Mixtral 8x7B on 5.NF.A.2
Common Core Standard 5.NF.A.2
This standard covers the following:
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
Problem: In their game, Kyle threw a ball for a distance of 18/4 yards, while Lisa threw the same ball for a distance of 19/9 yards. How many yards did the ball travel in total?
Mixtral 8x7B:
Reasoning: First, we need to find the simplified form of the fractions to determine the distance thrown by Kyle and Lisa. 18/4 = 9/2 and 19/9 = 19/9 Now, we add the distances together: 9/2 + 19/9 To add the fractions, we need a common denominator, which is 18 in this case. 9/2 = 81/18 and 19/9 = 20/18 Now, we can add the fractions: 81/18 + 20/18 = 101/18 ### Answer: The ball traveled 101/18 yards in total.
Expected answer: 119/18
Correct? No
Problem: Johnnie the monkey was given 18/7 bananas by the zookeeper in the morning, and 12/14 bananas in the afternoon. In total, how many bananas were given to Johnnie the monkey?
Mixtral 8x7B:
Reasoning: The zookeeper gave Johnnie 18/7 bananas in the morning. The zookeeper gave Johnnie 12/14 bananas in the afternoon. To find the total number of bananas given, we need to find a common denominator for 7 and 14. The least common multiple of 7 and 14 is 14. So, we convert 18/7 to 18/14. Now, we can add the bananas: 18/14 + 12/14 = (18+12)/14 = 30/14 = 15/7. ### Answer: 15/7 bananas
Expected answer: 24/7
Correct? No
Problem: The bottom of a door measures 4/19 inches from the floor, and the top of the door measures 9/10 inches from the ceiling. What is the total distance of the bottom and top of the door from the floor and ceiling, respectively?
Mixtral 8x7B:
Reasoning: The total distance from the bottom of the door to the floor and the top of the door to the ceiling is the sum of the two given distances. To add the fractions, we need a common denominator, which in this case is 190 (the least common multiple of 19 and 10). The bottom of the door is 4/19 inches from the floor, so in terms of a common denominator, it is (4/19)*(10/10) = 40/190 inches from the floor. The top of the door is 9/10 inches from the ceiling, so in terms of a common denominator, it is (9/10)*(19/19) = 171/190 inches from the ceiling. The total distance from the bottom of the door to the floor and the top of the door to the ceiling is 40/190 + 171/190 = 211/190 inches. ### Answer: 211/190 inches or approximately 1.11 inches.
Expected answer: 211/190
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?
Mixtral 8x7B:
Reasoning: Since both doors have the same measurements, the distance from the floor to the bottom of each door and the distance from the ceiling to the top of each door are the same. Therefore, the total distance from the floor to the bottoms of both doors and the total distance from the tops of both doors to the ceiling are both twice the distance from the floor to the bottom of one door and the distance from the ceiling to the top of one door, respectively. The total distance from the floor to the bottoms of both doors is 2 \* (40/190) = 80/190 inches. The total distance from the tops of both doors to the ceiling is 2 \* (171/190) = 342/190 inches. ### Answer: The total distance from the floor to the bottoms of both doors is 80/190 inches, and the total distance from the tops of both doors to the ceiling is 342/190 inches.
Expected answer: 211/95
Correct? No
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?
Mixtral 8x7B:
Reasoning: The total distance from the bottom of the door to the floor and the top of the door to the ceiling is the sum of the two given distances. To add the fractions, we need a common denominator, which in this case is 160 (the least common multiple of 16 and 10). The bottom of the door is 4/16 inches from the floor, so in terms of a common denominator, it is (4/16)*(10/10) = 40/160 inches from the floor. The top of the door is 9/10 inches from the ceiling, so in terms of a common denominator, it is (9/10)*(16/16) = 144/160 inches from the ceiling. The total distance from the bottom of the door to the floor and the top of the door to the ceiling is 40/160 + 144/160 = 184/160 inches. ### Answer: 184/160 inches or approximately 1.15 inches.
Expected answer: 23/20
Correct? Yes
Problem: Ralph's juice recipe requires 17/3 liters of apple juice. However, he only uses 15/11 liters of it. How many liters of apple juice are left unused?
Mixtral 8x7B:
Reasoning: To find out how much apple juice is left unused, we need to subtract the amount of apple juice Ralph used from the amount the recipe requires. Ralph used 15/1
Expected answer: 142/33
Correct? No
Problem: Billy is trying to roller skate in an empty parking lot. He initially travels 4 miles, but rolls back for 17/20 of a mile after spotting a pothole. How many miles did he ultimately travel forward?
Mixtral 8x7B:
Reasoning: Billy traveled 4 - 17/20 = (80/20 - 17/20) = (80-17)/20 = 63/20 = <<63/20=3.15>>3.15 miles forward. ### Answer: 3.15 miles
Expected answer: 63/20
Correct? No
Problem: A rocket was launched into orbit. On the first day, it traveled 15/3 light years. On the second day, it traveled an additional 2/7 light years. How far has the rocket traveled in total?
Mixtral 8x7B:
Reasoning: The rocket traveled 15/3 = <<15/3=5>>5 light years on the first day and 2/7 light years on the second day. The rocket traveled 5 + 2/7 = (35 + 2)/7 = <<(35+2)/7=23/7>>23/7 light years in total. ### Answer: 23/7 light years
Expected answer: 37/7
Correct? No
Problem: Captain Silverbeard found 10/13 of a treasure map at one shipwreck site and 16/19 of the same treasure map at another site. What is the total portion of the treasure map that he found?
Mixtral 8x7B:
Reasoning: The fractions 10/1
Expected answer: 398/247
Correct? No
Problem: A hiker decides to walk 9/6 miles North before walking 2/16 miles East. How many miles has the hiker traveled in total?
Mixtral 8x7B:
Reasoning: The hiker walked 9/6 = <<9/6=1.5>>1.5 miles North. The hiker walked 2/1
Expected answer: 13/8
Correct? No
Problem: In Jessica's sandbox, she has a pile of sand that is 16/9 cubic feet. She then removes 4/13 cubic feet of sand from the sandbox. How much sand does she have left in her sandbox?
Mixtral 8x7B:
Reasoning: Jessica removed 4/13 cubic feet of sand from the sandbox, so she has 16/9 - 4/1
Expected answer: 172/117
Correct? No
Problem: Jacob has a piece of rope that is 15/12 meters long and he adds a piece that is 17/17 meters long to it. What is the total length of the rope now?
Mixtral 8x7B:
Reasoning: The length of the second piece of rope is 17/1
Expected answer: 9/4
Correct? No
Problem: Mark has 1 full pair of pants and another 13/4 pairs from various incomplete sets. How many pairs of pants does he have in total?
Mixtral 8x7B:
Reasoning: Mark has 1 full pair of pants, and 13/4 of a pair is equivalent to 13/4 = 3.25 pairs. Since you can't have a fraction of a pair of pants, we'll round up to the nearest whole number, which is 4 pairs. Mark has 1+4 = <<1+4=5>>5 pairs of pants in total. ### Answer: 5
Expected answer: 17/4
Correct? No
Problem: Miss Jenny stayed after school to grade papers. She spent 8/8 hours on one subject and an additional 20/19 hours on another subject. How long did she spend grading papers in total?
Mixtral 8x7B:
Reasoning: Miss Jenny spent 8+20/19 = <<8+20/1
Expected answer: 39/19
Correct? No
Problem: A cloud was observed at a height of 12/3 kms, it later ascended by 15/12 kms. What was the resultant height of the cloud from the ground?
Mixtral 8x7B:
Reasoning: The cloud was first observed at a height of 12/3 = <<12/3=4>>4 kms. Then, it ascended by 15/12 = <<15/12=1.25>>1.25 kms. The resultant height of the cloud from the ground is 4 + 1.25 = <<4+1.25=5.25>>5.25 kms. ### Answer: 5.25 kms
Expected answer: 21/4
Correct? No
Problem: Jack rides his scooter 3/9 of a mile to the library. After leaving, he scoots another 17/15 of a mile to his grandparents' house. How many miles does Jack ride his scooter in total?
Mixtral 8x7B:
Reasoning: To find the total distance Jack traveled, we need to add the distance he rode to the library and the distance he rode to his grandparents' house. First, convert 3/9 to a decimal by dividing 3 by 9, which equals 0.333333333333. Next, convert 17/15 to a decimal by dividing 17 by 15, which equals 1.13333333333. Now, add 0.333333333333 and 1.13333333333 to get 1.46666666666. ### Answer: 1.47 miles (rounded to the nearest hundredth)
Expected answer: 22/15
Correct? No
Problem: There are 4 logs in a pile that each burn for 1/16 of an hour. The fire burns out and Tom brings 16 twigs, each of which burns for 1/12 of an hour. What is the total burn time for the logs and twigs?
Mixtral 8x7B:
Reasoning: The 4 logs burn for 4*(1/16) = <<4*(1/1
Expected answer: 19/12
Correct? No
Problem: If a ring maker uses 12/16 ounces of a silver for the base of the ring and 16/2 ounces to make the rest of the ring, how many ounces of silver did the ring maker use in total?
Mixtral 8x7B:
Reasoning: The ring maker used 12/16 ounces for the base of the ring, which simplifies to 3/4 ounces. The ring maker used 16/2 ounces to make the rest of the ring, which simplifies to 8 ounces. The ring maker used a total of 3/4 + 8 = 8 3/4 = <<3/4+8=8.75>>8.75 ounces of silver. ### Answer: 8.75 ounces
Expected answer: 35/4
Correct? No
Problem: A farmer has an apple tree that produced 10/11 bushels of apples in the morning and 17/11 bushels in the afternoon. How many bushels of apples did the tree produce in total?
Mixtral 8x7B:
Reasoning: The tree produced 10/11+17/11 = <<10/11+17/1
Expected answer: 27/11
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?
Mixtral 8x7B:
Reasoning: The tree produced 10/9+17/11 = <<10/9 + 17/11 = 187/99 = 1.888888888888889 ≈ 1.9>>1.9 bushels in one day. ### Answer: 1.9 bushels
Expected answer: 263/99
Correct? No
Problem: If Sam's binoculars increase his range of sight by 3/14 of a mile and Joe's binoculars increase his range of sight by exactly 1 mile (16/16), what is their combined range increase when they use the binoculars one after the other?
Mixtral 8x7B:
Reasoning: When Sam uses his binoculars, his range of sight is increased by 3/14 of a mile. When Joe uses his binoculars, his range of sight is increased by 1 mile (16/1
Expected answer: 17/14
Correct? No
Problem: Maria uses 15/10 yards of fabric for a section of a blanket and 9/18 more yards for another section. What is the total length of fabric Maria uses for these two sections?
Mixtral 8x7B:
Reasoning: The amount of fabric Maria uses for the second section, 9/1
Expected answer: 2
Correct? No
Problem: A turtle walks 10/5 miles forward, then walks backward 5/16 mile. How many miles has the turtle actually covered from its starting point?
Mixtral 8x7B:
Reasoning: The turtle first walks 10/5 = <<10/5=2>>2 miles forward. Then, it walks backward 5/1
Expected answer: 27/16
Correct? No
Problem: A painter uses 18/11 liters of blue paint and 1/8 liters of white paint to mix a shade of sky blue. How much paint in liters did he use in total?
Mixtral 8x7B:
Reasoning: To find the total amount of paint used, we need to add the amount of blue paint and the amount of white paint. First, we need to find a common denominator for the fractions 18/11 and 1/8. The least common multiple of 11 and 8 is 88, so we convert the fractions to have this common denominator: 18/11 = (18 \* 8) / 88 = 144/88 1/8 = (1 \* 11) / 88 = 11/88 Now, we can add the two fractions: 144/88 + 11/88 = (144 + 11) / 88 = 155/88 The painter used 155/88 liters of paint in total. ### Answer: 155/88 liters
Expected answer: 155/88
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?
Mixtral 8x7B:
Reasoning: To find the total amount of paint after adding 12/1
Expected answer: 3071/1144
Correct? No
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?
Mixtral 8x7B:
Reasoning: To find the total amount of paint used, we need to add the amount of blue paint and the amount of white paint. First, we need to find a common denominator for the fractions 18/11 and 1/7. The least common multiple of 11 and 7 is 77, so we convert the fractions to have this common denominator: 18/11 = (18 \* 7) / 77 = 126/77 1/7 = (1 \* 11) / 77 = 11/77 Now, we can add the two fractions: 126/77 + 11/77 = (126 + 11) / 77 = 137/77 The painter would have used 137/77 liters of paint in total. ### Answer: 137/77 liters
Expected answer: 137/77
Correct? Yes
Problem: A computer program executed 8 tasks in 4 minutes and then executed another 20 tasks in 14 minutes. What is the total number of tasks it executed per minute?
Mixtral 8x7B:
Reasoning: The program executed 8 tasks in 4 minutes, which is a rate of 8/4 = <<8/4=2>>2 tasks per minute. The program executed 20 tasks in 14 minutes, which is a rate of 20/14 = <<20/14=10/7>>10/7 tasks per minute. The program executed 2*7/7 + 10/7 = <<2*7/7 + 10/7=17/7>>17/7 tasks per minute in total. ### Answer: 17/7 (Note: The answer is expressed as a fraction since the number of tasks per minute is not a whole number.)
Expected answer: 24/7
Correct? No
Problem: At the end of a rainbow, there are pots filled with magical gold coins. One pot contains 12/13 of a pound of gold coins while another contains 3/2 pounds of gold coins. How much gold is there in total?
Mixtral 8x7B:
Reasoning: To find the total amount of gold coins, we need to add the amount of gold in the first pot to the amount in the second pot. First, convert 12/1
Expected answer: 63/26
Correct? No
Problem: In space, an alien named Zorg receives a video message from earth that is divided into parts. The first part of the message is 4/4 hours long, and the second part is 11/1 hour long. How long in total is the message Zorg received?
Mixtral 8x7B:
Reasoning: The first part of the message is 4/4 = <<4/4=1>>1 hour long, and the second part is 11/1 = <<11/1=11>>11 hours long. The total length of the message is 1 + 11 = <<1+11=12>>12 hours. ### Answer: 12 hours
Expected answer: 12
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?
Mixtral 8x7B:
Reasoning: The original message was 12 hours long, and the additional part of the message is 7/8 = <<7/8=0.875>>0.875 hours long. The total length of all parts of the message is 12 + 0.875 = <<12+0.875=12.875>>12.875 hours. ### Answer: 12.875 hours (Note: The answer is in decimal form because the length of the additional part of the message is a fraction.)
Expected answer: 103/8
Correct? No
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?
Mixtral 8x7B:
Reasoning: The first part of the message is now 4/8 = 0.5 hours long, and the second part is still 11/1 = 11 hours long. The total length of the message is 0.5 + 11 = <<0.5+11=11.5>>11.5 hours. ### Answer: 11.5 hours (Note: The answer is in decimal form because the first part of the message is now given in fraction form, and adding a fraction to a whole number results in a decimal answer.)
Expected answer: 23/2
Correct? No
Problem: In a park, 10 ducks are equally distributed among 5 ponds, implying each pond has 10 / 5 ducks. In the same park, 8 fish are distributed among 10 small pools, with each pool having 8 / 10 fish. How many animals are there in each pond and pool combined?
Mixtral 8x7B:
Reasoning: Each pond has 10 / 5 = <<10/5=2>>2 ducks. Each pool has 8 / 10 = <<8/10=0.8>>0.8 fish. But since we can't have a fraction of a fish, we round it to the nearest whole number, which is 1 fish. So, there are 2 ducks + 1 fish = <<2+1=3>>3 animals in each pond and pool combined. ### Answer: 3
Expected answer: 14/5
Correct? No
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. What is the total distance between Town A and Town C on the map?
Mixtral 8x7B:
Reasoning: To find the total distance between Town A and Town C, we first need to find the distance between Town A and Town B plus the distance between Town B and Town C. The distance between Town A and Town B is 15/1
Expected answer: 401/165
Correct? No
Problem: A soap company produces 13/18 tons of Soap A and 4/6 tons of Soap B in a day. How many tons of soap do they produce in total each day?
Mixtral 8x7B:
Reasoning: The soap company produces 13/1
Expected answer: 25/18
Correct? No
Problem: Mark bought a sleeping bag that was 19/2 feet long. However, he decides to cut off 13/12 feet from it to fit his height. How long is his sleeping bag now?
Mixtral 8x7B:
Reasoning: Mark cut off 13/12 feet from the sleeping bag, so the sleeping bag is now 19/2 - 13/12 = (9 - 13/4) = 31/4 = <<(9-13/4)=31/4=7.75>>7.75 feet long. ### Answer: 7.75 feet
Expected answer: 101/12
Correct? No
Problem: At the zoo, Mary feeds 6/20 pounds of food to the monkeys, and 18/15 pounds of food to the giraffes. How many pounds of food in total has she given to the monkeys and giraffes?
Mixtral 8x7B:
Reasoning: First, we need to simplify the fraction 18/15 to its simplest form, which is 6/5. Then, Mary fed 6/20+6/5 = (6/20)*(5/5)+(6/5)*(4/4) = 30/100+24/100 = 54/100 = 0.54 pounds of food to the monkeys and 6/5 pounds of food to the giraffes. Therefore, Mary has given a total of 0.54+6/5 = 0.54+(6/5)*(2/2) = 0.54+1.2 = 1.74 pounds of food to the monkeys and giraffes. ### Answer: 1.74 pounds
Expected answer: 3/2
Correct? No
Problem: Albert has a deck of 20/17 full sets of cards to start. He then collects another full set of 4/1 cards. How many full sets of cards does he have now?
Mixtral 8x7B:
Reasoning: First, we need to find out how many full sets Albert had initially. He had 20/17 sets, but since 1 set has 17 cards, Albert had 20 cards. Then, Albert collected another full set of 4 cards, so now he has 20+4 = <<20+4=24>>24 cards. Since Albert has 24 cards and 1 set has 17 cards, Albert now has 24/17 = <<24/17=1+7/17=1.411764705882353>>1 full set and 17/17 = <<17/17=1>>1 extra card. ### Answer: Albert has 1 full set of cards.
Expected answer: 88/17
Correct? No
Problem: A jeweler has 5/14 pound of silver and adds 18/19 pounds more to the supply. How many pounds of silver does the jeweler have now to make rings?
Mixtral 8x7B:
Reasoning: To find the total amount of silver the jeweler has now, we need to add the initial amount to the amount that was added. The jeweler has 5/14 + 18/19 = (135 + 204) / (14*19) = 339 / 266 = 1 13/266 pounds of silver now. ### Answer: 1 13/266 pounds of silver
Expected answer: 347/266
Correct? No
Problem: A turtle starts at a point and moves 11 meters northward. Then, it moves 15/15 of a meter back towards the starting point. How many meters is the turtle from its starting point after these two movement?
Mixtral 8x7B:
Reasoning: The turtle moves 15/15 = <<15/1
Expected answer: 10
Correct? No
Problem: Chloe has a chocolate bar that is 19/2 ounces. If she eats a piece that is 17/2 ounces, how many ounces of chocolate does she have left?
Mixtral 8x7B:
Reasoning: Chloe has 19/2 - 17/2 = <<19/2-17/2=1>>1 ounce of chocolate left. ### Answer: 1 ounce
Expected answer: 1
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?
Mixtral 8x7B:
Reasoning: Chloe has 1 + 4/14 = <<1+4/14=14/14=1>>1 ounce of chocolate from the first bar, and then she adds 4/14 ounces from the second bar. Chloe has 1 + 4/14 = 14/14 + 4/14 = 18/14 = 9/7 ounces of chocolate in total. ### Answer: 9/7 ounces (Note: The answer is expressed as a fraction, which is the most accurate way to represent the quantity. If you want to convert it to a decimal, you can divide 9 by 7 to get 1.28571428571, but note that this is an approximation.)
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?
Mixtral 8x7B:
Reasoning: If Chloe ate a piece that was 9/2 ounces, she would have 19/2 - 9/2 = <<19/2-9/2=5/2>>5/2 ounces of chocolate left. ### Answer: 5/2 ounces or 2.5 ounces (I have converted the fraction to a decimal for a better understanding)
Expected answer: 5
Correct? Yes
Problem: Sammy has a backpack with a capacity of 20/9 liters. If he adds another pouch to the backpack that can hold 8/4 more liters, what will be the total capacity of his backpack?
Mixtral 8x7B:
Reasoning: The pouch can hold 8/4 = <<8/4=2>>2 liters. The total capacity of the backpack will be 20/9 + 2 = <<20/9+2=2.4444444444444445>>2.44 liters. ### Answer: 2.44 liters
Expected answer: 38/9
Correct? No
Problem: Captain Hook has 11/8 ounces of gold. He finds an additional 5/5 ounces of gold on his latest treasure hunt. What is the total weight of the gold Captain Hook now has?
Mixtral 8x7B:
Reasoning: The amount of gold Captain Hook found on his latest treasure hunt is 5/5 = <<5/5=1>>1 ounce. The total weight of the gold Captain Hook now has is 11/8 + 1 = <<11/8+1=1.375>>1.375 ounces. ### Answer: 1.375 ounces
Expected answer: 19/8
Correct? No
Problem: If Jake originally had 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?
Mixtral 8x7B:
Reasoning: First, we need to simplify 20/15 to get 4/3. Then, Jake has 9/10 + 4/3 = (27+40)/30 = 67/30 = <<67/30=2.23333333333>>2.2333... dollars. However, money cannot be a decimal number. We need to convert 67/30 to a mixed number, which is 2 7/30. ### Answer: Jake has $2 7/30 in his wallet now.
Expected answer: 67/30
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?
Mixtral 8x7B:
Reasoning: First, we need to convert 11/5 to a mixed number, which is 2 1/5. Then, Jake has 2 7/30 + 2 1/5 = (2*30+7+2*5+1)/30 = 67/30 + 12/30 = 79/30 = <<79/30=2.63333333333>>2.6333... dollars. Again, we need to convert 79/30 to a mixed number, which is 2 17/30. ### Answer: Jake has $2 17/30 in his wallet now.
Expected answer: 133/30
Correct? No
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?
Mixtral 8x7B:
Reasoning: First, we need to simplify 20/15 to get 4/3. Then, Jake has 9/8 + 4/3 = (27+32)/24 = 59/24 = <<59/24=2.45833333333>>2.4583... dollars. However, money cannot be a decimal number. We need to convert 59/24 to a mixed number, which is 2 5/24. ### Answer: Jake has $2 5/24 in his wallet now.
Expected answer: 59/24
Correct? No
Problem: Paul has built the front half of a chair that measures 5/2 feet high. He also constructs the back portion of the chair that measures 20/14 feet. What is the combined height of the front and back portions of the chair that Paul has constructed?
Mixtral 8x7B:
Reasoning: The front portion of the chair is 5/2 feet high. The back portion of the chair is 20/14 feet high, which simplifies to 5/7 feet (since 20 and 14 are both evenly divisible by 2). The combined height of the front and back portions of the chair is 5/2 + 5/7 = (21+10)/14 = 31/14 feet. ### Answer: 31/14 feet
Expected answer: 55/14
Correct? No
Problem: John has 5 shirts and he donated 12/9 of them to charity. How many shirts does he have left?
Mixtral 8x7B:
Reasoning: John donated 12/9 x 5 = <<12/9*5=20/3=6.66666666667>>6.67 (approximately) shirts to charity. John has 5 - 6.67 = <<5-6.67=-1.67 (approximately)>>-1.67 (approximately) shirts left, which is not possible since the number of shirts must be a whole number. This problem is not possible due to the fraction of shirts being donated being greater than the total number of shirts. ### Answer: This problem is not possible.
Expected answer: 11/3
Correct? No
Problem: Bob has a jacket that measures 14/3 meters in length. However, he finds the jacket is slightly too long for him so he decides to cut off 14/16 meter from the original length. What is the length of Bob's jacket after the alteration?
Mixtral 8x7B:
Reasoning: The amount of length that Bob cuts off is 14/16 meters, which is equivalent to 14/1
Expected answer: 91/24
Correct? No
Problem: Officer Max spends 2/6 part of an hour completing paperwork. Then, he 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?
Mixtral 8x7B:
Reasoning: The part of an hour that Officer Max spends on paperwork is 2/6 = 0.3333333333333 hours. The part of an hour that Officer Max spends on patrolling the neighborhood is 14/7 = 2 hours. So, Officer Max uses 0.3333333333333 + 2 = 2.333333333333 parts of an hour for these two tasks. ### Answer: 2.333333333333 (rounded to 11 decimal places)
Expected answer: 7/3
Correct? No
Problem: John watched a movie for 10/12 of an hour and then watched a TV show for another 3/8 of an hour. What is the total time he spent watching in hours?
Mixtral 8x7B:
Reasoning: First, we need to find a common denominator for the fractions 10/12 and 3/8. The least common multiple of 12 and 8 is 24. Then, convert 10/1
Expected answer: 29/24
Correct? No
Problem: Mr. Carpenter makes crafting chairs a meticulous process. He takes 5/3 hours to build the frame and additional 10/13 hours to upholster it. How long does it take for him to build a chair from start to finish?
Mixtral 8x7B:
Reasoning: It takes Mr. Carpenter 5/3 + 10/1
Expected answer: 95/39
Correct? No
Problem: Anna has a bracelet that consists of small and large beads. The small beads are each 8/4 mm in diameter and the large beads are each 15/2 mm in diameter. If she adds a small and a large bead to her bracelet, what would be the total added diameter in mm?
Mixtral 8x7B:
Reasoning: The diameter of a small bead is 8/4 mm = <<8/4=2>>2 mm. The diameter of a large bead is 15/2 mm = <<15/2=7.5>>7.5 mm. The total added diameter is 2 mm (small bead) + 7.5 mm (large bead) = <<2+7.5=9.5>>9.5 mm. ### Answer: 9.5 mm
Expected answer: 19/2
Correct? No
Problem: A rocket travels 11/18 light-years to an alien planet, then travels another 8/2 light-years towards a distant star. What is the total distance covered by the rocket?
Mixtral 8x7B:
Reasoning: The rocket traveled 8/2 = <<8/2=4>>4 light-years towards the distant star. The total distance covered by the rocket is 11/18 + 4 = <<11/18+4=23.33333333333>>23.33 light-years. ### Answer: 23.33 light-years
Expected answer: 83/18
Correct? No
Problem: Johnathan needs 12/14 yards of one fabric to make a sleeping bag, and another 8/5 yards of a different fabric to create the liner. How many yards of fabric does he need in total to create his sleeping bag?
Mixtral 8x7B:
Reasoning: First, we need to find a common denominator for the fractions 12/14 and 8/5. The least common multiple of 14 and 5 is 70, so we convert both fractions to have this denominator: 12/14 = (12*5)/(14*5) = 60/70 8/5 = (8*14)/(5*14) = 112/70 Now, we can add the two fractions: 60/70 + 112/70 = (60+112)/70 = 172/70 Finally, we simplify the fraction to get: 172/70 = 172/7 = 24.57 (rounded to two decimal places) Since Johnathan can't buy a fraction of a yard, we need to round up to the nearest whole number. ### Answer: 25 yards of fabric does Johnathan need in total to create his sleeping bag.
Expected answer: 86/35
Correct? No
Problem: In a forest, there are 5/4 acres of pine trees and 1/2 acre of oak trees. What is the total acreage of pine and oak trees in the forest?
Mixtral 8x7B:
Reasoning: To find the total acreage of pine and oak trees, we need to add the acreage of pine trees and oak trees. The acreage of pine trees is 5/4 = <<5/4=1.25>>1.25 acres. The acreage of oak trees is 1/2 = <<1/2=0.5>>0.5 acres. So, the total acreage of pine and oak trees is 1.25 + 0.5 = <<1.25+0.5=1.75>>1.75 acres. ### Answer: 1.75 acres
Expected answer: 7/4
Correct? No
Problem: Jake has 12/7 of a yard of fabric. He finds another piece that measures 2/14 of a yard. If he combines both pieces, how much fabric does he have to make his shirt?
Mixtral 8x7B:
Reasoning: First, we need to simplify 2/14 to 1/7. Then, Jake has 12/7 + 1/7 = (12+1)/7 = 13/7 = <<12/7+1/7=13/7=1.85714285714>>1.857 yards of fabric. ### Answer: 1.857 yards of fabric
Expected answer: 13/7
Correct? No
Problem: At a park, a special tree produces on average 10/4 kilograms of fruit every summer. In the winter, it loses some of its fruit, amounting to 12/20 kg. What is the difference in kilograms of the fruit from summer to winter?
Mixtral 8x7B:
Reasoning: The tree produces 10/4 = <<10/4=2.5>>2.5 kg of fruit every summer. The tree loses 12/20 = <<12/20=0.6>>0.6 kg of fruit every winter. The difference in kilograms of the fruit from summer to winter is 2.5 - 0.6 = <<2.5-0.6=1.9>>1.9 kg. ### Answer: 1.9 kg
Expected answer: 19/10
Correct? No
Problem: A ballerina starts with a routine that lasts 13/5 minutes but decides to shorten it by 15/16 minutes. How long is her routine after shortening it?
Mixtral 8x7B:
Reasoning: The ballerina shortens her routine by 15/16 minutes. So, the length of her routine after shortening it is 13/5 - 15/1
Expected answer: 133/80
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?
Mixtral 8x7B:
Reasoning: The ballerina shortens her routine by 15/16 minutes and then adds a new dance move that lasts 2/20 minutes. First, we need to convert 2/20 to have the same denominator as 13/5 - 15/16. 2/20 = 1/10 Then, we subtract 15/16 from 13/5. 13/5 - 15/16 = (32/160) - (90/160) = -58/160 Now, we add the length of the new dance move to the result. -58/160 + 1/10 = (-58+16)/160 = -42/160 We can simplify this fraction by dividing both the numerator and the denominator by 2. -42/160 = -21/80 ### Answer: The ballerina's routine is now -21/80 minutes long. Note: The answer is negative because the ballerina subtracted more time than the length of her original routine. This could mean that the new dance move cannot fit into the remaining time.
Expected answer: 141/80
Correct? No
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?
Mixtral 8x7B:
Reasoning: The ballerina shortens her routine by 12/16 minutes instead of 15/16 minutes. So, the length of her routine after shortening it is 13/5 - 12/16 = 13/5 - 9/16 = (32-9)/40 = 23/40. ### Answer: 23/40 minutes.
Expected answer: 37/20
Correct? No
Problem: Miss Daisy has 19/6 kg of fertilizers for her flowers. If she uses 17/20 kg on her roses, how much fertilizers does she have left to use on her other flowers?
Mixtral 8x7B:
Reasoning: Miss Daisy used 17/20 kg of fertilizers on her roses. To find out how much fertilizers she has left, we need to subtract 17/20 from 19/6. To do this, we need a common denominator, which is 60 in this case. So, 19/6 = 31.67/60 and 17/20 = 51/60. Therefore, 31.67/60 - 51/60 = 31.67 - 51 / 60 = -19.33/60 = -0.322/10 = -0.0322 kg. However, the amount of fertilizers left cannot be negative. This means that Miss Daisy used more fertilizers than she had. ### Answer: Miss Daisy used more fertilizers than she had.
Expected answer: 139/60
Correct? No
Problem: Scientists have discovered that the moon is slowly moving away from Earth. If the distance increases by 4/16 meters every year, and unexpectedly there was an additional increase of 20/6 meters this year, what is the total change in distance this year?
Mixtral 8x7B:
Reasoning: The distance between the Earth and the moon increased by 4/16 meters every year, so this year it increased by 4/1
Expected answer: 43/12
Correct? No
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?
Mixtral 8x7B:
Reasoning: To find the total amount of money in Bob's wallet, we need to add the amounts in both pockets. First, convert 11/3 and 12/19 to a common denominator. The least common multiple of 3 and 19 is 57. 11/3 = (11*19)/57 = 209/57 12/19 = (12*3)/57 = 36/57 Now, add the amounts: 209/57 + 36/57 = 245/57 ### Answer: 245/57 dollars or approximately 4.3 dollars
Expected answer: 245/57
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?
Mixtral 8x7B:
Reasoning: To find the total amount of money in Bob's wallet, we need to add the amounts in both pockets. First, convert 11/3 and 12/19 to a common denominator. The least common multiple of 3 and 19 is 57. 11/3 = (11*19)/57 = 209/57 12/19 = (12*3)/57 = 36/57 Now, add the amounts: 209/57 + 36/57 = 245/57 To find out how much money Bob will have if he duplicates the total amount, we need to multiply the total amount by 2. 245/57 \* 2 = 490/57 ### Answer: Bob has 245/57 dollars in his wallet, and if he duplicates the total amount, he will have 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?
Mixtral 8x7B:
Reasoning: To find the total amount of money in Bob's wallet, we need to add the amounts in both pockets. Bob has 1 dollar in the first pocket and 12/19 dollars in the second pocket. Add the amounts: 1 + 12/19 = (1*19)/19 + 12/19 = 31/19 ### Answer: 31/19 dollars or approximately 1.63 dollars
Expected answer: 31/19
Correct? Yes
Problem: In an ocean, a shark swims a distance of 5/5 miles in the morning and adds an additional 12/18 miles in the afternoon. How many miles in total did the shark swim that day?
Mixtral 8x7B:
Reasoning: The shark swam 5/5 = <<5/5=1>>1 mile in the morning and 12/18 = <<12/18=2/3>>2/3 miles in the afternoon. The shark swam 1 + 2/3 = <<1+2/3=5/3>>5/3 miles in total that day. ### Answer: 5/3 miles
Expected answer: 5/3
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?
Mixtral 8x7B:
Reasoning: The shark swam 5/5 = <<5/5=1>>1 mile in the morning, 12/18 = <<12/1
Expected answer: 11/3
Correct? No
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?
Mixtral 8x7B:
Reasoning: If the shark swam 5/12 miles in the morning and 12/18 = 2/3 miles in the afternoon, then the shark swam 5/12 + 2/3 = 5/12 + 4/12 = 9/12 = 3/4 miles in total that day. ### Answer: 3/4 mile (Note: The fraction 3/4 can be simplified further, but I left it as is since you asked for the total distance the shark swam that day.)
Expected answer: 13/12
Correct? No
Problem: Jim types 20 words in 16 seconds and Mary types 9 words in 4 seconds. How many words per second do Jim and Mary type in total?
Mixtral 8x7B:
Reasoning: Jim types 20/16 = <<20/16=1.25>>1.25 words per second. Mary types 9/4 = <<9/4=2.25>>2.25 words per second. Together, Jim and Mary type 1.25 + 2.25 = <<1.25+2.25=3.5>>3.5 words per second. ### Answer: 3.5
Expected answer: 7/2
Correct? Yes
Problem: After typing together, Jim and Mary decide to slow down their pace and reduce their combined typing speed by 2 words every 11 seconds. What becomes their new combined typing speed?
Mixtral 8x7B:
Reasoning: Jim and Mary's combined typing speed is currently 3.5 words per second. Every 11 seconds, they reduce their combined typing speed by 2 words per second. After 11 seconds, their combined typing speed will be 3.5 - 2 = <<3.5-2=1.5>>1.5 words per second. ### Answer: 1.5 words per second.
Expected answer: 73/22
Correct? No
Problem: Max rode his scooter for 9/7 miles in the morning and then 1/9 miles less in the afternoon. How many miles did he ride his scooter in the afternoon?
Mixtral 8x7B:
Reasoning: Max rode 1/9 miles less in the afternoon than he did in the morning, so he rode (9/7 - 1/9) miles in the afternoon. To subtract the fractions, we need to get a common denominator, which is 63. (9/7 - 1/9) = (81/63 - 7/63) = 74/63 miles. However, this fraction is not in simplest form, so we simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 2: 74/63 = 37/31.5 miles. Since it is not possible to ride a fraction of a mile on a scooter, there is an error in the problem as given. ### Answer: The problem contains an error, as it is not possible to ride 37/31.5 miles.
Expected answer: 74/63
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?
Mixtral 8x7B:
Reasoning: Max rode 1/4 miles less in the afternoon than he did in the morning, so he rode (9/7 - 1/4) miles in the afternoon. To subtract the fractions, we need to get a common denominator, which is 28. (9/7 - 1/4) = (36/28 - 7/28) = 29/28 miles. Since it is not possible to ride a fraction of a mile on a scooter, we can assume that Max rounded up to the nearest whole mile. ### Answer: Max rode 29 miles in the afternoon on this different day.
Expected answer: 29/28
Correct? No
Problem: At a circus, a clown rode a unicycle for 9/8 hours. After a short break, she juggled for another 2/10 hours. How many hours in total did she perform?
Mixtral 8x7B:
Reasoning: The clown performed for 9/8 + 2/10 hours. To add the fractions, we need to find a common denominator, which is 40 in this case. 9/8 becomes 45/40 and 2/10 becomes 8/40. So, 45/40 + 8/40 = 53/40. The clown performed for 53/40 hours, which is equivalent to 1 hour and 13/40 hours. ### Answer: 1 13/40 hours
Expected answer: 53/40
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?
Mixtral 8x7B:
Reasoning: The clown took a break for 13/5 hours. She performed for 53/40 hours. To find the time remaining after her performance, we need to subtract the performance time from the break time: 13/5 - 53/40. To subtract the fractions, we need to find a common denominator, which is 200 in this case. 13/5 becomes 260/200 and 53/40 becomes 132.5/200. So, 260/200 - 132.5/200 = 127.5/200. The time remaining is 127.5/200 hours, which is equivalent to 0 hours and 127.5/200 hours. ### Answer: 0 127.5/200 hours (Note: This answer is in hours and decimal hours.)
Expected answer: 51/40
Correct? No
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?
Mixtral 8x7B:
Reasoning: The clown performed for 9/8 hours on the unicycle and 9/10 hours juggling. To add the fractions, we need to find a common denominator, which is 40 in this case. 9/8 becomes 45/40 and 9/10 becomes 36/40. So, 45/40 + 36/40 = 81/40. The clown performed for 81/40 hours, which is equivalent to 2 hours and 1/40 hours. ### Answer: 2 1/40 hours (Note: The answer is different from the previous problem because the number of hours the clown juggled has changed.)
Expected answer: 81/40
Correct? Yes
Problem: If Timmy dumps 7/2 kg of sand into his sandbox and later adds another 1/2 kg, how much sand is now in his sandbox?
Mixtral 8x7B:
Reasoning: Timmy added 7/2 + 1/2 = (7+1)/2 = <<(7+1)/2=8/2=4>>4 kg of sand in total. ### Answer: 4 kg
Expected answer: 4
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?
Mixtral 8x7B:
Reasoning: Timmy added 16/3 = <<16/3=5.33333333333>>5.333... kg of sand. To find the total amount of sand, we add the sand added in each step: 4 + 5.333... = <<4+5.33333333333=9.33333333333>>9.333... kg ### Answer: 9.333... kg (When expressing this as a decimal, it is approximately 9.33 kg, but the exact answer is 9.333... kg.)
Expected answer: 28/3
Correct? No
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?
Mixtral 8x7B:
Reasoning: Timmy added 7/2 + 1/20 = (70+2)/20 = <<(70+2)/20=72/20=3.6>>3.6 kg of sand in total. ### Answer: 3.6 kg (Note: I assumed that the original 7/2 kg of sand remained in the sandbox and Timmy added 1/20 kg to it. If the original sand was removed before adding 1/20 kg, then the total amount of sand in the sandbox would be just 1/20 = 0.05 kg.)
Expected answer: 71/20
Correct? No
Problem: A wizard brewed a potion that required 18/8 ounces of moon roots and 11/7 ounces of stardust. How many ounces of ingredients did the wizard use in total to prepare the potion?
Mixtral 8x7B:
Reasoning: The wizard used 18/8 ounces of moon roots and 11/7 ounces of stardust. To find the total amount of ingredients used, we need to add these two amounts together. First, convert 18/8 and 1
Expected answer: 107/28
Correct? No
Problem: An alien UFO traveled 3/10 of a mile, then immediately traveled an additional 16/20 of a mile. How many miles did the UFO travel in total?
Mixtral 8x7B:
Reasoning: The UFO traveled 3/10 + 16/20 = 3/10 + 8/10 = 11/10 = 1.1 miles in total. ### Answer: 1.1 miles
Expected answer: 11/10
Correct? No
Problem: A chair manufacturing firm makes 4/14 of a chair every hour with one machine, and another machine makes 20/4 chairs. How many chairs are made by both machines in one hour?
Mixtral 8x7B:
Reasoning: The first machine makes 4/14 = 1/3.5 chairs per hour. The second machine makes 20/4 = 5 chairs per hour. Together, both machines make 1/3.5 + 5 = (1+17.5)/3.5 = 18.5/3.5 = 5.3 chairs per hour. However, a fraction of a chair cannot be made, so the actual number of chairs made by both machines in one hour is 5 chairs. ### Answer: 5 chairs
Expected answer: 37/7
Correct? No
Problem: A blue shark swam for 2/4 miles and a hammerhead shark swam for 7/10 miles. How many miles did they swim together?
Mixtral 8x7B:
Reasoning: The blue shark swam 2/4 = <<2/4=0.5>>0.5 miles. The hammerhead shark swam 7/10 = <<7/10=0.7>>0.7 miles. Together, they swam 0.5 + 0.7 = <<0.5+0.7=1.2>>1.2 miles. ### Answer: 1.2 miles
Expected answer: 6/5
Correct? No
Problem: Lisa has two milk bottles. One bottle has 8/18 gallons of milk while the other bottle has 18/8 gallons. How much milk does Lisa have in total?
Mixtral 8x7B:
Reasoning: To find the total amount of milk Lisa has, we need to add the amount of milk in each bottle. However, the fractions are not in the same denominator. We need to convert them to a common denominator, which is the least common multiple (LCM) of 18 and 8, which is 72. The fraction 8/18 is equal to 72/144, and the fraction 18/8 is equal to 135/8. So, Lisa has 72/144 + 135/8 = 219/24 = <<219/24=9.125>>9.125 gallons of milk. ### Answer: 9.125 gallons of milk.
Expected answer: 97/36
Correct? No
Problem: A tree grows 1/10 of its height every month. This month, it additionally has grown 12/6 feet due to a fertilizer being applied. How much has the tree grown in height this month?
Mixtral 8x7B:
Reasoning: The tree grows 1/10 of its height every month, so it grows (1/10) \* height this month. Additionally, the tree has grown 12/6 = <<12/6=2>>2 feet due to the fertilizer. The total height the tree has grown this month is therefore (1/10) \* height + 2. Since we don't know the height of the tree, we can't determine a specific numerical value for the growth. However, we can express the growth as a sum of (1/10) \* height and 2. ### Answer: The tree has grown (1/10) \* height + 2 feet this month.
Expected answer: 21/10
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. What is the total area occupied by both tents?
Mixtral 8x7B:
Reasoning: The area occupied by the smaller tent is 8/20 = <<8/20=2/5>>2/5 acres. The total area occupied by both tents is 13/11 + 2/5 = (65+22)/55 = 87/55 ≈ <<87/55=1.5818181818181819>>1.58 acres. ### Answer: 1.58 (rounded to two decimal places)
Expected answer: 87/55
Correct? No
Problem: Captain Jack has a treasure map that shows the treasure is at a location that is (17 / 20) km to the East and then (15 / 3) km to the North from their starting point. How far must they travel in total to reach the treasure?
Mixtral 8x7B:
Reasoning: First, we need to find out how far Captain Jack must travel to the East. The distance to the East is (17 / 20) km. Next, we need to find out how far Captain Jack must travel to the North. The distance to the North is (15 / 3) km or 5 km. To find the total distance, we add the two distances: (17 / 20) + 5 = (17 / 20) + (100 / 20) = (117 / 20) = 5.85 km. ### Answer: 5.85 km
Expected answer: 117/20
Correct? No
Problem: At a campfire, Sarah collected 11/20 of a pound of firewood and Alex collected 9/7 pounds. How many pounds of firewood did they collect in total?
Mixtral 8x7B:
Reasoning: To find the total amount of firewood collected, we need to add the amount collected by Sarah and Alex. First, we need to make sure both quantities have the same unit of measurement. So, we'll convert 11/20 pounds to the same unit as 9/7 pounds, which is pounds. 11/20 pounds is already in pounds, so we don't need to convert it. Now, we can add the amounts: 9/7 + 11/20 To add these fractions, we need to find a common denominator, which is the least common multiple (LCM) of 7 and 20. The LCM of 7 and 20 is 140. Now, convert each fraction to have this common denominator: 9/7 * 20/20 = 180/140 11/20 * 7/7 = 77/140 Now, add the fractions: 180/140 + 77/140 = (180 + 77)/140 = 257/140 Since the resulting fraction is greater than 1, we can convert it back to a mixed number: 257/140 = 1 117/140 However, if we want to express the answer as a whole number and a fraction, we can simplify the fractional part: 117/140 simplifies to 39/40 So, the final answer is: ### Answer: 1 39/40 pounds
Expected answer: 257/140
Correct? No
Problem: Captain Bill sailed 19/5 miles north, before changing track and sailing an additional 12/15 miles north. How many miles north did Captain Bill sail in total?
Mixtral 8x7B:
Reasoning: Captain Bill sailed 12/15*5/1 = <<12/15*5/1=4/1=4>>4 nautical miles more after his first track. Captain Bill sailed 19/5 + 4 = <<19/5+4=23/5=4.6>>4.6 miles north in total. ### Answer: 4.6 (Note: The answer is given as a decimal approximation since the exact answer is a mixed number.)
Expected answer: 23/5
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?
Mixtral 8x7B:
Reasoning: Captain Bill sailed 20/17 miles south after backtracking. Captain Bill's total distance from the original starting point is the absolute difference between the distance he traveled north and the distance he backtracked. The absolute difference is |19/5 - 20/17| = |(19*17 - 20*5)/(5*17)| = |323 - 100)/85| = |223/85| = 2.623529411764706 miles. ### Answer: 2.62 miles (rounded to two decimal places)
Expected answer: 291/85
Correct? No
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?
Mixtral 8x7B:
Reasoning: Captain Bill sailed 12/15*18/2 = <<12/15*18/2=24/5=4.8>>4.8 nautical miles more after his first track. Captain Bill sailed 19/18 + 4.8 = <<19/18+4.8=23.8/18=1.3222222222222223>>1.322 miles north in total. ### Answer: 1.322 (rounded to five decimal places) (Note: The answer is given as a decimal approximation since the exact answer is a mixed number.)
Expected answer: 167/90
Correct? No
Problem: A restaurant uses 19/17 pounds of ham and 9/4 pounds of turkey for their signature sandwich. What is the total weight of the two types of meat per sandwich?
Mixtral 8x7B:
Reasoning: To find the total weight of the two types of meat per sandwich, we need to add the weight of ham and turkey. The weight of ham is 19/1
Expected answer: 229/68
Correct? No
Problem: Lucy has a sleeping bag that is 18/19 meter long. She got an extension for her sleeping bag which made it 8/11 meter longer. What's the total length of the sleeping bag now?
Mixtral 8x7B:
Reasoning: The extension to the sleeping bag is 18/19 + (18/1
Expected answer: 350/209
Correct? No
Problem: Sarah pours 10/13 gallon of water into a container. Then she adds another 8/2 gallons of water into it. How many total gallons of water are there in the container now?
Mixtral 8x7B:
Reasoning: Sarah added 8/2 = <<8/2=4>>4 gallons of water in the second pour. The total amount of water in the container is 10/13 + 4 = <<10/13+4=34/13>>34/13 gallons. However, since the answer is not in a whole number, we need to convert the fraction to a mixed number. 34/13 = 2 10/13 gallons. ### Answer: 2 10/13 gallons
Expected answer: 62/13
Correct? No
Problem: Mandy has 9/2 KGs of apples. She uses 1/4 KG of them to make apple pie. How many KGs of apples does she have left?
Mixtral 8x7B:
Reasoning: Mandy used 9/2 x 1/4 = <<(9/2)*(1/4)=(9/8)=1.125>>1.125 KGs of apples to make apple pie. Mandy has 9/2 - 1.125 = <<9/2-1.125=2.25-1.125=1.125>>1.125 KGs of apples left. ### Answer: 1.125 KGs
Expected answer: 17/4
Correct? No
Problem: John spends 12/7 hours fixing a watch and then spends an additional 3/9 hours polishing it. How many hours in total did he spent working on the watch?
Mixtral 8x7B:
Reasoning: First, we need to convert 3/9 to have the same denominator as 12/7. The least common multiple of 7 and 9 is 63, so: 3/9 = (3*7)/(9*7) = 21/63 Now, we can add the time John spent fixing and polishing the watch: 12/7 + 21/63 = (12*63)/(7*63) + (21*7)/(63*7) = 756/441 + 147/441 = 903/441 This fraction simplifies to: 903/441 = 3 15/441 Since John spent 3 full hours and a portion of an hour, we can say that he spent more than 3 hours working on the watch. ### Answer: John spent 3 15/441 hours working on the watch.
Expected answer: 43/21
Correct? No
Problem: Peggy the Penguin was swimming and had traveled for 5/4 miles when she turned around to go back to her family. She swam back for 1/12 miles before deciding to rest. How many miles is Peggy from her family?
Mixtral 8x7B:
Reasoning: Peggy swam a total of 5/4 - 1/12 = (15-1)/12 = 14/12 = 7/6 miles before resting. Peggy is now 7/6 * 2 = 7/3 miles away from her family, since she has to swim back that distance to reach them. ### Answer: 7/3 miles
Expected answer: 7/6
Correct? No
Problem: A farmer has a fields where he grows wheat. One part of the field is 4 acres and another part is 11/12 of an acre. How many acres in total does he use to grow wheat?
Mixtral 8x7B:
Reasoning: The farmer uses 11/1
Expected answer: 59/12
Correct? No
Problem: If a dress designer used 11/4 yards of red fabric, and then added 5/17 yards of blue fabric, how many yards of fabric did she use in total?
Mixtral 8x7B:
Reasoning: The designer used 11/4 + 5/17 = (136 + 20) / 68 = 156 / 68 = <<(136+20)/68=2.2941176470588235>>2.294 yards of fabric in total. ### Answer: 2.294 yards of fabric
Expected answer: 207/68
Correct? No
Problem: Jacob has 11/2 feet long guitar wire. If he uses 5/16 feet of it to fix a guitar, how much wire is remaining?
Mixtral 8x7B:
Reasoning: Jacob used 5/16 feet of wire, so he has 11/2 - 5/16 = (16*11 - 5*2)/(16*2) = 176/32-10/32 = 166/32 = 55/10 + 1/32 = 5.5 + 0.03125 = 5.53125 feet of wire remaining. ### Answer: 5.53125 feet of wire is remaining.
Expected answer: 83/16
Correct? No
Problem: Samantha has a 4 fluid ounce tube of toothpaste. In one week, she uses 17/14 fluid ounces. How much toothpaste does she have left after that week?
Mixtral 8x7B:
Reasoning: Samantha used 17/14 = <<17/14=1.21428571429>>1.21 (rounded to two decimal places) fluid ounces in a week. Samantha has 4 - 1.21 = <<4-1.21=2.79>>2.79 fluid ounces left after that week. ### Answer: 2.79 fluid ounces
Expected answer: 39/14
Correct? No
Problem: Maria has 12 candies. She gives each of her 6 friends an equal amount of candies. Maria also has 20 stickers and she gives each of her 20 friends a sticker. How many candies and stickers does each friend get in total?
Mixtral 8x7B:
Reasoning: Maria gives 12/6 = <<12/6=2>>2 candies to each of her 6 friends. So, each friend gets 2 candies. Maria gives 1 sticker to each of her 20 friends. So, each friend gets 1 sticker. In total, each friend gets 2 candies + 1 sticker = <<2+1=3>>3 items. ### Answer: 3 (Three items: 2 candies and 1 sticker.)
Expected answer: 3
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?
Mixtral 8x7B:
Reasoning: Maria gives 12 candies to her 6 friends, so each friend gets 12/6 = <<12/6=2>>2 candies. Maria gives 20 stickers to her 13 friends, so each friend gets 20/13 = <<20/13=1.53846153846>>1.54 stickers (rounded to two decimal places). In total, each friend gets 2 candies + 1.54 stickers = <<2+1.54=3.54>>3.54 items (rounded to two decimal places). ### Answer: 3.54 (Three and a half items: 2 candies and about 1.54 stickers.)
Expected answer: 46/13
Correct? No
Problem: During a rainy day, the first rainfall lasted for 4/13 hours, and the next rainfall was a little longer and lasted for 11/5 hours. How many hours did it rain in total?
Mixtral 8x7B:
Reasoning: The total time it rained is equal to the sum of the duration of the first and second rainfalls. The first rainfall lasted for 4/1
Expected answer: 163/65
Correct? No
Problem: Jane cuts 10/12 yards of fabric from a blanket. Then, she cuts an additional 10/10 yard. How many yards of fabric has she cut from the blanket in total?
Mixtral 8x7B:
Reasoning: Jane cut 10/10 = <<10/10=1>>1 yard in the second cut. Jane cut 10/12 + 1 = <<10/12+1=19/12=1+3/4=1.25>>1.25 yards in total. ### Answer: 1.25 yards
Expected answer: 11/6
Correct? No
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. What is the total amount of magic dust the fairy used?
Mixtral 8x7B:
Reasoning: The fairy sprinkled 11/12 + 9/10 = (11/12)*(10/10) + (9/10)*(12/12) = 110/120 + 108/120 = 218/120 = 1.8167 (rounded to four decimal places) ounces of magic dust in total. ### Answer: 1.8167 oz
Expected answer: 109/60
Correct? No
Problem: A word game assigns 3/11 of a point for each vowel used and 8/10 of a point for each consonant. If you use 1 vowel and 1 consonant, what will your score be?
Mixtral 8x7B:
Reasoning: The word game assigns 3/1
Expected answer: 59/55
Correct? No
Problem: You are writing a letter that is 4/1 pages long. You remove 14/9 pages from it. How many pages is the letter now?
Mixtral 8x7B:
Reasoning: The fraction of the letter that was removed is 14/9, but this is greater than 1, which is not possible since you can't remove more than the whole letter. This means that the original letter must have been at least 14/9 pages long. If the original letter was exactly 14/9 pages long, then removing 14/9 pages would leave no pages. But since the original letter was described as 4/1 pages long, it must have been longer than 14/9 pages. If we add one page to the original length of 14/9, we get a length of 23/9 pages. Removing 14/9 pages from this length leaves us with 23/9 - 14/9 = 9/9 = 1 page. So, the letter must have been at least 23/9 pages long, and removing 14/9 pages would leave a letter that is 1 page long. ### Answer: 1 (Note: The original description of the problem contained a contradiction, since it described a 4/1 page letter as being 4/1 pages long, but then said that 14/9 pages were removed. Since 14/9 is greater than 4/1, this would imply that the original letter was longer than 4/1 pages. I assumed that the original letter was meant to be 4 pages long, and made the necessary adjustments to the reasoning and answer.)
Expected answer: 22/9
Correct? No
Problem: Anne painted 16/20 of a table, and then Bob painted an additional 5/20 of the table. How much of the table has been painted in total?
Mixtral 8x7B:
Reasoning: Anne painted 16/20 = <<16/20=0.8>>0.8 of the table. Bob painted 5/20 = <<5/20=0.25>>0.25 of the table. Together, they painted 0.8 + 0.25 = <<0.8+0.25=1.05>>1.05 of the table. Since the table cannot be more than 100% painted, the answer is 100% or 1. ### Answer: 1 (or 100%) of the table has been painted in total.
Expected answer: 21/20
Correct? No
Problem: The star Alpha shines 17/3 times brighter than an average star, while the star Bravo shines 20/16 times as bright. How much brighter are both stars compared to an average star if you add up the relative brightness of these two stars?
Mixtral 8x7B:
Reasoning: The star Alpha shines 17/3 - (17/3 ÷ 2) = (17/3) × (2/2) - (17/3 ÷ 2) = (17/3) - (17/6) = 17/6 = <<(17/3)-((17/3)/2)=(17/3)*(2/2)-(17/3)/2=(17/3)-(17/6)=17/6>>17/6 times brighter than an average star. The star Bravo shines 20/16 = (20 ÷ 8) × (8 ÷ 16) = 2.5 × 0.5 = 1.25 = <<20/1
Expected answer: 83/12
Correct? No
Problem: There are 17/20 kg of red apples and 18/8 kg of green apples in a grocery store. How many kilograms of apples are in the store in total?
Mixtral 8x7B:
Reasoning: First, we need to convert the fractions so that they both have the same denominator. The least common multiple of 20 and 8 is 40, so: 17/20 kg of red apples = 17/20 \* (40/40) = 68/40 = 1.7/
Expected answer: 31/10
Correct? No
Problem: If a bus drives 12/20 of a mile then goes an additional 12/12 of a mile, how many miles did the bus travel in total?
Mixtral 8x7B:
Reasoning: The bus traveled 12/20 + 12/12 = (12/20)*(6/6) + (12/12)*(20/20) = (12*6)/(20*6) + (12*20)/(12*20) = 72/120 + 240/120 = 312/120 = 2.6
Expected answer: 8/5
Correct? No
Problem: In the first hour, a shark swims 3/9 miles and in the second hour height increases its speed to swim 13/5 miles. How many miles does the shark swim in total in these two hours?
Mixtral 8x7B:
Reasoning: To find the total distance the shark swam, we need to add the distance it covered in the first hour to the distance it covered in the second hour. The shark swam 3/9 miles in the first hour and 13/5 miles in the second hour. To add these fractions, we need to find a common denominator, which is 9*5 = 45. So, 3/9 = 15/45 and 13/5 = 117/45. Now, we can add the two fractions: 15/45 + 117/45 = 132/45. Simplifying this fraction, we get 132/45 = 24/5, which is equivalent to 4 4/5. ### Answer: The shark swims a total of 4 4/5 miles in these two hours.
Expected answer: 44/15
Correct? No
Problem: A drummer hits a rhythm where they hit once every 17/17 seconds for the first beat and then 2/12 seconds for the second beat. How long does it take for the drummer to hit the two beats together?
Mixtral 8x7B:
Reasoning: To find out how long it takes for the drummer to hit the two beats together, we need to find the least common multiple (LCM) of 17/17 and 2/12. First, we simplify 17/17 to 1. Next, we convert 2/12 to have the same denominator as 17/1
Expected answer: 7/6
Correct? No
Problem: If a fireplace burns 12/17 cord of wood in the morning and 8/19 cord in the evening, what is the total cord of wood it burns in a day?
Mixtral 8x7B:
Reasoning: First, we need to find a common denominator for the fractions 12/1
Expected answer: 364/323
Correct? No
Problem: A butterfly's flight consisted of two segments. The first segment was 18/19 of a mile and the second was 9/17 of a mile. How long was the entire flight?
Mixtral 8x7B:
Reasoning: To find the total distance of the flight, we need to add the distances of the two segments together. The first segment was 18/19 of a mile, and the second was 9/17 of a mile. So, the total distance was 18/19 + 9/17 = (18*17 + 9*19)/(19*17) = 309/323 miles. ### Answer: The entire flight was 309/323 of a mile.
Expected answer: 477/323
Correct? No
Problem: While measuring a map, Jenna finds that the distance between two cities is 13/10 inches, and the distance from the second city to the third city is 14/15 inches. What is the total distance Jenna measured between the three cities on the map?
Mixtral 8x7B:
Reasoning: To find the total distance between the three cities, we need to add the distance between the first and second city to the distance between the second and third city. The total distance is therefore 13/10 + 14/15 = (13*15 + 14*10)/(10*15) = 199/150 inches. ### Answer: 199/150 inches
Expected answer: 67/30
Correct? No
Problem: A helium balloon rises at a rate of 13/6 feet per second. After a gust of wind, its speed increases by 3/16 feet per second. What is the new speed of the balloon in feet per second?
Mixtral 8x7B:
Reasoning: The balloon's original speed is 13/6 feet per second, and its speed increases by 3/16 feet per second after the gust of wind. Therefore, its new speed is 13/6 + 3/16 = (20 + 3)/16 = 23/16 feet per second. ### Answer: 23/16 feet per second
Expected answer: 113/48
Correct? No
Problem: Scarlett has 16/10 gallons of red paint. If she uses 1/20 of a gallon for a small art project, how many gallons of red paint will she have left?
Mixtral 8x7B:
Reasoning: First, we need to convert 1/20 of a gallon to a fraction with a denominator of 10. 1/20 can be written as 1/20 x 1/2 = 1/40. Scarlett uses 16/1
Expected answer: 31/20
Correct? No
Problem: Susie has a box of 12 chocolate bars. She decides to eat 2/5 of a chocolate bar herself. How many chocolate bars are left in the box?
Mixtral 8x7B:
Reasoning: Susie ate 1/ (2/5) = 1 * 5/2 = 2.5/2 = 1.25 chocolate bars herself. Since she can't eat a fraction of a chocolate bar, she ate 2 whole chocolate bars and left 12 - 2 = <<12-2=10>>10 chocolate bars in the box. ### Answer: 10 chocolate bars are left in the box.
Expected answer: 58/5
Correct? No
Problem: A plane is flying at an altitude of 2 miles, then it descends by 10/15 of a mile. What is the new altitude of the plane?
Mixtral 8x7B:
Reasoning: The plane descends by 10/1
Expected answer: 4/3
Correct? No
Problem: A child goes down a slide that's 6/19 meters long, and then goes down another slide that's 17/4 meters long. How many total meters did they slide?
Mixtral 8x7B:
Reasoning: To find the total distance the child slid, we need to add the lengths of the two slides: The length of the first slide is 6/19 meters. The length of the second slide is 17/4 meters, which can be simplified to 42/8 meters or 21/4 meters. So, the child slid a total of 6/19 + 21/4 meters. To add these fractions, we need a common denominator, which is 76 in this case. So, the child slid a total of (6/19 \* 4/4) + (21/4 \* 19/19) meters = 24/76 + 399/76 meters = 423/76 meters. ### Answer: 423/76 meters or approximately 5.56 meters.
Expected answer: 347/76
Correct? No
Problem: A colonial fireplace burns firewood at a rate of 4/15 cords per hour in the early morning. In the late night, the rate increases to 14/15 cords per hour. How much firewood does the fireplace burn in total in one hour split between the early morning and late night?
Mixtral 8x7B:
Reasoning: The fireplace burns firewood at a rate of (4/1
Expected answer: 6/5
Correct? No
Problem: An alien travelled 9/20 of a light year towards earth then decided to move forward another 11/7 light years. How many light years has the alien travelled in total?
Mixtral 8x7B:
Reasoning: To find the total distance the alien traveled, we need to add the two distances together. The alien traveled 9/20 of a light year towards earth and then 11/7 more light years. To add these fractions, we need a common denominator, which is 140 (the least common multiple of 20 and 7). So, 9/20 = 63/140 and 11/7 = 154/140. Therefore, the alien traveled 63/140 + 154/140 = 217/140 light years in total. ### Answer: 217/140 light years
Expected answer: 283/140
Correct? No
Problem: If Bob has 10/2 of a cucumber and he adds it to 1/7 of another cucumber, how many cucumbers does he have in total?
Mixtral 8x7B:
Reasoning: First, we need to find out how much of a cucumber Bob has in total. He has 10/2 = <<10/2=5>>5/2 of a cucumber from the first one. Next, we need to find out how much of a cucumber the second one is. It's 1/7 of a cucumber. Now, we add these two amounts together: 5/2 + 1/7. To do this, we need a common denominator, which is 14. So, we get 35/14 + 2/14 = 37/14. This means that Bob has 37/14 of a cucumber in total. Since you can't have 14/14 of a cucumber, but rather one whole cucumber, we need to find out how many cucumbers Bob has. To do this, we divide the total amount of cucumber Bob has by the whole cucumber: 37/14 ÷ 2 = 18.5/7. Since you can't have 0.5 of a cucumber, but rather half a cucumber, we can say that Bob has 18/7 + 1/2 = 33/14 + 7/14 = 40/14 = 20/7 of a cucumber. Since you can't have 7/7 of a cucumber, but rather one whole cucumber, we need to find out how many cucumbers Bob has. To do this, we divide the total amount of cucumber Bob has by the whole cucumber: 20/7 ÷ 1 = 20/7. Since you can't have 7/7 of a cucumber, but rather one whole cucumber, we need to find out how many cucumbers Bob has. To do this, we divide the total amount of cucumber Bob has by the whole cucumber: 20/7 ÷ 7/7 = 20/7 \* 7/1 = 20. ### Answer: Bob has 20/1 or 20 cucumbers in total.
Expected answer: 36/7
Correct? No