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?
InternLM-Math Base 20B:
Reasoning: Kyle threw the ball for a distance of 18/4 = <<18/4=4.5>>4.5 yards, while Lisa threw the ball for a distance of 19/9 = <<19/9=2.1111111111111111>>2.1111111111111111 yards. The ball traveled a total of 4.5+2.1111111111111111 = <<4.5+2.1111111111111111=6.611111111111111>>6.611111111111111 yards. ### Answer: 6.611111111111111
Expected answer: 119/18
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: The ball traveled a total of 4.5+2.1111111111111111 = <<4.5+2.1111111111111111=6.611111111111111>>6.611111111111111 yards. Subtracting 3/13 = <<3/13=0.23076923076923077>>0.23076923076923077 yards from 6.611111111111111 = <<6.611111111111111-0.23076923076923077=6.380238023802381>>6.380238023802381 yards gives 6.380238023802381-0.23076923076923077 = <<6.380238023802381-0.23076923076923077=6.1494554147337855>>6.1494554147337855 yards. ### Answer: 6.1494554147337855
Expected answer: 1493/234
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: Kyle threw the ball for a distance of 15/4 = <<15/4=3.75>>3.75 yards, while Lisa threw the ball for a distance of 19/9 = <<19/9=2.1111111111111111>>2.1111111111111111 yards. The ball traveled a total of 3.75+2.1111111111111111 = <<3.75+2.1111111111111111=5.861111111111111>>5.861111111111111 yards. ### Answer: 5.861111111111111
Expected answer: 211/36
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: Johnnie the monkey was given 18/7+12/14 = <<18/7+12/14=3+1=4>>4 bananas in total. ### Answer: 4
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?
InternLM-Math Base 20B:
Reasoning: The total distance of the bottom of the door from the floor is 4/19 inches. The total distance of the top of the door from the ceiling is 9/10 inches. ### Answer: 4/19 inches and 9/10 inches
Expected answer: 211/190
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: 17/3 - 15/11 = <<17/3-15/11=2/33>>2/33 ### Answer: 2/33
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?
InternLM-Math Base 20B:
Reasoning: Billy traveled 4-17/20 = <<4-17/20=4-0.85=3.15>>3.15 miles forward. ### Answer: 3.15
Expected answer: 63/20
Correct? Yes
Problem: Suppose instead of travelling 4 miles initially, Billy actually traveled 6 miles before rolling back 17/20 of a mile to avoid the pothole. With this change in initial distance, how many miles did Billy ultimately travel forward?
InternLM-Math Base 20B:
Reasoning: Billy traveled 6-17/20 = <<6-17/20=6-0.85=5.15>>5.15 miles forward. ### Answer: 5.15
Expected answer: 103/20
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: The rocket traveled 15/3 + 2/7 = <<15/3+2/7=23/21>>23/21 light years in total. ### Answer: 23/21
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?
InternLM-Math Base 20B:
Reasoning: Captain Silverbeard found 10/13+16/19 = <<10/13+16/19=26/39>>26/39 of the treasure map. ### Answer: 26/39
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?
InternLM-Math Base 20B:
Reasoning: The hiker has traveled 9/6+2/16 = <<9/6+2/16=11/8>>11/8 miles in total. ### Answer: 11/8
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?
InternLM-Math Base 20B:
Reasoning: Jessica has 16/9 - 4/13 = <<16/9-4/13=112/117>>112/117 cubic feet of sand left in her sandbox. ### Answer: 112/117
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?
InternLM-Math Base 20B:
Reasoning: Jacob has a piece of rope that is 15/12 = <<15/12=5/4>>5/4 meters long and he adds a piece that is 17/17 = <<17/17=1>>1 meters long to it. The total length of the rope is 5/4+1 = <<5/4+1=9/4>>9/4 meters. ### Answer: 9/4
Expected answer: 9/4
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?
InternLM-Math Base 20B:
Reasoning: Jacob now wants to double the total length of the rope he has. If Jacob starts with the rope that is 5/4+1 = <<5/4+1=9/4>>9/4 meters long, and then adds another piece of the same length to it, the total length of the combined ropes will be 9/4+9/4 = <<9/4+9/4=18/4>>18/4 meters. ### Answer: 18/4
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?
InternLM-Math Base 20B:
Reasoning: Jacob has a piece of rope that is 7/12 = <<7/12=7/12>>7/12 meters long and he adds a piece that is 17/17 = <<17/17=1>>1 meters long to it. The total length of the rope is 7/12+1 = <<7/12+1=19/12>>19/12 meters. ### Answer: 19/12
Expected answer: 19/12
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: Mark has 1+13/4 = <<1+13/4=1+1.75=2.75>>2.75 pairs of pants. ### Answer: 2.75
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?
InternLM-Math Base 20B:
Reasoning: Miss Jenny spent 8/8+20/19 = <<8/8+20/19=8+20/19=8+1 1/19=9 1/19>>9 1/19 hours grading papers in total. ### Answer: 9 1/19
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?
InternLM-Math Base 20B:
Reasoning: 12/3 + 15/12 = <<12/3+15/12=5/2+15/12=25/12=2+1/12=2 1/12>>2 1/12 kms. ### Answer: 2 1/12
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?
InternLM-Math Base 20B:
Reasoning: Jack rides his scooter 3/9+17/15 = <<3/9+17/15=1 1/3>>1 1/3 miles in total. ### Answer: 1 1/3
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?
InternLM-Math Base 20B:
Reasoning: The logs burn for 4/16 = <<4/16=1/4>>1/4 of an hour. The twigs burn for 16/12 = <<16/12=4/3>>4/3 of an hour. The total burn time is 1/4 + 4/3 = <<1/4+4/3=17/12>>17/12 of an hour. ### Answer: 17/12
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?
InternLM-Math Base 20B:
Reasoning: The ring maker used 12/16 + 16/2 = <<12/16+16/2=12/16+8=20/16=5/2>>5/2 ounces of silver in total. ### Answer: 5/2
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?
InternLM-Math Base 20B:
Reasoning: The tree produced 10/11+17/11 = <<10/11+17/11=27/11>>27/11 bushels of apples in total. ### Answer: 27/11
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?
InternLM-Math Base 20B:
Reasoning: The tree produced 10/9+17/11 = <<10/9+17/11=59/99>>59/99 bushels of apples in total. ### Answer: 59/99
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?
InternLM-Math Base 20B:
Reasoning: Sam's binoculars increase his range of sight by 3/14 of a mile. Joe's binoculars increase his range of sight by 16/16 of a mile. 3/14 + 16/16 = <<3/14+16/16=19/14>>19/14 ### Answer: 19/14
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?
InternLM-Math Base 20B:
Reasoning: Maria uses 15/10 + 9/18 = <<15/10+9/18=27/18=3/2>>3/2 yards of fabric for the two sections. ### Answer: 3/2
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?
InternLM-Math Base 20B:
Reasoning: The turtle has covered 10/5-5/16 = <<10/5-5/16=25/16>>25/16 miles from its starting point. ### Answer: 25/16
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?
InternLM-Math Base 20B:
Reasoning: The painter used 18/11+1/8 = <<18/11+1/8=19/8>>19/8 liters of paint in total. ### Answer: 19/8
Expected answer: 155/88
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The computer program executed 8+20 = <<8+20=28>>28 tasks in 4+14 = <<4+14=18>>18 minutes. The computer program executed 28/18 = <<28/18=1.5555555555555556>>1.5555555555555556 tasks per minute. ### Answer: 1.5555555555555556
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?
InternLM-Math Base 20B:
Reasoning: 12/13 + 3/2 = <<12/13+3/2=1+1/26=26/26>>1 1/26 = 26/26 pounds of gold. ### Answer: 26/26
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?
InternLM-Math Base 20B:
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
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?
InternLM-Math Base 20B:
Reasoning: The total length of the message is 1+11+7/8 = <<1+11+7/8=20.875>>20.875 hours. ### Answer: 20.875
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?
InternLM-Math Base 20B:
Reasoning: The first part of the message is 4/8 = <<4/8=1/2>>1/2 hour long, and the second part is 11/1 = <<11/1=11>>11 hours long. The total length of the message is 1/2+11 = <<1/2+11=11.5>>11.5 hours. ### Answer: 11.5
Expected answer: 23/2
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: There are 10 / 5 + 8 / 10 = <<10/5+8/10=2+0.8=2.8>>2.8 animals in each pond and pool combined. ### Answer: 2.8
Expected answer: 14/5
Correct? Yes
Problem: In the same park, there are also 12 frogs evenly distributed across 4 lily pads, meaning each lily pad has 12 / 4 frogs. Adding this to the previous sum of animals in each pond and pool, what is the total number of animals on each respective setting (pond, pool, lily pad) combined?
InternLM-Math Base 20B:
Reasoning: There are 10 / 5 + 8 / 10 + 12 / 4 = <<10/5+8/10+12/4=2+0.8+3=5.8>>5.8 animals in each pond, pool, and lily pad combined. ### Answer: 5.8
Expected answer: 29/5
Correct? Yes
Problem: In the same park, let's consider a different scenario. Suppose there are now only 2 ducks equally distributed among 5 ponds. Given that each pond will have 2 / 5 ducks and each small pool still has 8 / 10 fish, what will be the total number of animals across each pond and pool in this new scenario?
InternLM-Math Base 20B:
Reasoning: There are 2 / 5 + 8 / 10 = <<2/5+8/10=0.4+0.8=1.2>>1.2 animals in each pond and pool combined. ### Answer: 1.2
Expected answer: 6/5
Correct? Yes
Problem: On a map, 15/11 inches represents the distance between Town A and Town B, and 16/15 inches represents the distance between Town B and Town C. What is the total distance between Town A and Town C on the map?
InternLM-Math Base 20B:
Reasoning: The total distance between Town A and Town C is 15/11 + 16/15 = <<15/11+16/15=31/11>>31/11 inches. ### Answer: 31/11
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?
InternLM-Math Base 20B:
Reasoning: 13/18 = <<13/18=0.7222222222222222>>0.7222222222222222 and 4/6 = <<4/6=0.6666666666666666>>0.6666666666666666. 13/18 + 4/6 = <<13/18+4/6=1.3888888888888888>>1.3888888888888888. ### Answer: 1.3888888888888888
Expected answer: 25/18
Correct? Yes
Problem: The soap company plans to double their daily production. After producing 13/18 tons of Soap A and 4/6 tons of Soap B each day, how many tons of soap will they produce in total when they double their production?
InternLM-Math Base 20B:
Reasoning: 13/18 = <<13/18=0.7222222222222222>>0.7222222222222222 and 4/6 = <<4/6=0.6666666666666666>>0.6666666666666666. 13/18 + 4/6 = <<13/18+4/6=1.3888888888888888>>1.3888888888888888. ### Answer: 1.3888888888888888
Expected answer: 25/9
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: 17/18 = <<17/18=0.9444444444444444>>0.9444444444444444 and 4/6 = <<4/6=0.6666666666666666>>0.6666666666666666. 17/18 + 4/6 = <<17/18+4/6=1.611111111111111>>1.611111111111111. ### Answer: 1.611111111111111
Expected answer: 29/18
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?
InternLM-Math Base 20B:
Reasoning: Mark's sleeping bag is 19/2 - 13/12 = <<19/2-13/12=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13/6=19/2-13
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?
InternLM-Math Base 20B:
Reasoning: Mary feeds 6/20+18/15 = <<6/20+18/15=1.8+1.2=2.8>>2.8 pounds of food to the monkeys and giraffes. ### Answer: 2.8
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?
InternLM-Math Base 20B:
Reasoning: Albert has 20/17 + 4/1 = <<20/17+4/1=20/17+4/1=24/17>>24/17 full sets of cards. ### Answer: 24/17
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?
InternLM-Math Base 20B:
Reasoning: The jeweler has 5/14+18/19 = <<5/14+18/19=23/38>>23/38 pounds of silver. ### Answer: 23/38
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?
InternLM-Math Base 20B:
Reasoning: The turtle moves 11-15/15 = <<11-15/15=11-1=10>>10 meters away from the starting point. ### Answer: 10
Expected answer: 10
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?
InternLM-Math Base 20B:
Reasoning: The turtle moves 10+15/20 = <<10+15/20=10+3/4=10.75>>10.75 meters away from the starting point. ### Answer: 10.75
Expected answer: 43/4
Correct? Yes
Problem: Reconsider the previous scenario, but this time the turtle returns 15/8 of a meter back towards the starting point instead of the former 15/15 meters. Now, how many meters is the turtle from its starting point after these two movements?
InternLM-Math Base 20B:
Reasoning: The turtle moves 11-15/8 = <<11-15/8=11-1.875=9.125>>9.125 meters away from the starting point. ### Answer: 9.125
Expected answer: 73/8
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: Chloe has 19/2 - 17/2 = <<19/2-17/2=2/2=1>>1 ounce of chocolate left. ### Answer: 1
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?
InternLM-Math Base 20B:
Reasoning: Chloe has 1 + 4/14 = <<1+4/14=18/14=9/7>>9/7 ounces of chocolate now. ### Answer: 9/7
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?
InternLM-Math Base 20B:
Reasoning: Chloe would have had 19/2 - 9/2 = <<19/2-9/2=10/2=5>>5 ounces of chocolate left. ### Answer: 5
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?
InternLM-Math Base 20B:
Reasoning: Sammy's backpack can hold 20/9+8/4 = <<20/9+8/4=44/9>>44/9 liters. ### Answer: 44/9
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?
InternLM-Math Base 20B:
Reasoning: 11/8 + 5/5 = <<11/8+5/5=11/8+1=12/8=3/2>>3/2 ounces. ### Answer: 3/2
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?
InternLM-Math Base 20B:
Reasoning: Jake received 20/15 = <<20/15=4/3>>4/3 dollars. Jake has 9/10+4/3 = <<9/10+4/3=21/10>>21/10 dollars in his wallet now. ### Answer: 21/10
Expected answer: 67/30
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?
InternLM-Math Base 20B:
Reasoning: The front portion of the chair is 5/2 = <<5/2=2.5>>2.5 feet high. The back portion of the chair is 20/14 = <<20/14=1.4285714285714285714285714285714>>1.4285714285714285714285714285714 feet high. The combined height of the front and back portions of the chair is 2.5+1.4285714285714285714285714285714 = <<2.5+1.4285714285714285714285714285714=3.9285714285714285714285714285714>>3.9285714285714285714285714285714 feet. ### Answer: 3.9285714285714285714285714285714
Expected answer: 55/14
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?
InternLM-Math Base 20B:
Reasoning: The new height of the chair is 3.9285714285714285714285714285714-2 = <<3.9285714285714285714285714285714-2=1.9285714285714285714285714285714>>1.9285714285714285714285714285714 feet. ### Answer: 1.9285714285714285714285714285714
Expected answer: 27/14
Correct? Yes
Problem: John has 5 shirts and he donated 12/9 of them to charity. How many shirts does he have left?
InternLM-Math Base 20B:
Reasoning: John donated 12/9 = <<12/9=1 1/3>>1 1/3 shirts to charity. John has 5-1 1/3 = <<5-1 1/3=3 2/3>>3 2/3 shirts left. ### Answer: 3 2/3
Expected answer: 11/3
Correct? Yes
Problem: John recalls that he actually only had 5/2 shirts to start with before he donated 12/9 of them to charity. How many shirts does he actually have left now?
InternLM-Math Base 20B:
Reasoning: John donated 12/9 = <<12/9=1 1/3>>1 1/3 shirts to charity. John has 5/2-1 1/3 = <<5/2-1 1/3=1/6>>1/6 shirts left. ### Answer: 1/6
Expected answer: 7/6
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?
InternLM-Math Base 20B:
Reasoning: Bob's jacket measures 14/3 - 14/16 = <<14/3-14/16=14/48>>14/48 meters in length after the alteration. ### Answer: 14/48
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?
InternLM-Math Base 20B:
Reasoning: Officer Max spends 2/6+14/7 = <<2/6+14/7=2/6+2/7=4/21>>4/21 parts of an hour for these two tasks. ### Answer: 4/21
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?
InternLM-Math Base 20B:
Reasoning: John watched the movie for 10/12 = <<10/12=5/6>>5/6 of an hour and the TV show for 3/8 = <<3/8=3/8>>3/8 of an hour. John spent 5/6+3/8 = <<5/6+3/8=19/24>>19/24 of an hour watching. ### Answer: 19/24
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?
InternLM-Math Base 20B:
Reasoning: Mr. Carpenter takes 5/3+10/13 = <<5/3+10/13=25/39>>25/39 hours to build a chair. ### Answer: 25/39
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?
InternLM-Math Base 20B:
Reasoning: The total added diameter is 8/4 + 15/2 = <<8/4+15/2=19/2>>19/2 mm. ### Answer: 19/2
Expected answer: 19/2
Correct? Yes
Problem: Suppose instead of the large bead of 15/2 mm diameter, Anna adds a different large bead to her bracelet that is 5/2 mm in diameter. Now, what would be the total added diameter if she adds this new large bead and the small bead to her bracelet?
InternLM-Math Base 20B:
Reasoning: The total added diameter is 8/4 + 5/2 = <<8/4+5/2=13/2>>13/2 mm. ### Answer: 13/2
Expected answer: 9/2
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?
InternLM-Math Base 20B:
Reasoning: The rocket travels 11/18+8/2 = <<11/18+8/2=11/18+4=15/18>>15/18 light-years. ### Answer: 15/18
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?
InternLM-Math Base 20B:
Reasoning: Johnathan needs 12/14+8/5 = <<12/14+8/5=1 3/7>>1 3/7 yards of fabric to create his sleeping bag. ### Answer: 1 3/7
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?
InternLM-Math Base 20B:
Reasoning: 5/4 + 1/2 = <<5/4+1/2=9/4>>9/4. The total acreage of pine and oak trees in the forest is 9/4. ### Answer: 9/4
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?
InternLM-Math Base 20B:
Reasoning: Jake has 12/7+2/14 = <<12/7+2/14=16/7>>16/7 yards of fabric. ### Answer: 16/7
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?
InternLM-Math Base 20B:
Reasoning: The difference in kilograms of the fruit from summer to winter is 10/4 - 12/20 = <<10/4-12/20=5/4>>5/4. ### Answer: 5/4
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?
InternLM-Math Base 20B:
Reasoning: 13/5 - 15/16 = <<13/5-15/16=1/16>>1/16 Her routine lasts 1/16 minutes after shortening it. ### Answer: 1/16
Expected answer: 133/80
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?
InternLM-Math Base 20B:
Reasoning: Miss Daisy has 19/6 - 17/20 = <<19/6-17/20=1/12>>1/12 kg of fertilizers left to use on her other flowers. ### Answer: 1/12
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?
InternLM-Math Base 20B:
Reasoning: 4/16 + 20/6 = <<4/16+20/6=20/16+20/6=40/16=5/2>>5/2 meters. The total change in distance this year is 5/2 meters. ### Answer: 5/2
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?
InternLM-Math Base 20B:
Reasoning: Bob has 11/3+12/19 = <<11/3+12/19=67/57>>67/57 dollars in his wallet. ### Answer: 67/57
Expected answer: 245/57
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: The shark swims 5/5+12/18 = <<5/5+12/18=5/5+2/3=7/3>>7/3 miles in total. ### Answer: 7/3
Expected answer: 5/3
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?
InternLM-Math Base 20B:
Reasoning: Jim types 20/16 = <<20/16=1.25>>1.25 words per second and Mary types 9/4 = <<9/4=2.25>>2.25 words per second. Jim and Mary type 1.25+2.25 = <<1.25+2.25=3.5>>3.5 words per second in total. ### 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?
InternLM-Math Base 20B:
Reasoning: Jim and Mary's new combined typing speed is 3.5-2/11 = <<3.5-2/11=1.2727272727272727>>1.2727272727272727 words per second. ### Answer: 1.2727272727272727
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?
InternLM-Math Base 20B:
Reasoning: Max rode his scooter for 1/9 miles less in the afternoon. Max rode his scooter for 9/7 - 1/9 = <<9/7-1/9=67/63>>67/63 miles in the afternoon. ### Answer: 67/63
Expected answer: 74/63
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?
InternLM-Math Base 20B:
Reasoning: The clown rode a unicycle for 9/8 = <<9/8=1.125>>1.125 hours. She juggled for 2/10 = <<2/10=0.2>>0.2 hours. The clown performed 1.125+0.2 = <<1.125+0.2=1.325>>1.325 hours in total. ### Answer: 1.325
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?
InternLM-Math Base 20B:
Reasoning: The clown took a total break of 13/5 = <<13/5=2.6>>2.6 hours. She performed for 1.325 hours. The clown had 2.6-1.325 = <<2.6-1.325=1.275>>1.275 hours remaining after her performance time is subtracted from her total break time. ### Answer: 1.275
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?
InternLM-Math Base 20B:
Reasoning: The clown rode a unicycle for 9/8 = <<9/8=1.125>>1.125 hours. She juggled for 9/10 = <<9/10=0.9>>0.9 hours. The clown performed 1.125+0.9 = <<1.125+0.9=2.025>>2.025 hours in total. ### Answer: 2.025
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?
InternLM-Math Base 20B:
Reasoning: Timmy dumps 7/2+1/2 = <<7/2+1/2=9/2>>9/2 kg of sand into his sandbox. ### Answer: 9/2
Expected answer: 4
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?
InternLM-Math Base 20B:
Reasoning: 18/8 = <<18/8=2.25>>2.25 ounces of moon roots and 11/7 = <<11/7=1.5714285714285714>>1.5714285714285714 ounces of stardust. The wizard used 2.25+1.5714285714285714 = <<2.25+1.5714285714285714=3.8214285714285714>>3.8214285714285714 ounces of ingredients in total. ### Answer: 3.8214285714285714
Expected answer: 107/28
Correct? Yes
Problem: The wizard decided to use 13/7 ounces of stardust instead of the initially intended 11/7 ounces while preparing the potion. So now, what would be the total number of ounces of ingredients used in this adjusted potion recipe?
InternLM-Math Base 20B:
Reasoning: 18/8 = <<18/8=2.25>>2.25 ounces of moon roots and 13/7 = <<13/7=1.8571428571428571>>1.8571428571428571 ounces of stardust. The wizard used 2.25+1.8571428571428571 = <<2.25+1.8571428571428571=4.107142857142857>>4.107142857142857 ounces of ingredients in total. ### Answer: 4.107142857142857
Expected answer: 115/28
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: The UFO traveled 3/10 + 16/20 = <<3/10+16/20=3/10+4/5=7/10+4/5=11/10=1+1/10=1 1/10>>1 1/10 miles in total. ### Answer: 1 1/10
Expected answer: 11/10
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?
InternLM-Math Base 20B:
Reasoning: The UFO traveled 3/10 + 16/18 = <<3/10+16/18=3/10+8/9=27/90+8/9=35/90=7/18>>7/18 miles in total. ### Answer: 7/18
Expected answer: 107/90
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?
InternLM-Math Base 20B:
Reasoning: 4/14 = <<4/14=1/3.5>>1/3.5 and 20/4 = <<20/4=5>>5. 1/3.5 + 5 = <<1/3.5+5=5.5/3.5>>5.5/3.5. ### Answer: 5.5/3.5
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?
InternLM-Math Base 20B:
Reasoning: 2/4 + 7/10 = <<2/4+7/10=9/10>>9/10. They swam 9/10 = <<9/10=0.9>>0.9 miles together. ### Answer: 0.9
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?
InternLM-Math Base 20B:
Reasoning: 8/18 = <<8/18=4/9>>4/9 and 18/8 = <<18/8=9/4>>9/4. 4/9 + 9/4 = <<4/9+9/4=13/9>>13/9. ### Answer: 13/9
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?
InternLM-Math Base 20B:
Reasoning: The tree grows 1/10 of its height every month. This month, it additionally has grown 12/6 feet due to a fertilizer being applied. The tree has grown 1/10+12/6 = <<1/10+12/6=3/5>>3/5 feet in height this month. ### Answer: 3/5
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?
InternLM-Math Base 20B:
Reasoning: The total area occupied by both tents is 13/11 + 8/20 = <<13/11+8/20=1 1/5>>1 1/5 acres. ### Answer: 1 1/5
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?
InternLM-Math Base 20B:
Reasoning: Captain Jack must travel 17/20 = <<17/20=0.85>>0.85 km to the East and then 15/3 = <<15/3=5>>5 km to the North. The total distance is 0.85+5 = <<0.85+5=5.85>>5.85 km. ### Answer: 5.85
Expected answer: 117/20
Correct? Yes
Problem: Upon reviewing his map, Captain Jack realized that the initial location of the treasure was at a distance of (17 / 7) km to the East instead of (17 / 20) km. Given the treasure is (15 / 3) km to the North from their starting point, how far would Captain Jack need to travel in total to reach the treasure if he started from the beginning again using the corrected distance to the East?
InternLM-Math Base 20B:
Reasoning: Captain Jack must travel 17/7 = <<17/7=2.43>>2.43 km to the East and then 15/3 = <<15/3=5>>5 km to the North. The total distance is 2.43+5 = <<2.43+5=7.43>>7.43 km. ### Answer: 7.43
Expected answer: 52/7
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?
InternLM-Math Base 20B:
Reasoning: Sarah collected 11/20 = <<11/20=0.55>>0.55 pounds of firewood and Alex collected 9/7 = <<9/7=1.2857142857142857>>1.2857142857142857 pounds of firewood. Sarah and Alex collected 0.55+1.2857142857142857 = <<0.55+1.2857142857142857=1.8357142857142857>>1.8357142857142857 pounds of firewood in total. ### Answer: 1.8357142857142857
Expected answer: 257/140
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?
InternLM-Math Base 20B:
Reasoning: Sarah and Alex collected 1.8357142857142857 = <<1.8357142857142857=1.8357142857142857>>1.8357142857142857 pounds of firewood in total. Sarah, Alex, and Kim have 1.8357142857142857+11 = <<1.8357142857142857+11=12.8357142857142857>>12.8357142857142857 pounds of firewood in total. ### Answer: 12.8357142857142857
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?
InternLM-Math Base 20B:
Reasoning: Sarah collected 10/20 = <<10/20=0.5>>0.5 pounds of firewood and Alex collected 9/7 = <<9/7=1.2857142857142857>>1.2857142857142857 pounds of firewood. Sarah and Alex collected 0.5+1.2857142857142857 = <<0.5+1.2857142857142857=1.7857142857142857>>1.7857142857142857 pounds of firewood in total. ### Answer: 1.7857142857142857
Expected answer: 25/14
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: Captain Bill sailed 19/5+12/15 = <<19/5+12/15=19/3+4/5=23/15>>23/15 miles north in total. ### Answer: 23/15
Expected answer: 23/5
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?
InternLM-Math Base 20B:
Reasoning: 19/17 + 9/4 = <<19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/17+9/4=19/
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?
InternLM-Math Base 20B:
Reasoning: Lucy's sleeping bag is 18/19 + 8/11 = <<18/19+8/11=26/19>>26/19 meter long. ### Answer: 26/19
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?
InternLM-Math Base 20B:
Reasoning: Sarah pours 10/13+8/2 = <<10/13+8/2=10/13+4=14/13>>14/13 gallons of water into the container. There are 14/13 = <<14/13=1 1/13>>1 1/13 gallons of water in the container now. ### Answer: 1 1/13
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?
InternLM-Math Base 20B:
Reasoning: Mandy has 9/2 - 1/4 = <<9/2-1/4=7/4>>7/4 KGs of apples left. ### Answer: 7/4
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?
InternLM-Math Base 20B:
Reasoning: John spends 12/7+3/9 = <<12/7+3/9=15/7>>15/7 hours working on the watch. ### Answer: 15/7
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?
InternLM-Math Base 20B:
Reasoning: Peggy swam back for 1/12 miles, so she is 5/4 - 1/12 = <<5/4-1/12=19/12>>19/12 miles from her family. ### Answer: 19/12
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?
InternLM-Math Base 20B:
Reasoning: 4+11/12 = <<4+11/12=4+0.9166666666666666=4.916666666666667>>4.916666666666667 acres. ### Answer: 4.916666666666667
Expected answer: 59/12
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?
InternLM-Math Base 20B:
Reasoning: 4.916666666666667+17/11 = <<4.916666666666667+17/11=4.916666666666667+1.5454545454545454=6.462222222222222>>6.462222222222222 acres. ### Answer: 6.462222222222222
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?
InternLM-Math Base 20B:
Reasoning: 4/9+11/12 = <<4/9+11/12=4/9+0.9166666666666666=1.0833333333333334>>1.0833333333333334 acres. ### Answer: 1.0833333333333334
Expected answer: 49/36
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?
InternLM-Math Base 20B:
Reasoning: The designer used 11/4+5/17 = <<11/4+5/17=1 1/2+5/17=1 7/34>>1 7/34 yards of fabric in total. ### Answer: 1 7/34
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?
InternLM-Math Base 20B:
Reasoning: Jacob has 11/2 - 5/16 = <<11/2-5/16=11/2-5/32=11*16/32-5/32=11*16-5/32=176-5/32=171/32>>171/32 feet of wire remaining. ### Answer: 171/32
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?
InternLM-Math Base 20B:
Reasoning: Samantha uses 17/14 fluid ounces of toothpaste in one week. She has 4-17/14 = <<4-17/14=1/14>>1/14 fluid ounces of toothpaste left after that week. ### Answer: 1/14
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?
InternLM-Math Base 20B:
Reasoning: Maria gives each of her 6 friends 12/6 = <<12/6=2>>2 candies. Maria gives each of her 20 friends 20/20 = <<20/20=1>>1 sticker. Each friend gets 2+1 = <<2+1=3>>3 candies and stickers in total. ### Answer: 3
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?
InternLM-Math Base 20B:
Reasoning: Maria gives each of her 6 friends 12/6 = <<12/6=2>>2 candies. Maria gives each of her 13 friends 20/13 = <<20/13=1.5384615384615385>>1.5384615384615385 stickers. Each friend gets 2+1.5384615384615385 = <<2+1.5384615384615385=3.5384615384615385>>3.5384615384615385 candies and stickers in total. ### Answer: 3.5384615384615385
Expected answer: 46/13
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: The total rainfall was 4/13+11/5 = <<4/13+11/5=1 1/5>>1 1/5 hours. ### Answer: 1 1/5
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?
InternLM-Math Base 20B:
Reasoning: Jane cuts 10/12 + 10/10 = <<10/12+10/10=20/12>>20/12 yards of fabric from the blanket in total. ### Answer: 20/12
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?
InternLM-Math Base 20B:
Reasoning: The fairy sprinkled 11/12 + 9/10 = <<11/12+9/10=119/60>>119/60 oz of magic dust. ### Answer: 119/60
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?
InternLM-Math Base 20B:
Reasoning: You will get 3/11 + 8/10 = <<3/11+8/10=1 1/5>>1 1/5 points. ### Answer: 1 1/5
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?
InternLM-Math Base 20B:
Reasoning: You removed 14/9 pages from a 4/1 page letter. The letter is now 4/1 - 14/9 = <<4/1-14/9=46/9>>46/9 pages long. ### Answer: 46/9
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?
InternLM-Math Base 20B:
Reasoning: Anne painted 16/20 = <<16/20=0.8>>0.8 of the table, and then Bob painted 5/20 = <<5/20=0.25>>0.25 of the table. Therefore, the total amount of the table that has been painted is 0.8+0.25 = <<0.8+0.25=1.05>>1.05. ### Answer: 1.05
Expected answer: 21/20
Correct? Yes
Problem: After Anne and Bob painted parts of the table, Carl decided to add to their work by painting another 11/5 of the table. Now, how much of the table has been painted in total?
InternLM-Math Base 20B:
Reasoning: Anne and Bob painted 1.05 of the table, and then Carl painted 11/5 = <<11/5=2.2>>2.2 of the table. Therefore, the total amount of the table that has been painted is 1.05+2.2 = <<1.05+2.2=3.25>>3.25. ### Answer: 3.25
Expected answer: 13/4
Correct? Yes
Problem: Suppose before Carl added more paint, instead of Bob painting an additional 5/20 of the table, he could only manage to paint 5/14 of it. In this case, how much of the table has been painted by Anne and Bob together?
InternLM-Math Base 20B:
Reasoning: Anne painted 16/20 = <<16/20=0.8>>0.8 of the table, and then Bob painted 5/14 = <<5/14=0.357>>0.357 of the table. Therefore, the total amount of the table that has been painted is 0.8+0.357 = <<0.8+0.357=1.157>>1.157. ### Answer: 1.157
Expected answer: 81/70
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?
InternLM-Math Base 20B:
Reasoning: The relative brightness of Alpha is 17/3 = <<17/3=5.666666666666667>>5.666666666666667, and the relative brightness of Bravo is 20/16 = <<20/16=1.25>>1.25. The relative brightness of both stars is 5.666666666666667+1.25 = <<5.666666666666667+1.25=6.916666666666667>>6.916666666666667. ### Answer: 6.916666666666667
Expected answer: 83/12
Correct? Yes
Problem: Taking into account the previous situation, if we adjust the brightness of star Alpha such that it only shines 8/3 times brighter than an average star instead of 17/3 times, how much brighter would Alpha and Bravo combined be in comparison to an average star?
InternLM-Math Base 20B:
Reasoning: The relative brightness of Alpha is 8/3 = <<8/3=2.6666666666666665>>2.6666666666666665, and the relative brightness of Bravo is 20/16 = <<20/16=1.25>>1.25. The relative brightness of both stars is 2.6666666666666665+1.25 = <<2.6666666666666665+1.25=3.9166666666666665>>3.9166666666666665. ### Answer: 3.9166666666666665
Expected answer: 47/12
Correct? Yes
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?
InternLM-Math Base 20B:
Reasoning: 17/20 + 18/8 = <<17/20+18/8=1+9/8=17/8>>17/8 kg of apples are in the store in total. ### Answer: 17/8
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?
InternLM-Math Base 20B:
Reasoning: 12/20 + 12/12 = <<12/20+12/12=1+3/5=8/5>>8/5. The bus traveled 8/5 miles in total. ### Answer: 8/5
Expected answer: 8/5
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?
InternLM-Math Base 20B:
Reasoning: 12/20 + 12/12 + 12/20 + 12/12 = <<12/20+12/12+12/20+12/12=1+3/5+1+3/5=2+6/5=32/5>>32/5. The bus traveled 32/5 miles in total. ### Answer: 32/5
Expected answer: 16/5
Correct? No
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?
InternLM-Math Base 20B:
Reasoning: 14/20 + 12/12 = <<14/20+12/12=7/5+12/12=19/12>>19/12. The bus traveled 19/12 miles in total. ### Answer: 19/12
Expected answer: 17/10
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?
InternLM-Math Base 20B:
Reasoning: The shark swims 3/9+13/5 = <<3/9+13/5=1+1/45>>1+1/45 miles in total in these two hours. ### Answer: 1+1/45
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?
InternLM-Math Base 20B:
Reasoning: 17/17 + 2/12 = <<17/17+2/12=17/17+1/6=23/17>>23/17 seconds. ### Answer: 23/17 seconds
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?
InternLM-Math Base 20B:
Reasoning: 12/17 + 8/19 = <<12/17+8/19=20/19>>20/19. The total cord of wood it burns in a day is 20/19. ### Answer: 20/19
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?
InternLM-Math Base 20B:
Reasoning: The entire flight was 18/19+9/17 = <<18/19+9/17=1 3/17>>1 3/17 miles. ### Answer: 1 3/17
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?
InternLM-Math Base 20B:
Reasoning: The total distance is 13/10 + 14/15 = <<13/10+14/15=27/30+28/30=55/30=11/6>>11/6 inches. ### Answer: 11/6
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?
InternLM-Math Base 20B:
Reasoning: The new speed of the balloon is 13/6+3/16 = <<13/6+3/16=13/4+3/16=13*4/4+3/16=52/16+3/16=55/16=2 7/16>>2 7/16 feet per second. ### Answer: 2 7/16
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?
InternLM-Math Base 20B:
Reasoning: Scarlett uses 1/20 of a gallon for a small art project. She has 16/10 - 1/20 = <<16/10-1/20=15/10>>15/10 gallons of red paint left. ### Answer: 15/10
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?
InternLM-Math Base 20B:
Reasoning: Susie eats 12/5 = <<12/5=2.4>>2.4 chocolate bars. 12-2.4 = <<12-2.4=9.6>>9.6 chocolate bars are left in the box. ### Answer: 9.6
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?
InternLM-Math Base 20B:
Reasoning: The new altitude of the plane is 2-10/15 = <<2-10/15=2-2/3=4/3>>4/3 miles. ### Answer: 4/3
Expected answer: 4/3
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?
InternLM-Math Base 20B:
Reasoning: The new altitude of the plane is 2-12/15 = <<2-12/15=2-4/5=2/5>>2/5 miles. ### Answer: 2/5
Expected answer: 6/5
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?
InternLM-Math Base 20B:
Reasoning: The child slides 6/19+17/4 = <<6/19+17/4=1.5>>1.5 meters. ### Answer: 1.5
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?
InternLM-Math Base 20B:
Reasoning: The fireplace burns 4/15+14/15 = <<4/15+14/15=1+1=2>>2 cords of firewood in one hour. ### Answer: 2
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?
InternLM-Math Base 20B:
Reasoning: The alien travelled 9/20+11/7 = <<9/20+11/7=1.5>>1.5 light years in total. ### Answer: 1.5
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?
InternLM-Math Base 20B:
Reasoning: Bob has 5/2 of a cucumber and 1/7 of another cucumber. 5/2 + 1/7 = <<5/2+1/7=29/14>>29/14 ### Answer: 29/14
Expected answer: 36/7
Correct? No