need to add the acreage of pine trees, 5/3, to the acreage of oak trees, 1/2. 
To do this, we need a common denominator. The least common denominator for 3 and 2 is 6.
5/3 acres is equivalent to 10/6 acres, and 1/2 acre is equivalent to 3/6 acres.
Therefore, the total acreage of pine and oak trees is 10/6 + 3/6 = 13/6 acres.
### Answer: 13/6 acres 

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 Pro:

Reasoning: 4/16 of a yard is equivalent to 1/4 of a yard. 
We need to find a common denominator for 7 and 4, which is 28. 
13/7 is equivalent to 52/28, and 1/4 is equivalent to 7/28.
Therefore, Jake will have 52/28 - 7/28 = 45/28 yards of fabric left.
### Answer: 45/28 yards 

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 Pro:

Reasoning: 12/6 of a yard simplifies to 2 yards.
2/14 of a yard simplifies to 1/7 of a yard.
Combining both pieces, Jake has 2 + 1/7 = 2 1/7 yards of fabric.
### Answer: 2 1/7 yards 

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 Pro:

Reasoning: 
First, simplify the fraction 10/4 to get 5/2.
Then, calculate the difference: 5/2 - 11/20 = 50/20 - 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 Pro:

Reasoning: We need to add the length of the new dance move (2/20 minutes) to the length of her shortened routine (133/80 minutes). 
First, simplify 2/20 to 1/10.  Then get a common denominator: the LCM of 10 and 80 is 80. 
The equivalent fraction for 1/10 is (1/10)*(8/8) = 8/80.
Now we can add: 133/80 + 8/80 = 141/80
### Answer: 141/80 minutes 

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 Pro:

Reasoning:  We need to subtract the new shortened amount (12/16) from the original length (13/5): 13/5 - 12/16.
To subtract fractions, they need a common denominator, which is the least common multiple (LCM) of 5 and 16.  The LCM of 5 and 16 is 80.
We get equivalent fractions with a denominator of 80: (13/5)*(16/16) = 208/80 and (12/16)*(5/5) = 60/80.
Now we can subtract: 208/80 - 60/80 = 148/80. This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 4, resulting in 37/20.
### Answer: 37/20 minutes 

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 Pro:

Reasoning: From the previous problem, we know Miss Daisy had 139/60 kg of fertilizer left after using some on her roses.
She found 11/11 kg which simplifies to 1 kg.
Therefore, Miss Daisy now has 139/60 kg + 1 kg of fertilizer.
To add these quantities, we need a common denominator.  Since 1 = 60/60, we have 139/60 kg + 60/60 kg = 199/60 kg.
### Answer: 199/60 kg

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 Pro:

Reasoning:  We need to subtract the weight of fertilizers used for the roses from the new initial weight of fertilizers: 14/6 kg - 17/20 kg.
The least common multiple of 6 and 20 is 60. Thus, we have 14/6 = (14*10)/(6*10) = 140/60, and 17/20 = (17*3)/(20*3) = 51/60.
Therefore, 14/6 kg - 17/20 kg = 140/60 kg - 51/60 kg = 89/60 kg.
### Answer: 89/60 kg.

Expected answer: 89/60

Correct? Yes

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 Pro:

Reasoning: We need to add the regular yearly increase to the predicted additional increase next year: 4/16 meters + 16/6 meters. 
First, simplify 4/16 to 1/4.
To add these fractions, they need a common denominator. The least common denominator for 4 and 6 is 12.
Therefore: (1/4 * 3/3) + (16/6 * 2/2) = 3/12 + 32/12 = 35/12 meters. 

### Answer: 35/12 meters. 

Expected answer: 25/4

Correct? No

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 Pro:

Reasoning: We still need to add the regular yearly increase to the corrected unexpected increase: 4/16 meters + 20/18 meters.

First, simplify the fraction 20/18 by dividing the numerator and denominator by their greatest common factor, 2: 20/18 = 10/9.

Now, find a common denominator for 16 and 9, which is 144: 
(4/16 * 9/9) + (10/9 * 16/16) = 36/144 + 160/144 = 196/144 meters.

This fraction can be simplified by dividing the numerator and denominator by their greatest common factor, 4: 196/144 = 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 Pro:

Reasoning: First, find the total amount of money Bob has in his wallet. We need to add the amount of money in both pockets: 11/3 + 12/19.
To add fractions, we need a common denominator. The least common denominator for 3 and 19 is 57.
We can rewrite 11/3 as 209/57 and 12/19 as 36/57.
Adding these fractions gives us 209/57 + 36/57 = 245/57 dollars.
Now, to duplicate this amount, we simply multiply by 2: (245/57) * 2 = 490/57 dollars.
### Answer: 490/57 dollars. 

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 Pro:

Reasoning:  We need to add 3/3 to 12/19 to find the total.
First, we should simplify 3/3 to 1.
Then, to add 1 to 12/19, we need a common denominator. We can rewrite 1 as 19/19.
Adding these fractions gives us 19/19 + 12/19 = 31/19 dollars.
### Answer: 31/19 dollars. 

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 Pro:

Reasoning:
* We know from before that the shark swam 5/3 miles in the morning and afternoon.
* Simplifying 18/9, we get 2 miles.
* To add the distances, we need to express 2 miles as a fraction with a denominator of 3.  We get 6/3.
* Therefore, the shark swam a total of 5/3 + 6/3 = 11/3 miles.

### Answer: 11/3 miles 

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 Pro:

Reasoning:
* We need to add the distance the shark swam in the morning (5/12 miles) to the distance it swam in the afternoon (12/18 miles).
* First, we simplify 12/18 to 2/3.
* To add fractions, we need a common denominator. The least common denominator for 12 and 3 is 12.
* We convert 2/3 to 8/12.
* Finally, we add the two fractions: 5/12 + 8/12 = 13/12 miles

### Answer: 13/12 miles 

Expected answer: 13/12

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 Pro:

Reasoning: We need to subtract the clown's performance time (53/40 hours) from her total break time (13/5 hours).
First, we need to find a common denominator for these fractions. The least common denominator for 5 and 40 is 40.
The fraction 13/5 is equivalent to (13/5)*(8/8) = 104/40.
Therefore, the remaining break time is (104/40) - (53/40) = 51/40 hours
This can be represented by the mixed number 1 11/40.

### 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 Pro:

Reasoning: We need to find a common denominator for the fractions 9/8 and 9/10. The least common denominator is 40. 
The fraction 9/8 is equivalent to (9/8) * (5/5) = 45/40.
The fraction 9/10 is equivalent to (9/10) * (4/4) = 36/40
She performed for (45/40) + (36/40) = 81/40 hours
The fraction 81/40 can be rewritten as the mixed number 2 1/40

### Answer: 2 1/40 hours 

Expected answer: 81/40

Correct? Yes

Problem: Following the last scenario, if Timmy later dumps another 16/3 kg of sand into the sandbox, how much sand does the sandbox contain now?

Gemini-1.5 Pro:

Reasoning: Timmy started with 4 kg of sand and added 16/3 kg, for a total of 4 + 16/3 kg.
We can rewrite 4 as 12/3 to get a common denominator: 12/3 + 16/3 = 28/3 kg
### Answer: 28/3 kg 

Expected answer: 28/3

Correct? Yes

Problem: In the previous sandbox problem, if Timmy initially dumped 7/2 kg of sand into his sandbox but this time around, he decided to add only 1/20 kg of sand to it instead, how much sand is now in his sandbox?

Gemini-1.5 Pro:

Reasoning: To add the weight of the sand, we first need to have a common denominator. The least common denominator of 2 and 20 is 20. 
Therefore, we need to rewrite 7/2 as an equivalent fraction with a denominator of 20. We can do this by multiplying the numerator and denominator by 10: (7/2) * (10/10) = 70/20. 
Now we can add the weight of the added sand: 70/20 kg + 1/20 kg = 71/20 kg.
### Answer: 71/20 kg 

Expected answer: 71/20

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 Pro:

Reasoning: First, we need to find the least common denominator for 10 and 18, which is 90. 
Next, we need to convert our fractions to have a denominator of 90: 3/10 = 27/90 and 16/18 = 80/90
Now we can add our fractions: 27/90 + 80/90 = 107/90 miles
This is an improper fraction so we can simplify it to: 1 and 17/90 miles 
### Answer: 1 and 17/90 miles 

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 Pro:

Reasoning: We will use the simplified form of 20/4 chairs which is 5/1 chairs from the previous problem.
We need to find a common denominator for 17/14 and 5/1 which we will choose to be 14. 
We can rewrite 5/1 as 5/1 * 14/14 = 70/14 chairs.
Finally, we add the chairs made by the first machine and the second machine: 70/14 + 17/14 = 87/14.
### Answer: 87/14 chairs 

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 Pro:

Reasoning: We need to add the distance the great white shark swam to the distance the blue shark and hammerhead shark swam together (1 and 1/5 miles or 6/5 miles).
First, we should convert our mixed number to a fraction. 1 and 1/5 is equivalent to 6/5.
Next, we need to find the least common denominator for 6/5 and 9/14, which is 70.
6/5 is equivalent to 84/70, and 9/14 is equivalent to 45/70.
We can now add the distances: 84/70 + 45/70 = 129/70 miles.
We can simplify this fraction to 1 and 59/70. 
### Answer: 1 and 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 Pro:

Reasoning: We need to find a common denominator for our fractions. The least common denominator for our fractions is 44. 
2/4 is equivalent to 22/44, and 7/11 is equivalent to 28/44. 
Altogether, the sharks swam 22/44 + 28/44 = 50/44 miles. 
We can simplify this fraction, 50/44, to 25/22. 
25/22 is equivalent to 1 and 3/22.
### Answer: 1 and 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 Pro:

Reasoning: 6/16 gallons is equivalent to 3/8 gallons. From the previous problem, Lisa has a total of 2 25/36 gallons, which is equivalent to 97/36 gallons. Now we add 3/8 gallons to that total: 97/36 + 3/8 = 194/72 + 27/72 = 221/72 gallons. This is equivalent to 3 1/72 gallons. 
### Answer: 3 1/72 gallons

Expected answer: 221/72

Correct? No

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 Pro:

Reasoning: We need to find the sum of the areas of all three tents: 13/11 + 8/20 + 1/10.
To add these fractions, we first need to find a common denominator.  The least common denominator for 11, 20, and 10 is 220.
We convert each fraction as follows: 13/11 = 260/220, 8/20 = 88/220, and 1/10 = 22/220.
Now, we can add the fractions: 260/220 + 88/220 + 22/220 = 370/220.
Finally, we simplify the fraction 370/220 to 37/22 or 1 15/22. 
### Answer: 1 15/22 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 Pro:

Reasoning:  We need to add the area of the large tent to the area of the small tent. That is 13/11 + 10/20. 
Before adding, we need to find a common denominator for the two fractions. The least common denominator is 220, so 13/11 becomes 260/220, and 10/20 becomes 110/220. 
Now we can add the fractions: 260/220 + 110/220 = 370/220.
Finally, we can simplify the fraction 370/220 to 37/22 or 1 15/22.
### Answer: 1 15/22 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 Pro:

Reasoning: Sarah and Alex collected a total of 1 117/140 pounds of firewood. Kim brought an additional 11 pounds. To find the total, we add these amounts:  1 117/140 + 11. 

Adding the whole numbers: 1 + 11 = 12

The total amount of firewood is the sum of the whole and fractional parts: 12  117/140 

### Answer: 12 117/140 pounds 

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 Pro:

Reasoning: 
First, we need to find a common denominator for our fractions 10/20 and 9/7. Both fractions can share a common denominator of 140.
Let's convert 10/20 to a fraction with a denominator of 140: (10/20) * (7/7) = 70/140
Let's convert 9/7 to a fraction with a denominator of 140: (9/7)*(20/20) = 180/140
Now, we can add our fractions together: 70/140 + 180/140 = 250/140.
Finally, let's simplify our fraction and convert it into a mixed number: 250/140 = 1 11/14

### Answer: 1 11/14 pounds 

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 Pro:

Reasoning:  We need to subtract the distance Captain Bill traveled south from the total distance he traveled north. This means we need to subtract 20/17 miles from 23/5 miles.

First, we need to find a common denominator: 
* The least common denominator for 5 and 17 is 85.  
* We can rewrite 23/5 as  391/85 (23 * 17 = 391)
* We can rewrite 20/17 as 100/85 (20 * 5 = 100)

Now we can subtract: 391/85 - 100/85 = 291/85 miles.

### Answer: 291/85 miles 

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 Pro:

Reasoning: We need to add the two distances Captain Bill sailed north. The first distance is 19/18 miles and the second distance is 12/15 miles. To add fractions, they must have a common denominator. The least common denominator of 18 and 15 is 90. We can rewrite 19/18 as 95/90 and 12/15 as 72/90. Therefore, Captain Bill sailed a total of 95/90 + 72/90 = 167/90 miles north.
### Answer: 167/90 miles 

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 Pro:

Reasoning: To find the intended weight of the meat, we need to subtract the excess meat (13/9 pounds) from the actual weight (229/68 pounds). 

First, we need to find a common denominator for 9 and 68, which is 612. 

We can rewrite 13/9 as 884/612 and 229/68 as 2061/612.

Subtracting the excess meat, we get 2061/612 - 884/612 = 1177/612 pounds.

### Answer: 1177/612 pounds 

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 Pro:

Reasoning: We will follow a similar process as before, but we will use 6/4 pounds for the turkey instead of 9/4 pounds.
The least common denominator for 17 and 4 is still 68.
We can rewrite 19/17 as 76/68 and 6/4 as 102/68.
Adding the two fractions, we get 76/68 + 102/68 = 178/68 pounds.
This fraction can be simplified by dividing the numerator and denominator by 2, resulting in 89/34 pounds.
### Answer: 89/34 pounds

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 Pro:

Reasoning: The total length of the sleeping bag is 18/19 + 8/8 meters. 8/8 is equal to 1.
To add the fraction and the whole number, we need a common denominator: the least common denominator for 19 and 1 is 19.
We can rewrite 1 as 19/19 (1*19 / 1*19 = 19/19).
Finally, 18/19 + 19/19 = 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 Pro:

Reasoning: 16/2 gallons is equivalent to 8 gallons.
Sarah added 8 + 10/13 = <<8+10/13=114/13>>114/13 gallons of water into the container. 
### Answer: 114/13 gallons 

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 Pro:

Reasoning: Mandy has 9/2-1/4 = 18/4-1/4 = 17/4 KGs of apples left after baking.
After finding more apples, she has a total of 17/4 + 3/19 = 337/76 KGs of apples. 
### Answer: 337/76 KGs. 

Expected answer: 335/76

Correct? No

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 Pro:

Reasoning: Mandy has 9/7-1/4 = 36/28-7/28 = 29/28 KGs of apples left. 
### Answer: 29/28 KGs. 

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 Pro:

Reasoning: We know John spent 2 1/21 hours fixing and polishing the watch. To find the total time, we need to add the additional time spent on adjustments: 2 1/21 hours + 12/13 hours.

First, convert the mixed number to a fraction: 2 1/21 = (2 * 21 + 1)/21 = 43/21

Next, find a common denominator for 21 and 13. The least common denominator is 273.

Converting 43/21 to a fraction with a denominator of 273: (43/21) * (13/13) = 559/273
Converting 12/13 to a fraction with a denominator of 273: (12/13) * (21/21) = 252/273

Now we can add the fractions: 559/273 + 252/273 = 811/273

Simplifying the fraction: 811/273 =  3 8/273

### Answer: 3 8/273 hours

Expected answer: 811/273

Correct? No

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 Pro:

Reasoning: To find the total time, we need to add the time spent on each task: 12/7 hours + 3/15 hours.

Before adding, we need to find a common denominator for the fractions. The least common denominator for 7 and 15 is 105.

Converting 12/7 to a fraction with a denominator of 105: (12/7) * (15/15) = 180/105
Converting 3/15 to a fraction with a denominator of 105: (3/15) * (7/7) = 21/105

Now we can add the fractions: 180/105 + 21/105 = 201/105

Simplifying the fraction: 201/105 = 67/35 = 1 32/35

### Answer: 1 32/35 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 Pro:

Reasoning: If Peggy swam 1/15 miles back, she traveled 1/15 * 4/5 = <<1/15*4/5=4/75>> 4/75 of the initial 5/4 miles back. 
That means she has 1 - 4/75 = <<1-4/75= 71/75>> 71/75 of the 5/4 miles remaining. 
Therefore, Peggy is (71/75) * (5/4) = <<(71/75)*(5/4)=71/60>> 71/60 miles away from her family. 
### 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 Pro:

Reasoning: We need to add the size of the vegetable patch to the previous total: 59/12 + 17/11 = <<59/12+17/11=865/132>>865/132 acres. 
### Answer: 865/132 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 Pro:

Reasoning: We need to add the corrected size of the first part to the size of the second part: 4/9 + 11/12 

To add these fractions, we need a common denominator. The least common denominator for 9 and 12 is 36.

*  (4/9) * (4/4) = 16/36
* (11/12) * (3/3) = 33/36

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

### Answer: 49/36 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 Pro:

Reasoning: Our previous total was 207/68 yards, and we need to add 19/10 yards. First, we find a common denominator: (207/68) + (19/10) = (1035/340) + (646/340)
Then we add the fractions: (1035/340) + (646/340) = 1681/340
### Answer: 1681/340 yards 

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 Pro:

Reasoning: First simplify the fraction representing the blue fabric: 5/5 = 1 yard
To add the fractions, they must share a common denominator: (11/4) + (1/1) = (11/4) + (4/4) 
Adding the fractions with like denominators gives us our answer: (11/4) + (4/4) = 15/4
### Answer: 15/4 yards 

Expected answer: 15/4

Correct? Yes

Problem: Jacob bought another 3/4 feet of wire in addition to what was left over from before. How much guitar wire does he have in total now?

Gemini-1.5 Pro:

Reasoning: Total wire = Remaining wire + New wire = 83/16 + 3/4.
Let us simplify this: 83/16 + 3/4 = 83/16 + (3*4)/(4*4) = 83/16 + 12/16 = (83+12)/16 = 95/16 feet.
### Answer: 95/16 feet 

Expected answer: 95/16

Correct? Yes

Problem: In the previous scenario, what if Jacob initially had 11/2 feet long guitar wire but ended up using 9/16 feet to fix the guitar instead of 5/16 feet. How much guitar wire would be remaining in that case?

Gemini-1.5 Pro:

Reasoning: Remaining wire = Total wire - Wire used for fixing = 11/2 - 9/16.
Let us simplify this: 11/2 - 9/16 = (11*8)/(2*8) - 9/16 = 88/16 - 9/16 = (88-9)/16 = 79/16 feet.
### Answer: 79/16 feet 

Expected answer: 79/16

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 Pro:

Reasoning: 12 candies / 6 friends = <<12/6=2>>2 candies per friend.
20 stickers / 13 friends = <<20/13=1.53846153846>>1.54 stickers per friend (rounded to the nearest hundredth).
Not every friend will get the same amount of both candies and stickers because the stickers don't divide evenly amongst her friends. 
### Answer:  It is not possible for each friend to get the same amount of both candies and stickers. 

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 Pro:

Reasoning: We need to add the rainfall from the first day, which was 163/65 hours, to the rainfall of the second day, which was 11/19 hours:  163/65 + 11/19.
To add these fractions, they need a common denominator.  The least common denominator for 65 and 19 is 1235.
We convert both fractions: 163/65 = 3197/1235 and 11/19 = 715/1235
Finally, we add the fractions: 3197/1235 + 715/1235 = 3912/1235
### Answer: 3912/1235 hours 

Expected answer: 3812/1235

Correct? No

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 Pro:

Reasoning: Previously, Jane had cut 1 and 10/12 yards from the blanket.  We need to add 4/12 to that amount.
1 + 10/12 + 4/12 = 1 and 14/12 yards.
We can simplify 1 and 14/12 to 2 and 2/12 because 12/12 is equal to 1.
We can further simplify 2 and 2/12 to 2 and 1/6.
### Answer: 2 and 1/6 yards 

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 Pro:

Reasoning: 10/10 yard is equal to 1 yard.
Jane cut 11/12 + 1 = 1 and 11/12 yards in total. 
### Answer: 1 and 11/12 yards 

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 Pro:

Reasoning: First, find the total amount of magic dust used on the field and apple trees: 11/12 + 9/10.

A common denominator for 12 and 10 is 60. Convert the fractions:
- 11/12 = 55/60
- 9/10 = 54/60

Add the fractions: 55/60 + 54/60 = 109/60 oz

Now, subtract the amount used (109/60 oz) from the initial amount (14/3 oz). First, convert 14/3 to have a denominator of 60:
- 14/3 = 280/60

Finally, subtract: 280/60 - 109/60 = 171/60 oz

Simplify the fraction: 171/60 = 2 51/60 = 2 17/20 oz

### Answer: 2 17/20 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 Pro:

Reasoning: To find the total amount of magic dust, we need to add the amount used on the field to the amount accidentally used on the grove: 11/12 + 16/10.

First find a common denominator for 12 and 10, which is 60.
Then convert each fraction to have a denominator of 60:
- 11/12 = 55/60
- 16/10 = 96/60 

Now add the two fractions: 55/60 + 96/60 = 151/60

Finally, simplify the fraction by converting 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 Pro:

Reasoning: Your previous score was 118/110 points and you just earned 19/7 points.
Your total score is 118/110 + 19/7 = 301/77 points.
### Answer: 301/77 points. 

Expected answer: 1458/385

Correct? No

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 Pro:

Reasoning: You will earn 5/11 * 1 = 5/11 of a point for vowels.
You will earn 8/10 * 1 = 8/10 of a point for consonants.
Your total score will be 5/11 + 8/10 = 138/110 points.
### Answer: 138/110 points. 

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 Pro:

Reasoning: The letter is currently 22/9 pages long, which is equal to 88/36 pages. 
Adding 7/12 of a page, or 21/36 of a page, brings the length to 88/36+21/36 = 109/36 pages.
### Answer: 109/36 pages. 

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 Pro:

Reasoning: A length of 15/1 pages is equal to 135/9 pages.
Removing 14/9 pages from 135/9 pages leaves 135/9-14/9 = 121/9 pages.
### Answer: 121/9 pages. 

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 Pro:

Reasoning: We know from the previous problem that the store has 3 1/10 kg of red and green apples. We need to add the weight of the yellow apples, which is 17/15 kg. 
First, convert 3 1/10 to a fraction. 3 1/10 = 31/10
We need to find a common denominator for 31/10 and 17/15. The Least Common Multiple of 10 and 15 is 30. We can multiply 31/10 by 3/3 to get 93/30. We can multiply 17/15 by 2/2 to get 34/30.
93/30 + 34/30 = 127/30
We can simplify 127/30 to get 4 7/30
### Answer: 4 7/30 kilograms 

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 Pro:

Reasoning: First simplify 18/8, which is equal to 9/4
We need to find the sum of 3/20 and 9/4, so we need to find a common denominator for the fractions. The Least Common Multiple of 20 and 4 is 20. We can multiply 9/4 by 5/5 to get 45/20
3/20 + 45/20 = 48/20
We can simplify 48/20 to get 12/5, which is equal to 2 2/5
### Answer: 2 2/5 kilograms 

Expected answer: 12/5

Correct? Yes

Problem: After the bus has traveled 12/20 of a mile, then an additional 12/12 of a mile, it makes the same journey back. How many miles did the bus travel in total?

Gemini-1.5 Pro:

Reasoning: We already know the bus travels 8/5 miles in one direction.
The bus travels 8/5 + 8/5 = <<8/5+8/5=16/5>>16/5 miles traveling there and back. 
### Answer: 16/5 miles 

Expected answer: 16/5

Correct? Yes

Problem: If instead of driving 12/20 of a mile initially, the bus drives 14/20 of a mile in the beginning and then goes an additional 12/12 of a mile, how many miles did the bus travel in total?

Gemini-1.5 Pro:

Reasoning: 12/12 of a mile is equal to 1 mile.
The bus traveled 14/20 + 1 = <<14/20+1=34/20>>34/20 miles.
Simplifying the fraction, the bus traveled 34/20 = <<34/20=17/10>>17/10 miles.
### Answer: 17/10 miles 

Expected answer: 17/10

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 Pro:

Reasoning: We know from the previous problem that the shark swam a total of 44/15 miles in the first two hours. To find the total distance for three hours, we need to add the distance from the third hour: 44/15 miles + 14/9 miles.
The least common denominator for 15 and 9 is 45.
Converting 44/15 to a fraction with a denominator of 45: (44/15)*(3/3) = 132/45.
Converting 14/9 to a fraction with a denominator of 45: (14/9)*(5/5) = 70/45.
Now, we can add the distances: 132/45 miles + 70/45 miles = 202/45 miles.
### Answer: 202/45 miles. 

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 Pro:

Reasoning:  We need to add the distance from the first hour (3/7 miles) to the distance from the second hour (13/5 miles).
To add these fractions, we need a common denominator. The least common denominator for 7 and 5 is 35.
Converting 3/7 to a fraction with a denominator of 35: (3/7)*(5/5) = 15/35.
Converting 13/5 to a fraction with a denominator of 35: (13/5)*(7/7) = 91/35.
Now we can add the two distances: 15/35 miles + 91/35 miles = 106/35 miles.
### Answer: 106/35 miles. 

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 Pro:

Reasoning: To find when the beats coincide, we need to find the least common multiple (LCM) of the two fractions' denominators. 

* First, simplify the second fraction: 2/12 simplifies to 1/6.

* Now we need the LCM of 17 and 6, which is 102.

* This means the first beat (16/17 seconds) will need to be multiplied by 6, and the second beat (1/6 seconds) will need to be multiplied by 17 to have matching denominators.

*  Therefore, it takes 102/102 seconds (which equals 1 second) for the first beat to coincide with the second beat.

### Answer: 1 second. 

Expected answer: 113/102

Correct? No

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 Pro:

Reasoning: We need to add the wood burned during the day (364/323 cord) to the wood burned at night (19/20 cord). First, we need to find a common denominator: the least common denominator for 323 and 20 is 6460.  Therefore, 364/323 = 7280/6460 and 19/20 = 6194/6460. Adding those fractions, we get 7280/6460 + 6194/6460 = 13474/6460. This fraction can be simplified to 6737/3230
### Answer: 6737/3230 

Expected answer: 13417/6460

Correct? No

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 Pro:

Reasoning: We need to add the distance of the third segment to the total distance from the first two segments: 477/323 + 19/20
To add fractions, they need to have a common denominator, so we multiply each fraction by a suitable form of 1: (477/323)*(20/20) + (19/20)*(323/323) = 9540/6460 + 6137/6460
Now that the fractions have the same denominator, we can add them: 9540/6460 + 6137/6460 = 15677/6460
The butterfly has now flown a total of 15677/6460 miles.
### Answer: 15677/6460 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 Pro:

Reasoning: We follow the same process as before, but this time with the adjusted length of the first segment.
The total length of the flight is now 18/12 + 9/17 miles.
Again, we need a common denominator to add these fractions: (18/12)*(17/17) + (9/17)*(12/12) = 306/204 + 108/204.
Adding the fractions with a common denominator: 306/204 + 108/204 = 414/204.
This fraction can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 6: (414/6)/(204/6) = 69/34.
The new total length of the butterfly's flight is 69/34 miles.
### Answer: 69/34 miles 

Expected answer: 69/34

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 Pro:

Reasoning: Since each balloon rises at a speed of 113/48 feet per second, their combined speed is simply twice this amount.
Therefore, their combined speed is (113/48) * 2 = 113/24 feet per second. 
### Answer: 113/24 feet per second. 

Expected answer: 113/24

Correct? Yes

Problem: After finishing the small art project, Scarlett decides to mix the remaining red paint with 5/7 gallons of yellow paint to make orange paint. How many gallons of paint does she have now?

Gemini-1.5 Pro:

Reasoning:
We need to add the remaining red paint, 1 11/20 gallons, to the yellow paint, 5/7 gallons. 
First, convert the mixed number to a fraction: 1 11/20 = 31/20.
To add fractions, they need a common denominator. The least common denominator for 20 and 7 is 140. 
Adjusting both fractions: (31/20)*(7/7) = 217/140 and (5/7)*(20/20) = 100/140.
Now, add the fractions: 217/140 + 100/140 = 317/140.
Finally, simplify the fraction to a mixed number: 317/140 = 2 37/140 gallons.

### Answer: 2 37/140 gallons 

Expected answer: 317/140

Correct? Yes

Problem: Suppose Scarlett initially had 16/10 gallons of red paint. But this time, she uses 2/20 of a gallon for her small project instead. How many gallons of red paint does she have left now?

Gemini-1.5 Pro:

Reasoning:
First, we need to convert 16/10 to a fraction with a denominator of 20: (16/10) * (2/2) = 32/20
Now, subtract the amount used for the project: 32/20 - 2/20 = 30/20.
Finally, simplify the fraction 30/20 to a mixed number: 30/20 = 3/2 = 1 1/2 gallons.
### Answer: 1 1/2 gallons 

Expected answer: 3/2

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 Pro:

Reasoning: The plane descends by 12/15 = <<12/15=4/5>>4/5 of a mile.
The new altitude of the plane is 2 - 4/5 = <<2-4/5=6/5>>6/5 miles.
### Answer: 6/5 miles

Expected answer: 6/5

Correct? Yes

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 Pro:

Reasoning: We need to add the length of the first slide to the length of the second slide: 6/5 + 17/4 
To add fractions, they must have a common denominator. The least common denominator for 5 and 4 is 20.
6/5 is equivalent to 6/5 * 4/4 = 24/20
17/4 is equivalent to 17/4 * 5/5 = 85/20
Therefore, the total length the child slid is 24/20 + 85/20 = 109/20 meters.
### Answer: 109/20 meters. 

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 Pro:

Reasoning: First find the combined rate of the early morning and late night: (4/15) + (14/15) = 18/15
Then add the peak hour rate to find the total rate: (18/15) + (6/5) = 36/15
### Answer: 36/15 cords 

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 Pro:

Reasoning: We need to add the new early morning rate to the late night rate.
(8/15) + (14/15) = 22/15
### Answer: 22/15 cords  

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 Pro:

Reasoning: First we need to calculate the total distance the alien traveled in the first two parts of the journey.  We can do this by adding the two fractions, which we previously found to be a total of 283/140 light years.

Next, we can simplify the third distance, 14/2 light years, to 7 light years. 

To make it easier to add this distance to the first two, we can express it with a denominator of 140: 7 light years is equivalent to 980/140 light years.

Therefore, the total distance the alien travelled is 283/140 + 980/140 = 1263/140 light years.

### Answer: 1263/140 light years. 

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 Pro:

Reasoning: First, we simplify 11/11 to 1.
So, the problem becomes (9/20) + 1.
To add these, we need a common denominator.  We can rewrite 1 as 20/20.
Therefore, the alien would have traveled 9/20 + 20/20 = 29/20 light years.

### Answer: 29/20 light years. 

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 Pro:

Reasoning: Bob had 5 1/7 cucumbers, and doubling that means he multiplies his amount by 2. 
Doubling his whole cucumbers: 5 cucumbers * 2 = 10 cucumbers
Doubling his fraction of a cucumber: (1/7) * 2 = 2/7 of a cucumber
Adding the whole and fractional parts together: 10 cucumbers + (2/7) cucumbers = 10 2/7 cucumbers
### Answer: 10 2/7 cucumbers 

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 Pro:

Reasoning: First, simplify 10/2, which equals 5 cucumbers.
Next, convert the fraction 17/7 into a mixed number: 2 3/7 cucumbers
Now, add the whole cucumbers: 2 + 5 = 7 cucumbers
This leaves us with 7 whole cucumbers and the remaining 3/7 of a cucumber. 
### Answer: 7 3/7 cucumbers 

Expected answer: 52/7

Correct? Yes