LLemma 7B 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?
LLemma 7B:
Reasoning: The ball traveled 18/4 + 19/9 = <<18/4+19/9=1.8+2.2=4>>4 yards. ### Answer: 4
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?
LLemma 7B:
Reasoning: 18/7 + 12/14 = <<18/7+12/14=18/7+3/7=21/7>>21/7 bananas in total. ### Answer: 21/7
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?
LLemma 7B:
Reasoning: The bottom of the door is 4/19 inches from the floor, and the top of the door is 9/10 inches from the ceiling. The bottom of the door is 4/19 inches from the floor, and the top of the door is 9/10 inches from the ceiling. The total distance of the bottom and top of the door from the floor and ceiling, respectively, is 4/19 + 9/10 = <<4/19 + 9/10 = 113/190>>113/190. ### Answer: 113/190
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?
LLemma 7B:
Reasoning: Ralph's juice recipe requires 17/3 liters of apple juice. However, he only uses 15/11 liters of it. 17/3 - 15/11 = <<17/3 - 15/11 = 17/3 * 11/15 = 17*11/3*15 = 117/45>>117/45 liters of apple juice are left unused. ### Answer: 117/45
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?
LLemma 7B:
Reasoning: Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back 17/20 of a mile. Billy rolls back
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?
LLemma 7B:
Reasoning: The rocket traveled 15/3 + 2/7 = <<15/3+2/7=15*7+2*3/3*7=105+6=111>>111 light years in total. ### Answer: 111
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?
LLemma 7B:
Reasoning: 10/13 + 16/19 = <<10/13+16/19=10/13+8/13=18/13>>18/13 ### Answer: 18/13
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?
LLemma 7B:
Reasoning: The hiker has walked 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?
LLemma 7B:
Reasoning: Jessica has <<16/9-4/13=16/9*13/4=<<16*13/9*4=16*13/3=<<16*13=208>>208>>>>208 cubic feet of sand left in her sandbox. ### Answer: 208
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?
LLemma 7B:
Reasoning: 15/12 + 17/17 = <<15/12+17/17=15/12+17/17=15/12*17/17+17/17*15/12=255/189>>255/189 meters. ### Answer: 255/189
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?
LLemma 7B:
Reasoning: Mark has 1 full pair of pants and another 13/4 pairs from various incomplete sets. Mark has 1+13/4 = <<1+13/4=5.75>>5.75 pairs of pants. ### Answer: 5.75
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?
LLemma 7B:
Reasoning: Jenny spent 8/8 hours on one subject. Jenny spent 20/19 hours on another subject. Jenny spent 8/8 + 20/19 = <<8/8+20/19=1.94444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444
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?
LLemma 7B:
Reasoning: 12/3 = <<12/3=4>>4 kms 15/12 = <<15/12=1.25>>1.25 kms 4 + 1.25 = <<4+1.25=5.25>>5.25 kms ### Answer: 5.25
Expected answer: 21/4
Correct? Yes
Problem: Let's now consider this scenario: the cloud was initially at a height of 12/3 kms, then later it ascended by 7/12 kms instead of the previous 15/12 kms. What would be the resultant height of the cloud from the ground in this case?
LLemma 7B:
Reasoning: 12/3 = <<12/3=4>>4 kms 7/12 = <<7/12=0.5833333333333333>>0.5833333333333333 kms 4 + 0.5833333333333333 = <<4+0.5833333333333333=4.583333333333333>>4.583333333333333 kms ### Answer: 4.583333333333333
Expected answer: 55/12
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?
LLemma 7B:
Reasoning: 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. 3/9 + 17/15 = <<3/9 + 17/15 = 103/45>>103/45 miles ### Answer: 103/45
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?
LLemma 7B:
Reasoning: 4/16 + 16/12 = <<4/16 + 16/12>> ### Answer: 1/3
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?
LLemma 7B:
Reasoning: 12/16 = <<12/16=0.75>>0.75 and 16/2 = <<16/2=8>>8. 0.75 + 8 = <<0.75+8=8.75>>8.75 ### Answer: 8.75
Expected answer: 35/4
Correct? Yes
Problem: The ring maker decides to add an ornamental filigree to the ring, which requires an additional 18/20 ounces of silver. How many total ounces of silver did the ring maker use including the filigree?
LLemma 7B:
Reasoning: 18/20 = <<18/20=0.9>>0.9 0.9 + 8.75 = <<0.9+8.75=9.65>>9.65 ### Answer: 9.65
Expected answer: 193/20
Correct? No
Problem: If initially, the ring maker used 10/16 ounces of a silver for the base of the ring instead of 12/16 ounces, while still using 16/2 ounces to make the rest of the ring, how many total ounces of silver did the ring maker use then?
LLemma 7B:
Reasoning: 10/16 = <<10/16=0.625>>0.625 and 16/2 = <<16/2=8>>8. 0.625 + 8 = <<0.625+8=8.625>>8.625 ### Answer: 8.625
Expected answer: 69/8
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?
LLemma 7B:
Reasoning: 10/11 + 17/11 = <<10/11+17/11=27/11>>27/11 bushels 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?
LLemma 7B:
Reasoning: 10/9 + 17/11 = <<10/9+17/11=100/99>>100/99 bushels in total. ### Answer: 100/99
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?
LLemma 7B:
Reasoning: Sam's binoculars increase his range of sight by 3/14 of a mile. Joe's binoculars increase his range of sight by exactly 1 mile. Their combined range increase is 3/14 + 1 = <<3/14 + 1 = 17/14 = 1 5/14>>1 5/14 of a mile. ### Answer: 1 5/14
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?
LLemma 7B:
Reasoning: 15/10 + 9/18 = <<15/10+9/18=15/10*18/18+9/18*10/10=15*18/10*18+9*10/10*18=270/180+90/180=460/180=23/9>>23/9 yards Maria uses 23/9 yards for these two sections. ### Answer: 23/9
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?
LLemma 7B:
Reasoning: The turtle walks 10/5 = <<10/5=2>>2 miles forward, then walks backward 5/16 = <<5/16=0.3125>>0.3125 miles. The turtle walks 2 - 0.3125 = <<2-0.3125=1.6875>>1.6875 miles from its starting point. ### Answer: 1.6875
Expected answer: 27/16
Correct? Yes
Problem: In the previous question, we considered the turtle walking forward 10/5 miles and walking backward 5/16 mile. Now, assume instead that the turtle walks backward a distance of 5/6 miles instead of 5/16 mile after walking forward. Now, how far is the turtle from its starting point?
LLemma 7B:
Reasoning: The turtle walks 10/5 = <<10/5=2>>2 miles forward, then walks backward 5/6 = <<5/6=0.8333333333333334>>0.8333333333333334 miles. The turtle walks 2 - 0.8333333333333334 = <<2-0.8333333333333334=1.1666666666666667>>1.1666666666666667 miles from its starting point. ### Answer: 1.1666666666666667
Expected answer: 7/6
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?
LLemma 7B:
Reasoning: 18/11+1/8 = <<18/11+1/8=1.5>>1.5 liters of paint in total. ### Answer: 1.5
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?
LLemma 7B:
Reasoning: 8 tasks in 4 minutes = 8/4 = <<8/4=2>>2 tasks per minute. 20 tasks in 14 minutes = 20/14 = <<20/14=1.43>>1.43 tasks per minute. 2+1.43 = <<2+1.43=3.43>>3.43 tasks per minute. ### Answer: 3.43
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?
LLemma 7B:
Reasoning: 12/13 + 3/2 = <<12/13 + 3/2 = 13/26 + 3/2 = 13/26 + 18/26 = 31/26 = 1 5/26>>1 5/26 pounds of gold. ### Answer: 1 5/26
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?
LLemma 7B:
Reasoning: 4/4 = 1, so the first part of the message is 1 hour long. 11/1 = 11, so the second part of the message is 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?
LLemma 7B:
Reasoning: 7/8 = 7/8, so the additional part of the message is 7/8 hour long. The total length of all parts of the message is 12+7/8 = <<12+7/8=12.875>>12.875 hours. ### Answer: 12.875
Expected answer: 103/8
Correct? Yes
Problem: Upon reviewing the original video message, Zorg realised that the first part of the video message was actually half as long at 4/8 hours instead of 4/4. The second part of the message still remains 11/1 hour long. What is the total length of the message that Zorg has corrected?
LLemma 7B:
Reasoning: 4/8 = 1/2, so the first part of the message is 1/2 hour long. 11/1 = 11, so the second part of the message is 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?
LLemma 7B:
Reasoning: Each pond has 10 / 5 = <<10/5=2>>2 ducks. Each pool has 8 / 10 = <<8/10=0.8>>0.8 fish. There are 2 + 0.8 = <<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?
LLemma 7B:
Reasoning: Each lily pad has 12 / 4 = <<12/4=3>>3 frogs. There are 2.8 + 3 = <<2.8+3=5.8>>5.8 animals on each setting combined. ### Answer: 5.8
Expected answer: 29/5
Correct? No
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?
LLemma 7B:
Reasoning: Each pond has 2 / 5 = <<2/5=0.4>>0.4 ducks. Each pool has 8 / 10 = <<8/10=0.8>>0.8 fish. There are 0.4 + 0.8 = <<0.4+0.8=1.2>>1.2 animals in each pond and pool combined. ### Answer: 1.2
Expected answer: 6/5
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?
LLemma 7B:
Reasoning: 15/11 = <<15/11=1.3636363636363636363636363636364>> 16/15 = <<16/15=1.06666666666666666666666666666667>> 1.3636363636363636363636363636364 + 1.06666666666666666666666666666667 = <<1.4296363636363636363636363636364>> ### Answer: 1.4296363636363636363636363636364
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?
LLemma 7B:
Reasoning: 13/18 + 4/6 = <<13/18+4/6=13/18+2/3=13/18+8/18=21/18=13/9=1 3/9=1 1/3=3/3=1>>1 1/3 tons of soap in total each day. ### Answer: 1 1/3
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?
LLemma 7B:
Reasoning: Mark cut off 13/12 feet from his sleeping bag. The length of his sleeping bag now is 19/2 - 13/12 = <<19/2-13/12=11/12>>11/12 feet. ### Answer: 11/12
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?
LLemma 7B:
Reasoning: Mary feeds 6/20 pounds of food to the monkeys, and 18/15 pounds of food to the giraffes. Mary feeds 6/20 + 18/15 = <<6/20+18/15=1.08>>1.08 pounds of food to the monkeys and giraffes. ### Answer: 1.08
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?
LLemma 7B:
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?
LLemma 7B:
Reasoning: The jeweler has 5/14 + 18/19 = <<5/14 + 18/19=11/19>>11/19 pounds of silver. The jeweler has 11/19 + 5/14 = <<11/19 + 5/14=11/19>>11/19 pounds of silver to make rings. ### Answer: 11/19
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?
LLemma 7B:
Reasoning: The turtle is 11-15/15 = <<11-15/15=11-1=10>>10 meters from its starting point after these two movements. ### 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?
LLemma 7B:
Reasoning: The turtle is 10+15/20 = <<10+15/20=10+3/4=10.75>>10.75 meters from its original starting point now. ### 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?
LLemma 7B:
Reasoning: The turtle is 11-15/8 = <<11-15/8=11-15/8=11-1.875=9.125>>9.125 meters from its starting point after these two movements. ### 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?
LLemma 7B:
Reasoning: Chloe has <<19/2=9.5>>9.5 ounces of chocolate. Chloe eats <<17/2=8.5>>8.5 ounces of chocolate. Chloe has <<9.5-8.5=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?
LLemma 7B:
Reasoning: Chloe has <<1-4/14=13/14>>13/14 ounces of chocolate. ### Answer: 13/14
Expected answer: 9/7
Correct? No
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?
LLemma 7B:
Reasoning: Chloe had <<19/2=9.5>>9.5 ounces of chocolate. Chloe ate <<9/2=4.5>>4.5 ounces of chocolate. Chloe had <<9.5-4.5=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?
LLemma 7B:
Reasoning: Sammy's backpack can hold 20/9 + 8/4 = <<20/9+8/4=100/36=25/9>>25/9 liters. ### Answer: 25/9
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?
LLemma 7B:
Reasoning: Captain Hook has 11/8 + 5/5 = <<11/8+5/5=11/8+5/5>>11/8+5/5 ounces of gold. ### Answer: 11/8+5/5
Expected answer: 19/8
Correct? Yes
Problem: After counting his newly found gold, Captain Hook discovers an additional 7/11 ounces of gold hidden in a small pouch he had forgotten about. What is the total weight of all the gold Captain Hook now has?
LLemma 7B:
Reasoning: Captain Hook has 11/8 + 5/5 + 7/11 = <<11/8+5/5+7/11=11/8+5/5+7/11>>11/8+5/5+7/11 ounces of gold. ### Answer: 11/8+5/5+7/11
Expected answer: 265/88
Correct? No
Problem: In the previous treasure hunt, Captain Hook had originally found 11/8 ounces of gold. But let's say, instead of finding 5/5 ounces of gold as he did in his latest treasure hunt, he discovered 7/5 ounces of gold. How much total weight of gold would Captain Hook have had then?
LLemma 7B:
Reasoning: Captain Hook would have had 11/8 + 7/5 = <<11/8+7/5=11/8+7/5>>11/8+7/5 ounces of gold. ### Answer: 11/8+7/5
Expected answer: 111/40
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?
LLemma 7B:
Reasoning: Jake originally had 9/10 of a dollar. Jake received 20/15 of a dollar. Jake has 9/10 + 20/15 = <<(9/10)+(20/15)>> of a dollar. ### Answer: 1 1/3
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?
LLemma 7B:
Reasoning: 5/2 + 20/14 = <<5/2 + 20/14 = 100/28 + 400/28 = 500/28 = 17.8571428571428571428571428571429>>17.8571428571428571428571428571429 feet ### Answer: 17.8571428571428571428571428571429
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?
LLemma 7B:
Reasoning: John has 5-12/9 = <<5-12/9=1.1111111111111112>>1.1111111111111112 shirts left. ### Answer: 1.1111111111111112
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?
LLemma 7B:
Reasoning: Bob's jacket is 14/3 - 14/16 = <<14/3 - 14/16=14/48=7/24>>7/24 meters long after the alteration. ### Answer: 7/24
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?
LLemma 7B:
Reasoning: 2/6 + 14/7 = <<2/6 + 14/7>> 2/6 + 14/7 = 2*7/6*7 + 14*6/7*6 = <<2*7/6*7 + 14*6/7*6>> = 14/42 + 84/42 = <<14/42 + 84/42>> = 98/42 = <<98/42>> ### Answer: 98/42
Expected answer: 7/3
Correct? Yes
Problem: Following his patrol, Officer Max then begins his shift at the police station which typically lasts 20 hours. How many hours are left in his shift after he finishes his paperwork and neighborhood patrol?
LLemma 7B:
Reasoning: 20 - 98/42 = <<20 - 98/42>> 20 - 98/42 = 20*42/1 - 98/42 = <<20*42/1 - 98/42>> = 840/42 - 98/42 = <<840/42 - 98/42>> = 742/42 = <<742/42>> ### Answer: 742/42
Expected answer: 53/3
Correct? Yes
Problem: Now consider a day when Officer Max spends 2/5 part of an hour, instead of 2/6 part of an hour, completing paperwork but still spends 14/7 parts of an hour patrolling the neighborhood. How much time, in parts of an hour, does Officer Max use for these two tasks in this scenario?
LLemma 7B:
Reasoning: 2/5 + 14/7 = <<2/5 + 14/7>> 2/5 + 14/7 = 2*7/5*7 + 14*5/7*5 = <<2*7/5*7 + 14*5/7*5>> = 14/35 + 70/35 = <<14/35 + 70/35>> = 84/35 = <<84/35>> ### Answer: 84/35
Expected answer: 12/5
Correct? Yes
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?
LLemma 7B:
Reasoning: 10/12 + 3/8 = <<10/12 + 3/8 = 10/12 + 3/8*3/3 = 10/12 + 9/24 = 20/24 + 9/24 = 29/24>>29/24 hours. John spent 29/24 hours watching in total. ### Answer: 29/24
Expected answer: 29/24
Correct? Yes
Problem: If John watched a movie for 10/12 of an hour and then watched a TV show for another 3/8 of an hour, and then repeated this same routine, what is the total time he spent watching in hours?
LLemma 7B:
Reasoning: 10/12 + 3/8 + 10/12 + 3/8 = <<10/12 + 3/8 + 10/12 + 3/8 = 10/12 + 3/8 + 10/12 + 3/8*2/2 = 10/12 + 3/8 + 20/12 + 6/8 = 30/12 + 9/8 = 30/12 + 9/8*6/6 = 30/12 + 54/48 = 30/12 + 27/24 = 57/24>>57/24 hours. John spent 57/24 hours watching in total. ### Answer: 57/24
Expected answer: 29/12
Correct? No
Problem: If instead of watching the movie for 10/12 of an hour, John watched it for 10/7 of an hour, and he still watched the TV show for another 3/8 of an hour, what is the total time he spent watching in hours?
LLemma 7B:
Reasoning: 10/7 + 3/8 = <<10/7 + 3/8 = 10/7 + 3/8*7/7 = 10/7 + 21/56 = 50/56 + 21/56 = 71/56>>71/56 hours. John spent 71/56 hours watching in total. ### Answer: 71/56
Expected answer: 101/56
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?
LLemma 7B:
Reasoning: Mr. Carpenter takes 5/3 + 10/13 = <<5/3+10/13=15/13>>15/13 hours to build a chair from start to finish. ### Answer: 15/13
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?
LLemma 7B:
Reasoning: The diameter of a small bead is 8/4 = <<8/4=2>>2 mm and the diameter of a large bead is 15/2 = <<15/2=7.5>>7.5 mm. The diameter of a small and a large bead is 2+7.5 = <<2+7.5=9.5>>9.5 mm. ### Answer: 9.5
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?
LLemma 7B:
Reasoning: The diameter of a small bead is 8/4 = <<8/4=2>>2 mm and the diameter of a large bead is 5/2 = <<5/2=2.5>>2.5 mm. The diameter of a small and a large bead is 2+2.5 = <<2+2.5=4.5>>4.5 mm. ### Answer: 4.5
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?
LLemma 7B:
Reasoning: 11/18 + 8/2 = <<11/18 + 8/2>> 11/18 + 8/2 = <<11/18 + 8/2>> ### Answer: 11/18 + 8/2
Expected answer: 83/18
Correct? Yes
Problem: Let's reconsider our previous journey of the rocket. Assume that instead of traveling 8/2 light-years towards a distant star after reaching the alien planet, the rocket only traveled 8/13 light-years. In this case, what would be the total distance covered by the rocket?
LLemma 7B:
Reasoning: 11/18 + 8/13 = <<11/18 + 8/13>> 11/18 + 8/13 = <<11/18 + 8/13>> ### Answer: 11/18 + 8/13
Expected answer: 287/234
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?
LLemma 7B:
Reasoning: Johnathan needs 12/14 + 8/5 = <<12/14 + 8/5 = 12/14 + 16/14 = 28/14 = 28/14 * 100/100 = 2800/1400 = 14/7 = 2>>2 yards of fabric to create his sleeping bag. ### Answer: 2
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?
LLemma 7B:
Reasoning: 5/4 + 1/2 = <<5/4+1/2=11/4>>11/4 acres of pine and oak trees in the forest. ### Answer: 11/4
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?
LLemma 7B:
Reasoning: Jake has 12/7 + 2/14 = <<12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=12/7+2/14=
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?
LLemma 7B:
Reasoning: The difference in kilograms of the fruit from summer to winter is 10/4 - 12/20 = <<10/4 - 12/20 = 15/20 = 3/4>>3/4 kg. ### Answer: 3/4
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?
LLemma 7B:
Reasoning: 13/5 - 15/16 = <<13/5 - 15/16=13/5 - (15*4)/(16*5) = (13*16 - 15*4)/(5*16) = (208-60)/80 = 148/80 = 7/4>>7/4 minutes. The routine lasts 7/4 = <<7/4=1.75>>1.75 minutes after shortening it. ### Answer: 1.75
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?
LLemma 7B:
Reasoning: Miss Daisy has <<19/6-17/20=19/6-85/120=19/6-5/12=11/12>>11/12 kg of fertilizers left to use on her other flowers. ### Answer: 11/12
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?
LLemma 7B:
Reasoning: The distance increases by 4/16 + 20/6 = <<4/16 + 20/6 = 100/24 = 50/12 = 25/6>>25/6 meters this year. ### Answer: 25/6
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?
LLemma 7B:
Reasoning: Bob has 11/3 + 12/19 = <<11/3+12/19=11/3*19/19+12/19*3/3=11*19/3*3+12*3/19*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19=11*19+12*3/3*19
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?
LLemma 7B:
Reasoning: 5/5 + 12/18 = <<5/5+12/18=13/18>>13/18 miles in total. ### Answer: 13/18
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?
LLemma 7B:
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. 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?
LLemma 7B:
Reasoning: Jim and Mary's combined typing speed is 3.5-2 = <<3.5-2=1.5>>1.5 words per second. Their new combined typing speed is 1.5-2 = <<1.5-2=-0.5>>-0.5 words per second. ### Answer: -0.5
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?
LLemma 7B:
Reasoning: 9/7 - 1/9 = <<(9/7)*(9/9)-(1/9)*(7/7)>>(81/63)-(7/63)=<<81/63-7/63>>80/63=1 17/63 miles. Max rode his scooter 1 17/63 miles in the afternoon. ### Answer: 1 17/63
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?
LLemma 7B:
Reasoning: The clown rode a unicycle for 9/8 hours, and then she juggled for 2/10 hours. 9/8 + 2/10 = <<(9/8 + 2/10)*100/100>>(9/8 + 2/10)*100/100 = <<(900/800 + 200/800)*100/100>>(900/800 + 200/800)*100/100 = <<(1100/800)*100/100>>(1100/800)*100/100 = <<110000/80000>>110000/80000 = <<11/8>>11/8 = <<1.375>>1.375 hours in total did she perform. ### Answer: 1.375
Expected answer: 53/40
Correct? No
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?
LLemma 7B:
Reasoning: 7/2 + 1/2 = <<7/2+1/2=4>>4 kg ### Answer: 4
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?
LLemma 7B:
Reasoning: 4 + 16/3 = <<4+16/3=14/3>>14/3 kg ### Answer: 14/3
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?
LLemma 7B:
Reasoning: 7/2 + 1/20 = <<7/2+1/20=3.5>>3.5 kg ### Answer: 3.5
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?
LLemma 7B:
Reasoning: 18/8 + 11/7 = <<18/8 + 11/7>> ### Answer: 1.5
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?
LLemma 7B:
Reasoning: 3/10 + 16/20 = <<3/10 + 16/20=19/20>>19/20 of a mile. The UFO traveled 19/20 of a mile. ### Answer: 19/20
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?
LLemma 7B:
Reasoning: 4/14 + 20/4 = <<4/14+20/4=1/14+5=6/14=3/7>>3/7 of a chair is made by both machines in one hour. ### Answer: 3/7
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?
LLemma 7B:
Reasoning: 2/4 + 7/10 = <<2/4+7/10=17/20>>17/20 miles. ### Answer: 17/20
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?
LLemma 7B:
Reasoning: Lisa has 8/18+18/8 = <<8/18+18/8=1>>1 gallon of milk. ### Answer: 1
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?
LLemma 7B:
Reasoning: The tree has grown 12/6/10 = <<12/6/10=1.2>>1.2 feet this month. ### Answer: 1.2
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?
LLemma 7B:
Reasoning: 13/11 + 8/20 = <<13/11+8/20=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=65/55=13/11+2/5=6
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?
LLemma 7B:
Reasoning: Captain Jack must travel 17/20 + 15/3 = <<17/20 + 15/3>> km to reach the treasure. ### Answer: <<17/20 + 15/3>>
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?
LLemma 7B:
Reasoning: Sarah collected 11/20 of a pound of firewood. Alex collected 9/7 pounds. Sarah and Alex collected 11/20 + 9/7 = <<11/20 + 9/7>> pounds of firewood. ### Answer: 1.17 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?
LLemma 7B:
Reasoning: Captain Bill sailed 19/5 + 12/15 = <<19/5+12/15=19/5+12/15=117/15>>117/15 miles north. Captain Bill sailed 117/15 miles north in total. ### Answer: 117/15
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?
LLemma 7B:
Reasoning: 19/17 + 9/4 = <<19/17+9/4=19/17+36/48=19/17+9/8=19/17+18/17=37/17=2 1/17>>2 1/17 pounds of meat per sandwich. ### Answer: 2 1/17
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?
LLemma 7B:
Reasoning: Lucy's sleeping bag is 18/19 meter long. Lucy got an extension for her sleeping bag which made it 8/11 meter longer. The total length of the sleeping bag is 18/19 + 8/11 = <<18/19 + 8/11=1.55>>1.55 meters. ### Answer: 1.55
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?
LLemma 7B:
Reasoning: 10/13+8/2=<<10/13+8/2=10/13+16/2=10/13+8/13=18/13>>18/13 gallons of water are there in the container now. ### Answer: 18/13
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?
LLemma 7B:
Reasoning: Mandy has 9/2 - 1/4 = <<9/2-1/4=13/4>>13/4 KGs of apples left. ### Answer: 13/4
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?
LLemma 7B:
Reasoning: John spends 12/7 + 3/9 = <<12/7+3/9=12/7+3/7=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?
LLemma 7B:
Reasoning: Peggy the Penguin traveled 5/4 miles and then 1/12 miles. Peggy the Penguin traveled 5/4 + 1/12 = <<5/4+1/12=11/12>>11/12 miles. ### Answer: 11/12
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?
LLemma 7B:
Reasoning: 4+11/12 = <<4+11/12=55/12>>55/12 acres in total. ### Answer: 55/12
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?
LLemma 7B:
Reasoning: 11/4 + 5/17 = <<11/4+5/17=11*17/4*17+5*4/4*17=187/68>>187/68 yards of fabric. ### Answer: 187/68
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?
LLemma 7B:
Reasoning: Jacob has 11/2 - 5/16 = <<11/2 - 5/16=10.3125>>10.3125 feet of wire remaining. ### Answer: 10.3125
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?
LLemma 7B:
Reasoning: Samantha has 4-17/14 = <<4-17/14=1/7>>1/7 fluid ounces left after that week. ### Answer: 1/7
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?
LLemma 7B:
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?
LLemma 7B:
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=1.5>>1.5 stickers. Each friend gets 2+1.5 = <<2+1.5=3.5>>3.5 candies and stickers in total. ### Answer: 3.5
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?
LLemma 7B:
Reasoning: 4/13 + 11/5 = <<4/13 + 11/5 = 103/65>>103/65 hours. ### Answer: 103/65
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?
LLemma 7B:
Reasoning: Jane cut 10/12 + 10/10 = <<10/12+10/10=10/6>>10/6 yards of fabric in total. ### Answer: 10/6
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?
LLemma 7B:
Reasoning: 11/12 + 9/10 = <<11/12+9/10=11/12+9/10=110/120+108/120=218/120=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/60=109/6
Expected answer: 109/60
Correct? Yes
Problem: A fairy sprinkles 11/12 oz of magic dust over an enchanted field. She then sprinkles an additional 9/10 oz of dust over a grove of enchanted apple trees. Then, she flies over to a nearby forest where she originally had 14/3 oz of magic dust. After using the dust over the field and apple trees, how much magic dust is left for the fairy now?
LLemma 7B:
Reasoning: 14/3 - 11/12 - 9/10 = <<14/3 - 11/12 - 9/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/12 - 90/10=140/3 - 110/1
Expected answer: 57/20
Correct? No
Problem: A fairy sprinkles 11/12 oz of magic dust over an enchanted field. She then planned to sprinkle an additional 9/10 oz of dust over a grove of enchanted apple trees, but she accidentally sprinkles more, as much as 16/10 oz. What is the total amount of magic dust the fairy used now?
LLemma 7B:
Reasoning: 11/12 + 9/10 + 16/10 = <<11/12+9/10+16/10=11/12+9/10+16/10=110/120+108/120+160/120=284/120=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/60=142/6
Expected answer: 151/60
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?
LLemma 7B:
Reasoning: 3/11 + 8/10 = <<3/11+8/10=11/110+80/110=99/110=0.87272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727272727
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?
LLemma 7B:
Reasoning: You remove 14/9 pages from the letter. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9 pages from 4/1 pages. You remove 14/9
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?
LLemma 7B:
Reasoning: Anne painted 16/20 = <<16/20=0.8>>0.8 of the table, and then Bob painted an additional 5/20 = <<5/20=0.25>>0.25 of the table. Anne painted 0.8+0.25 = <<0.8+0.25=1.05>>1.05 of the table, and then Bob painted an additional 0.25 of the table. Anne painted 1.05 of the table, and then Bob painted an additional 0.25 of the table. Anne painted 1.05+0.25 = <<1.05+0.25=1.3>>1.3 of the table in total. ### Answer: 1.3
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?
LLemma 7B:
Reasoning: Alpha shines 17/3 times brighter than an average star, so it shines <<17/3=5.666666666666667>> times brighter than an average star. Bravo shines 20/16 times as bright as an average star, so it shines <<20/16=1.25>> times brighter than an average star. Alpha shines <<5.666666666666667+1.25=6.916666666666667>> times brighter than an average star. Bravo shines <<5.666666666666667+1.25=6.916666666666667>> times brighter than an average star. ### 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?
LLemma 7B:
Reasoning: Alpha shines 8/3 times brighter than an average star, so it shines <<8/3=2.6666666666666665>> times brighter than an average star. Bravo shines 20/16 times as bright as an average star, so it shines <<20/16=1.25>> times brighter than an average star. Alpha shines <<2.6666666666666665+1.25=3.9166666666666665>> times brighter than an average star. Bravo shines <<5.666666666666667+1.25=6.916666666666667>> times brighter than an average star. ### Answer: 6.916666666666667
Expected answer: 47/12
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?
LLemma 7B:
Reasoning: 17/20 + 18/8 = <<17/20+18/8=17/20+9/10=17/20+(9/10)*(2/2)=(17/20)*(2/2)+(9/10)*(2/2)=(17/20)+(9/10)=(17+9)/(20)=26/20=13/10>>13/10 kg of apples are in the store in total. ### Answer: 13/10
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?
LLemma 7B:
Reasoning: The bus travelled 12/20 + 12/12 = <<12/20+12/12=12/20+3/5=12/20+12/20=24/20=12/10=6/5>>6/5 miles in total. ### Answer: 6/5
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?
LLemma 7B:
Reasoning: The shark swims 3/9 + 13/5 = <<3/9 + 13/5 = 107/45>>107/45 miles in total in these two hours. ### Answer: 107/45
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?
LLemma 7B:
Reasoning: The drummer hits the first beat every 17/17 seconds and the second beat every 2/12 seconds. The drummer hits the two beats together every 17/17 seconds + 2/12 seconds = <<17/17+2/12=17/17+1/6=17/17+17/102=1009/102>>1009/102 seconds. ### Answer: 1009/102
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?
LLemma 7B:
Reasoning: 12/17 + 8/19 = <<12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 + 8/19=12/17 + 16/38=12/17 +
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?
LLemma 7B:
Reasoning: The first segment was 18/19 of a mile and the second was 9/17 of a mile. The entire flight was 18/19 + 9/17 = <<18/19 + 9/17>>. ### Answer: 1.001
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?
LLemma 7B:
Reasoning: 13/10 + 14/15 = <<13/10 + 14/15 = 13/10 + 28/30 = 41/30 = 1.36666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
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?
LLemma 7B:
Reasoning: The new speed is 13/6 + 3/16 = <<13/6 + 3/16=13/4>>13/4 feet per second. ### Answer: 13/4
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?
LLemma 7B:
Reasoning: Scarlett has 16/10 - 1/20 = <<16/10-1/20=15/20=3/4>>3/4 gallons of red paint left. ### Answer: 3/4
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?
LLemma 7B:
Reasoning: 12 - 2/5 = <<12-2/5=12-4/5=12*5/5-4/5=5-4/5=1>>1 ### Answer: 1
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?
LLemma 7B:
Reasoning: 2 - 10/15 = <<2 - 10/15 = 2 - 2/3 = 4/3 = 1 1/3>>1 1/3 miles The new altitude of the plane is 1 1/3 miles. ### Answer: 1 1/3
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?
LLemma 7B:
Reasoning: 2 - 12/15 = <<2 - 12/15 = 2 - 4/5 = 6/5 = 1 1/5>>1 1/5 miles The new altitude of the plane is 1 1/5 miles. ### Answer: 1 1/5
Expected answer: 6/5
Correct? Yes
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?
LLemma 7B:
Reasoning: The first slide is 6/19 meters long, and the second slide is 17/4 meters long. The total length of the slides is <<6/19+17/4=6/19+68/40=102/40=25/10=2.5>>2.5 meters. ### Answer: 2.5
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?
LLemma 7B:
Reasoning: The fireplace burns 4/15 + 14/15 = <<4/15+14/15=18/15>>18/15 cords in the early morning. The fireplace burns 1-18/15 = <<1-18/15=7/15>>7/15 cords in the late night. The fireplace burns 18/15 + 7/15 = <<18/15+7/15=25/15=1>>1 cord in total in one hour split between the early morning and late night. ### Answer: 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?
LLemma 7B:
Reasoning: 9/20 + 11/7 = <<(9*7)/(20*7)+(11*20)/(7*20)=(63)/(140)+(220)/(140)=(63+220)/(140)=(283)/(140)>>(283)/(140) light years. ### Answer: (283)/(140)
Expected answer: 283/140
Correct? Yes
Problem: After traveling ((9 / 20) + (11 / 7)) light years towards earth, the alien continues its journey for an additional 14/2 light years. How many light years in total has the alien traveled?
LLemma 7B:
Reasoning: 9/20 + 11/7 + 14/2 = <<(9*7)/(20*7)+(11*20)/(7*20)+(14*10)/(2*10)=(63)/(140)+(220)/(140)+(140)/(140)=(63+220+140)/(140)=(423)/(140)>>(423)/(140) light years. ### Answer: (423)/(140)
Expected answer: 1263/140
Correct? No
Problem: The alien originally travelled ((9 / 20) + (11 / 7)) light years towards earth. But what if instead, the alien had only travelled (9 / 20) + (11 / 11) light years to start with? How many light years would the alien have travelled then?
LLemma 7B:
Reasoning: 9/20 + 11/11 = <<(9*11)/(20*11)+(11*20)/(11*20)=(99)/(220)+(220)/(220)=(99+220)/(220)=(319)/(220)>>(319)/(220) light years. ### Answer: (319)/(220)
Expected answer: 29/20
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?
LLemma 7B:
Reasoning: Bob has 10/2 = <<10/2=5>>5 cucumbers. He adds 1/7 of another cucumber. Bob has 5 + 1/7 = <<5+1/7=35/7>>35/7 cucumbers. ### Answer: 35/7
Expected answer: 36/7
Correct? No