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 34B:
Reasoning: Kyle threw the ball for 18/4 = <<18/4=4.5>>4.5 yards. Lisa threw the ball for 19/9 = <<19/9=2.111111111111111>>2.111111111111111 yards. The ball traveled 4.5+2.111111111111111 = <<4.5+2.111111111111111=6.611111111111111>>6.611111111111111 yards in total. ### 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?
LLemma 34B:
Reasoning: The ball traveled 6.611111111111111 yards in total. The ball bounced 3/13 = <<3/13=0.230769230769231>>0.230769230769231 yards. The remaining distance is 6.611111111111111-0.230769230769231 = <<6.611111111111111-0.230769230769231=6.38034188034188>>6.38034188034188 yards. ### Answer: 6.38034188034188
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?
LLemma 34B:
Reasoning: Kyle threw the ball for 15/4 = <<15/4=3.75>>3.75 yards. Lisa threw the ball for 19/9 = <<19/9=2.111111111111111>>2.111111111111111 yards. The ball traveled 3.75+2.111111111111111 = <<3.75+2.111111111111111=5.861111111111111>>5.861111111111111 yards in total. ### Answer: 5.861111111111111
Expected answer: 211/36
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 34B:
Reasoning: Johnnie the monkey was given 18/7+12/14 = <<18/7+12/14=18/7+6/7=24/7>>24/7 bananas in the afternoon. In total, Johnnie the monkey was given 18/7+24/7 = <<18/7+24/7=42/7>>42/7 bananas. ### Answer: 42/7
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 34B:
Reasoning: The bottom of the door is 9/10 - 4/19 = <<9/10-4/19=11/19>>11/19 inches from the ceiling. The top of the door is 4/19 - 9/10 = <<4/19-9/10=-11/95>>-11/95 inches from the floor. ### Answer: 11/19, -11/95
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 34B:
Reasoning: Ralph uses 15/11 - 17/3 = <<15/11-17/3=-1/33>>-1/33 liters of apple juice. There are 17/3 - 15/11 = <<17/3-15/11=1/33>>1/33 liters of apple juice left unused. ### Answer: 1/33
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?
LLemma 34B:
Reasoning: Billy rolled back 17/20 of a mile. Billy rolled back 17/20 = <<17/20=0.85>>0.85 miles. Billy rolled forward 4-0.85 = <<4-0.85=3.15>>3.15 miles. ### 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?
LLemma 34B:
Reasoning: Billy rolled back 17/20 of a mile. Billy rolled back 17/20 = <<17/20=0.85>>0.85 miles. Billy rolled forward 6-0.85 = <<6-0.85=5.15>>5.15 miles. ### Answer: 5.15
Expected answer: 103/20
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 34B:
Reasoning: The rocket traveled 15/3+2/7 = <<15/3+2/7=17/3>>17/3 light years in total. ### Answer: 17/3
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 34B:
Reasoning: Captain Silverbeard found 10/13+16/19 = <<10/13+16/19=10/13+16/19>>10/13+16/19 of the treasure map. ### Answer: 10/13+16/19
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 34B:
Reasoning: The hiker walked 9/6+2/16 = <<9/6+2/16=15/8>>15/8 miles in total. ### Answer: 15/8
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 34B:
Reasoning: Jessica has 16/9-4/13 = <<16/9-4/13=12/9>>12/9 cubic feet of sand left in her sandbox. ### Answer: 12/9
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 34B:
Reasoning: 15/12 + 17/17 = <<15/12+17/17=15/12+1=15/12+12/12=27/12>>27/12 meters. ### Answer: 27/12
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?
LLemma 34B:
Reasoning: Jacob starts with 27/12 meters of rope. If he doubles the length of the rope, he will have 27/12 + 27/12 = <<27/12+27/12=27/12+12/12=27/12+12/12=39/12>>39/12 meters of rope. ### Answer: 39/12
Expected answer: 9/2
Correct? No
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?
LLemma 34B:
Reasoning: 7/12 + 17/17 = <<7/12+17/17=7/12+1=7/12+12/12=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?
LLemma 34B:
Reasoning: Mark has 13/4 = <<13/4=3.25>>3.25 pairs of pants from incomplete sets. Mark has 1+3.25 = <<1+3.25=4.25>>4.25 pairs of pants in total. ### Answer: 4.25
Expected answer: 17/4
Correct? Yes
Problem: Mark already had 1 full pair of pants and another 13/4 pairs from various incomplete sets. If he goes shopping and buys an additional 13/3 pairs of pants, how many pairs of pants does he have in total now?
LLemma 34B:
Reasoning: Mark has 13/4 = <<13/4=3.25>>3.25 pairs of pants from incomplete sets. Mark has 1+3.25 = <<1+3.25=4.25>>4.25 pairs of pants in total. Mark buys 13/3 = <<13/3=4.33>>4.33 pairs of pants. Mark has 4.25+4.33 = <<4.25+4.33=8.58>>8.58 pairs of pants in total now. ### Answer: 8.58
Expected answer: 103/12
Correct? No
Problem: Instead of starting with 1 full pair of pants and another 13/4 pairs, let's say Mark originally had 1 full pair of pants and 9/4 pairs from various incomplete sets. How many pairs of pants would he then have in total?
LLemma 34B:
Reasoning: Mark has 9/4 = <<9/4=2.25>>2.25 pairs of pants from incomplete sets. Mark has 1+2.25 = <<1+2.25=3.25>>3.25 pairs of pants in total. ### Answer: 3.25
Expected answer: 13/4
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 34B:
Reasoning: Miss Jenny spent 8/8+20/19 = <<8/8+20/19=10/9>>10/9 hours grading papers in total. ### Answer: 10/9
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 34B:
Reasoning: The cloud was observed at a height of 12/3 kms = <<12/3=4>>4 kms. The cloud later ascended by 15/12 kms = <<15/12=5/4>>5/4 kms. The resultant height of the cloud from the ground = 4+5/4 = <<4+5/4=21/4>>21/4 kms. ### Answer: 21/4
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 34B:
Reasoning: The cloud was observed at a height of 12/3 kms = <<12/3=4>>4 kms. The cloud later ascended by 7/12 kms = <<7/12=1/2>>1/2 kms. The resultant height of the cloud from the ground = 4+1/2 = <<4+1/2=9/2>>9/2 kms. ### Answer: 9/2
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 34B:
Reasoning: Jack rides his scooter 17/15+3/9 = <<17/15+3/9=10/5=2>>2 miles in total. ### Answer: 2
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 34B:
Reasoning: The logs burn for 4*1/16 = <<4*1/16=1/4>>1/4 of an hour. The twigs burn for 16*1/12 = <<16*1/12=4/3>>4/3 of an hour. The total burn time is 1/4 + 4/3 = <<1/4+4/3=13/12>>13/12 of an hour. ### Answer: 13/12
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?
LLemma 34B:
Reasoning: The ring maker used 12/16+16/2 = <<12/16+16/2=12/8>>12/8 ounces of silver in total. ### Answer: 12/8
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?
LLemma 34B:
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?
LLemma 34B:
Reasoning: The tree produced 10/9+17/11 = <<10/9+17/11=100/99>>100/99 bushels of apples in one day. ### 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 34B:
Reasoning: Sam's binoculars increase his range of sight by 3/14 of a mile. Joe's binoculars increase his range of sight by 16/14 of a mile. Their combined range increase is 3/14+16/14 = <<3/14+16/14=19/14>>19/14 of a mile. ### 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?
LLemma 34B:
Reasoning: Maria uses 15/10+9/18 = <<15/10+9/18=27/18>>27/18 yards of fabric for these two sections. ### Answer: 27/18
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 34B:
Reasoning: The turtle walked 10/5-5/16 = <<10/5-5/16=12/16=3/4>>3/4 miles forward. ### Answer: 3/4
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?
LLemma 34B:
Reasoning: The painter used 18/11+1/8 = <<18/11+1/8=20/11>>20/11 liters of paint in total. ### Answer: 20/11
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 34B:
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=1.5>>1.5 tasks per minute. ### Answer: 1.5
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 34B:
Reasoning: 12/13 + 3/2 = <<12/13+3/2=12/13+18/13=30/13>>30/13 pounds of gold. ### Answer: 30/13
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 34B:
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Expected answer: 12
Correct? No
Problem: In a park, 10 ducks are equally distributed among 5 ponds, implying each pond has 10 / 5 ducks. In the same park, 8 fish are distributed among 10 small pools, with each pool having 8 / 10 fish. How many animals are there in each pond and pool combined?
LLemma 34B:
Reasoning: In each pond, there are 10 / 5 = <<10/5=2>>2 ducks and 8 / 10 = <<8/10=0.8>>0.8 fish. In each pond and pool combined, there are 2 + 0.8 = <<2+0.8=2.8>>2.8 animals. ### 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 34B:
Reasoning: In each pond and pool combined, there are 2 + 0.8 = <<2+0.8=2.8>>2.8 animals. In each lily pad, there are 12 / 4 = <<12/4=3>>3 frogs. In each pond, pool, and lily pad combined, there are 2.8 + 3 = <<2.8+3=5.8>>5.8 animals. ### 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 34B:
Reasoning: In each pond, there are 2 / 5 = <<2/5=0.4>>0.4 ducks and 8 / 10 = <<8/10=0.8>>0.8 fish. In each pond and pool combined, there are 0.4 + 0.8 = <<0.4+0.8=1.2>>1.2 animals. ### 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 34B:
Reasoning: 15/11 + 16/15 = <<15/11+16/15=16/5>>16/5 inches represents the total distance between Town A and Town C on the map. ### Answer: 16/5
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 34B:
Reasoning: 13/18 = <<13/18=2/3>>2/3 tons of Soap A and 4/6 = <<4/6=2/3>>2/3 tons of Soap B are produced in a day. 13/18 + 4/6 = <<13/18+4/6=2/3+2/3=4/3>>4/3 tons of soap are produced in total each day. ### Answer: 4/3
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 34B:
Reasoning: Mark cut off 13/12 feet from the sleeping bag. The sleeping bag is now 19/2 - 13/12 = <<19/2-13/12=15/6>>15/6 feet long. ### Answer: 15/6
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 34B:
Reasoning: Mary feeds 6/20 = <<6/20=3/10>>3/10 pounds of food to the monkeys. Mary feeds 18/15 = <<18/15=6/5>>6/5 pounds of food to the giraffes. Mary feeds 3/10+6/5 = <<3/10+6/5=19/10>>19/10 pounds of food in total to the monkeys and giraffes. ### Answer: 19/10
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 34B:
Reasoning: Albert has 20/17+4/1 = <<20/17+4/1=24/17>>24/17 full sets of cards now. ### 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 34B:
Reasoning: The jeweler has 5/14+18/19 = <<5/14+18/19=113/133>>113/133 pounds of silver now. ### Answer: 113/133
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 34B:
Reasoning: The turtle moved 15/15 = <<15/15=1>>1 meter back towards the starting point. The turtle is 11-1 = <<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 34B:
Reasoning: The turtle moved 15/20 = <<15/20=3/4>>3/4 meter towards the starting point. The turtle is 10+3/4 = <<10+3/4=13/4>>13/4 meters from its starting point now. ### Answer: 13/4
Expected answer: 43/4
Correct? No
Problem: Reconsider the previous scenario, but this time the turtle returns 15/8 of a meter back towards the starting point instead of the former 15/15 meters. Now, how many meters is the turtle from its starting point after these two movements?
LLemma 34B:
Reasoning: The turtle moved 15/8 = <<15/8=1.875>>1.875 meters back towards the starting point. The turtle is 11-1.875 = <<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 34B:
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?
LLemma 34B:
Reasoning: Chloe has 1 + 4/14 = <<1+4/14=14/14+4/14=18/14>>18/14 ounces of chocolate now. ### Answer: 18/14
Expected answer: 9/7
Correct? Yes
Problem: Originally, Chloe had a chocolate bar that was 19/2 ounces. What if instead, at the beginning she had eaten a piece that was 9/2 ounces? How many ounces of chocolate would she have had left then?
LLemma 34B:
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?
LLemma 34B:
Reasoning: Sammy's backpack can hold 20/9+8/4 = <<20/9+8/4=38/9>>38/9 liters. ### Answer: 38/9
Expected answer: 38/9
Correct? Yes
Problem: In addition to his already expanded backpack, Sammy finds another tiny side pocket that can carry an extra 3/8 of a liter. What is the total capacity of his backpack now?
LLemma 34B:
Reasoning: Sammy's backpack can hold 38/9+3/8 = <<38/9+3/8=41/9>>41/9 liters. ### Answer: 41/9
Expected answer: 331/72
Correct? No
Problem: Instead of the backpack having an initial capacity of 20/9 liters, let's say it could only carry 20/12 liters. If Sammy still adds the same extra pouch of 8/4 liters, what would the total capacity of his backpack be then?
LLemma 34B:
Reasoning: Sammy's backpack can hold 20/12+8/4 = <<20/12+8/4=32/12>>32/12 liters. ### Answer: 32/12
Expected answer: 11/3
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 34B:
Reasoning: Captain Hook has 11/8+5/5 = <<11/8+5/5=16/8>>16/8 ounces of gold. ### Answer: 16/8
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?
LLemma 34B:
Reasoning: Jake received 20/15 = <<20/15=4/3>>4/3 of a dollar. Jake has 9/10+4/3 = <<9/10+4/3=13/10>>13/10 of a dollar in his wallet now. ### Answer: 13/10
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?
LLemma 34B:
Reasoning: The front portion of the chair is 5/2 feet high. The back portion of the chair is 20/14 feet high. The combined height of the front and back portions of the chair is 5/2+20/14 = <<5/2+20/14=10/7>>10/7 feet. ### Answer: 10/7
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 34B:
Reasoning: John donated 12/9 of 5 = <<12/9*5=10/3=3 1/3>>3 1/3 shirts to charity. John has 5-3 1/3 = <<5-10/3=5/3=1 2/3>>1 2/3 shirts left. ### Answer: 1 2/3
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 34B:
Reasoning: Bob's jacket is 14/3 - 14/16 = <<14/3-14/16=14/4>>14/4 meters long after the alteration. ### Answer: 14/4
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 34B:
Reasoning: Officer Max spends 2/6+14/7 = <<2/6+14/7=14/7+2/6=34/14>>34/14 parts of an hour for these two tasks. ### Answer: 34/14
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?
LLemma 34B:
Reasoning: John watched a movie for 10/12+3/8 = <<10/12+3/8=13/8>>13/8 hours. ### Answer: 13/8
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?
LLemma 34B:
Reasoning: Mr. Carpenter takes 5/3+10/13 = <<5/3+10/13=13/3>>13/3 hours to build a chair from start to finish. ### Answer: 13/3
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 34B:
Reasoning: The small bead is 8/4 mm in diameter and the large bead is 15/2 mm in diameter. The total added diameter is 8/4+15/2 = <<8/4+15/2=11/2>>11/2 mm. ### Answer: 11/2
Expected answer: 19/2
Correct? No
Problem: A rocket travels 11/18 light-years to an alien planet, then travels another 8/2 light-years towards a distant star. What is the total distance covered by the rocket?
LLemma 34B:
Reasoning: 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?
LLemma 34B:
Reasoning: Johnathan needs 12/14+8/5 = <<12/14+8/5=12/7>>12/7 yards of fabric to create his sleeping bag. ### Answer: 12/7
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?
LLemma 34B:
Reasoning: 5/4+1/2 = <<5/4+1/2=9/4>>9/4 acres of pine and oak trees in the forest. ### 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?
LLemma 34B:
Reasoning: Jake has 12/7+2/14 = <<12/7+2/14=14/7>>14/7 yards of fabric. ### Answer: 14/7
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?
LLemma 34B:
Reasoning: The tree produces 10/4 - 12/20 = <<10/4-12/20=1/5>>1/5 kg of fruit in the winter. The difference in kilograms of the fruit from summer to winter is 10/4 - 1/5 = <<10/4-1/5=19/20>>19/20 kg. ### Answer: 19/20
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 34B:
Reasoning: The ballerina shortens her routine by 15/16 minutes. The ballerina's routine is 13/5 - 15/16 = <<13/5-15/16=1/80>>1/80 minutes long after shortening it. ### Answer: 1/80
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 34B:
Reasoning: Miss Daisy uses 17/20 kg of fertilizers on her roses. She has 19/6 - 17/20 = <<19/6-17/20=1/10>>1/10 kg of fertilizers left to use on her other flowers. ### Answer: 1/10
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 34B:
Reasoning: The distance increased by 4/16+20/6 = <<4/16+20/6=10/6>>10/6 meters this year. ### Answer: 10/6
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 34B:
Reasoning: Bob has 11/3+12/19 = <<11/3+12/19=11/3*19/19+12/19*3/3=57/19+36/19=93/19>>93/19 dollars in total in his wallet. ### Answer: 93/19
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 34B:
Reasoning: The shark swam 12/18 miles in the afternoon. The shark swam 5/5+12/18 = <<5/5+12/18=17/18>>17/18 miles in total that day. ### Answer: 17/18
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 34B:
Reasoning: Jim types 20/16 = <<20/16=5/4>>5/4 words per second. Mary types 9/4 = <<9/4=9/4>>9/4 words per second. Jim and Mary type 5/4+9/4 = <<5/4+9/4=14/4>>14/4 words per second in total. ### Answer: 14/4
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 34B:
Reasoning: Jim and Mary type 14/4 = <<14/4=14/4>>14/4 words per second. Jim and Mary type 14/4-2/11 = <<14/4-2/11=28/11>>28/11 words per second after slowing down. ### Answer: 28/11
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 34B:
Reasoning: Max rode his scooter for 9/7-1/9 = <<9/7-1/9=10/7>>10/7 miles in the afternoon. ### Answer: 10/7
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 34B:
Reasoning: The clown performed for 9/8+2/10 = <<9/8+2/10=11/10>>11/10 hours in total. ### Answer: 11/10
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 34B:
Reasoning: Timmy dumps 7/2 kg of sand into his sandbox. Timmy adds 1/2 kg of sand to his sandbox. Timmy has 7/2+1/2 = <<7/2+1/2=8/2=4>>4 kg of sand in his sandbox. ### 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 34B:
Reasoning: Timmy dumps 16/3 kg of sand into the sandbox. Timmy has 4+16/3 = <<4+16/3=12/3+16/3=28/3>>28/3 kg of sand in his sandbox. ### Answer: 28/3
Expected answer: 28/3
Correct? Yes
Problem: In the previous sandbox problem, if Timmy initially dumped 7/2 kg of sand into his sandbox but this time around, he decided to add only 1/20 kg of sand to it instead, how much sand is now in his sandbox?
LLemma 34B:
Reasoning: Timmy dumps 7/2 kg of sand into his sandbox. Timmy adds 1/20 kg of sand to his sandbox. Timmy has 7/2+1/20 = <<7/2+1/20=71/20>>71/20 kg of sand in his sandbox. ### Answer: 71/20
Expected answer: 71/20
Correct? Yes
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 34B:
Reasoning: The wizard used 18/8+11/7 = <<18/8+11/7=39/14>>39/14 ounces of ingredients in total. ### Answer: 39/14
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 34B:
Reasoning: The UFO traveled 16/20 = <<16/20=8/10>>8/10 miles in total. The UFO traveled 3/10+8/10 = <<3/10+8/10=11/10>>11/10 miles in total. ### Answer: 11/10
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?
LLemma 34B:
Reasoning: The UFO traveled 16/18 = <<16/18=8/9>>8/9 miles in total. The UFO traveled 3/10+8/9 = <<3/10+8/9=39/90>>39/90 miles in total. ### Answer: 39/90
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?
LLemma 34B:
Reasoning: The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes 4/14 of a chair every hour. The second machine makes 20/4 chairs every hour. The first machine makes
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 34B:
Reasoning: The blue shark swam for 2/4 miles. The hammerhead shark swam for 7/10 miles. The blue shark and the hammerhead shark swam for 2/4+7/10 = <<2/4+7/10=19/20>>19/20 miles together. ### Answer: 19/20
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 34B:
Reasoning: Lisa has 8/18+18/8 = <<8/18+18/8=10>>10 gallons of milk in total. ### Answer: 10
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 34B:
Reasoning: The tree has grown 12/6 = <<12/6=2>>2 feet due to the fertilizer. The tree has grown 1/10 of its height every month. The tree has grown 1/10 of its height 12 times this month. The tree has grown 12/10 = <<12/10=1.2>>1.2 times its height this month. The tree has grown 1.2+2 = <<1.2+2=3.2>>3.2 feet this month. ### Answer: 3.2
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 34B:
Reasoning: The total area occupied by both tents is 13/11+8/20 = <<13/11+8/20=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/11+2/5=13/
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 34B:
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. Captain Jack must travel 0.85 + 5 = <<0.85+5=5.85>>5.85 km in total to reach the treasure. ### 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?
LLemma 34B:
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. Captain Jack must travel 2.43 + 5 = <<2.43+5=7.43>>7.43 km in total to reach the treasure. ### 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?
LLemma 34B:
Reasoning: Sarah collected 11/20 = <<11/20=0.55>>0.55 pounds of firewood. Alex collected 9/7 = <<9/7=1.28>>1.28 pounds of firewood. Sarah and Alex collected 0.55+1.28 = <<0.55+1.28=1.83>>1.83 pounds of firewood in total. ### Answer: 1.83
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 34B:
Reasoning: Captain Bill sailed 19/5+12/15 = <<19/5+12/15=19/5*3/3+12/15*1/1=57/15+12/15=69/15>>69/15 miles north in total. ### Answer: 69/15
Expected answer: 23/5
Correct? Yes
Problem: After traveling north for a total distance, Captain Bill decided to backtrack and went 20/17 miles south. How many miles away from the original starting point was Captain Bill located then?
LLemma 34B:
Reasoning: Captain Bill was 20/17 miles south of the original starting point. ### Answer: 20/17
Expected answer: 291/85
Correct? No
Problem: After reconsidering the calculations, Captain Bill realized that he actually sailed 19/18 miles north initially instead of 19/5 miles before changing track and sailing an additional 12/15 miles north. In light of this new information, how many miles north did Captain Bill sail in total now?
LLemma 34B:
Reasoning: Captain Bill sailed 19/18+12/15 = <<19/18+12/15=19/18*6/6+12/15*1/1=114/108+12/15=126/108>>126/108 miles north in total. ### Answer: 126/108
Expected answer: 167/90
Correct? No
Problem: A restaurant uses 19/17 pounds of ham and 9/4 pounds of turkey for their signature sandwich. What is the total weight of the two types of meat per sandwich?
LLemma 34B:
Reasoning: The restaurant uses 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=1
Expected answer: 229/68
Correct? No
Problem: Lucy has a sleeping bag that is 18/19 meter long. She got an extension for her sleeping bag which made it 8/11 meter longer. What's the total length of the sleeping bag now?
LLemma 34B:
Reasoning: Lucy's sleeping bag is 18/19+8/11 = <<18/19+8/11=100/199>>100/199 meters long now. ### Answer: 100/199
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 34B:
Reasoning: Sarah adds 8/2 = <<8/2=4>>4 gallons of water into the container. There are 10/13+4 = <<10/13+4=14/13>>14/13 gallons of water in the container now. ### Answer: 14/13
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 34B:
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?
LLemma 34B:
Reasoning: John spent 12/7+3/9 = <<12/7+3/9=15/9>>15/9 hours working on the watch. ### Answer: 15/9
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 34B:
Reasoning: Peggy swam 1/12 miles before resting. Peggy is <<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?
LLemma 34B:
Reasoning: 4+11/12 = <<4+11/12=4 1/12>>4 1/12 acres in total. ### Answer: 4 1/12
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 34B:
Reasoning: 11/4+5/17 = <<11/4+5/17=11/4*17/17+5/17=355/68+5/17=360/68>>360/68 yards of fabric. ### Answer: 360/68
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 34B:
Reasoning: Jacob uses 5/16 feet of wire to fix a guitar. Jacob has 11/2 - 5/16 = <<11/2-5/16=103/16>>103/16 feet of wire remaining. ### Answer: 103/16
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 34B:
Reasoning: Samantha uses 17/14 fluid ounces in one week. She has 4-17/14 = <<4-17/14=1/14>>1/14 fluid ounces 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?
LLemma 34B:
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 34B:
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=1.5454545454545454>>1.5454545454545454 stickers. Each friend gets 2+1.5454545454545454 = <<2+1.5454545454545454=3.5454545454545454>>3.5454545454545454 candies and stickers in total. ### Answer: 3.5454545454545454
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 34B:
Reasoning: The first rainfall lasted for 4/13 hours, and the next rainfall lasted for 11/5 hours. The total time it rained is 4/13 + 11/5 = <<4/13+11/5=11/5>>11/5 hours. ### Answer: 11/5
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?
LLemma 34B:
Reasoning: Jane cuts 10/12+10/10 = <<10/12+10/10=10/6>>10/6 yards of fabric from the blanket 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 34B:
Reasoning: The fairy sprinkled 11/12+9/10 = <<11/12+9/10=101/30>>101/30 oz of dust. ### Answer: 101/30
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?
LLemma 34B:
Reasoning: 3/11 + 8/10 = <<3/11+8/10=11/10>>11/10 ### Answer: 11/10
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 34B:
Reasoning: You remove 14/9 pages from the letter. The letter is now 4/1-14/9 = <<4/1-14/9=1/9>>1/9 pages long. ### Answer: 1/9
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 34B:
Reasoning: Bob painted 5/20 of the table. Anne and Bob painted 16/20+5/20 = <<16/20+5/20=21/20>>21/20 of the table in total. ### Answer: 21/20
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?
LLemma 34B:
Reasoning: Carl painted 11/5 of the table. Anne, Bob, and Carl painted 21/20+11/5 = <<21/20+11/5=111/20>>111/20 of the table in total. ### Answer: 111/20
Expected answer: 13/4
Correct? No
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?
LLemma 34B:
Reasoning: Bob painted 5/14 of the table. Anne and Bob painted 16/20+5/14 = <<16/20+5/14=37/20>>37/20 of the table in total. ### Answer: 37/20
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?
LLemma 34B:
Reasoning: Alpha shines 17/3 = <<17/3=5.666666666666667>>5.666666666666667 times brighter than an average star. Bravo shines 20/16 = <<20/16=1.25>>1.25 times brighter than an average star. If you add up the relative brightness of these two stars, you get 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?
LLemma 34B:
Reasoning: Alpha shines 8/3 = <<8/3=2.666666666666667>>2.666666666666667 times brighter than an average star. Bravo shines 20/16 = <<20/16=1.25>>1.25 times brighter than an average star. If you add up the relative brightness of these two stars, you get 2.666666666666667+1.25 = <<2.666666666666667+1.25=3.916666666666667>>3.916666666666667. ### Answer: 3.916666666666667
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 34B:
Reasoning: There are 17/20+18/8 = <<17/20+18/8=17/5>>17/5 kg of apples in the store in total. ### Answer: 17/5
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 34B:
Reasoning: The bus traveled 12/20+12/12 = <<12/20+12/12=1>>1 mile in total. ### Answer: 1
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 34B:
Reasoning: The shark swims 3/9+13/5 = <<3/9+13/5=16/5>>16/5 miles in total in these two hours. ### Answer: 16/5
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 34B:
Reasoning: The drummer hits the first beat every 17/17 seconds. The drummer hits the second beat every 2/12 seconds. The drummer hits the two beats together every 17/17 + 2/12 = <<17/17+2/12=19/12>>19/12 seconds. ### Answer: 19/12
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 34B:
Reasoning: 12/17 + 8/19 = <<12/17+8/19=20/19>>20/19 cord of wood. ### 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?
LLemma 34B:
Reasoning: The entire flight was 18/19+9/17 = <<18/19+9/17=17/17>>17/17 mile. ### Answer: 17/17
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?
LLemma 34B:
Reasoning: The distance between the first and second cities is 13/10 inches. The distance between the second and third cities is 14/15 inches. The total distance is 13/10 + 14/15 = <<13/10+14/15=19/15>>19/15 inches. ### Answer: 19/15
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 34B:
Reasoning: The balloon's new speed is 13/6+3/16 = <<13/6+3/16=19/8>>19/8 feet per second. ### Answer: 19/8
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 34B:
Reasoning: Scarlett used 1/20 of a gallon for a small art project. Scarlett used 16/10 * 1/20 = <<16/10*1/20=4/50>>4/50 gallons of red paint for a small art project. Scarlett has 16/10 - 4/50 = <<16/10-4/50=156/50>>156/50 gallons of red paint left. ### Answer: 156/50
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 34B:
Reasoning: Susie eats 2/5 of a chocolate bar. Susie eats 2/5*12 = <<2/5*12=2.4>>2.4 chocolate bars. There are 12-2.4 = <<12-2.4=9.6>>9.6 chocolate bars 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?
LLemma 34B:
Reasoning: The plane descends by 10/15 = <<10/15=2/3>>2/3 of a mile. The new altitude of the plane is 2-2/3 = <<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?
LLemma 34B:
Reasoning: The plane descends by 12/15 = <<12/15=4/5>>4/5 of a mile. The new altitude of the plane is 2-4/5 = <<2-4/5=6/5>>6/5 miles. ### Answer: 6/5
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 34B:
Reasoning: The child slid 6/19+17/4 = <<6/19+17/4=103/38>>103/38 meters altogether. ### Answer: 103/38
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 34B:
Reasoning: The fireplace burns 4/15+14/15 = <<4/15+14/15=18/15=6/5=1.2>>1.2 cords of firewood in total in one hour split between the early morning and late night. ### Answer: 1.2
Expected answer: 6/5
Correct? Yes
Problem: If the colonial fireplace burns firewood at a combined rate of 4/15 cords per hour in the early morning and 14/15 cords per hour in the late night, and during the peak hours, it burns an additional 6/5 cords per hour. Then how much total firewood does the fireplace burn in one hour considering early morning, late night, and peak hours?
LLemma 34B:
Reasoning: The fireplace burns 4/15+14/15+6/5 = <<4/15+14/15+6/5=18/15+6/5=24/15=8/5=1.6>>1.6 cords of firewood in total in one hour considering early morning, late night, and peak hours. ### Answer: 1.6
Expected answer: 12/5
Correct? No
Problem: Continuing from the previous scenario, let's suppose the colonial fireplace in the early morning burns firewood at a slightly different rate of 8/15 cords per hour instead of 4/15 cords per hour. The late night burning rate remains the same at 14/15 cords per hour. Given these new circumstances, how much firewood does the fireplace burn in total in one hour split between the early morning and late night?
LLemma 34B:
Reasoning: The fireplace burns 8/15+14/15 = <<8/15+14/15=22/15=1.4666666666666667>>1.4666666666666667 cords of firewood in total in one hour split between the early morning and late night. ### Answer: 1.4666666666666667
Expected answer: 22/15
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 34B:
Reasoning: The alien travelled 9/20+11/7 = <<9/20+11/7=117/70>>117/70 light years in total. ### Answer: 117/70
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?
LLemma 34B:
Reasoning: Bob has 10/2+1/7 = <<10/2+1/7=17/7>>17/7 cucumbers in total. ### Answer: 17/7
Expected answer: 36/7
Correct? No