LLemma 34B on 4.NBT.B.6
Common Core Standard 4.NBT.B.6
This standard covers the following:
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Problem: There are 535 fish in a large tank and a shark eats 461 of them in one sitting. If the shark continues this pattern and only eats when there are 461 or more fish to consume, how many fish will be leftover after its dinner?
LLemma 34B:
Reasoning: The shark eats 461 fish. There are 535-461 = <<535-461=74>>74 fish left over after the shark's dinner. ### Answer: 74
Expected answer: 74
Correct? Yes
Problem: A baker baked a total of 928 cookies. He decided to distribute equal amounts of cookies to 186 orphanages. After giving out as many entire sets of cookies as possible to each orphanage, how many cookies does the baker have left?
LLemma 34B:
Reasoning: The baker gave out 928/186 = <<928/186=5>>5 sets of cookies to each orphanage. The baker has 928-186*5 = <<928-186*5=10>>10 cookies left. ### Answer: 10
Expected answer: 184
Correct? No
Problem: A pizza store has 975 slices of pizza ready to serve. If each pizza box can contain 196 slices, how many left over slices will there be after all the pizza boxes are full?
LLemma 34B:
Reasoning: 975/196 = <<975/196=5>>5 pizza boxes can be filled. There will be 975-5*196 = <<975-5*196=11>>11 slices left over. ### Answer: 11
Expected answer: 191
Correct? No
Problem: A wizard casts a spell to summon 932 magical stones. Each powerful creature he summons requires 193 stones. After summoning several creatures, how many stones will the wizard have left?
LLemma 34B:
Reasoning: The wizard will have 932-193*3 = <<932-193*3=10>>10 stones left. ### Answer: 10
Expected answer: 160
Correct? No
Problem: A builder has a job to install 660 square foot tiles in a house. Each tile can cover 335 square feet. After installing tiles evenly across the available space, how many square feet will the last tile need to cover?
LLemma 34B:
Reasoning: 660/335 = <<660/335=2>>2 tiles will cover 660 square feet. The last tile will need to cover 660-335*2 = <<660-335*2=30>>30 square feet. ### Answer: 30
Expected answer: 325
Correct? No
Problem: A juice company produced 473 gallons of juice. If the company bottles the juice in 22-gallon containers, how many gallons of juice will be left after filling up all the containers?
LLemma 34B:
Reasoning: 473/22 = <<473/22=21.5>>21.5 containers will be filled. 473-21.5*22 = <<473-21.5*22=1.5>>1.5 gallons of juice will be left. ### Answer: 1.5
Expected answer: 11
Correct? No
Problem: A toy factory produced 979 toy cars in a day. If they packed these cars into boxes, each containing 108 cars, how many toy cars will be left unpacked at the end of the day?
LLemma 34B:
Reasoning: 979/108 = <<979/108=9>>9 boxes of toy cars can be packed. 9*108 = <<9*108=972>>972 toy cars will be packed. 979-972 = <<979-972=7>>7 toy cars will be left unpacked. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: The toy factory now produced 979 toy cars in a day and decided to package these cars into larger boxes, each containing 684 cars. After all the cars have been packed into the larger boxes, how many toy cars would be left unpacked at the end of the day?
LLemma 34B:
Reasoning: 979/684 = <<979/684=1>>1 box of toy cars can be packed. 684 toy cars will be packed. 979-684 = <<979-684=295>>295 toy cars will be left unpacked. ### Answer: 295
Expected answer: 295
Correct? Yes
Problem: A crayon factory has the capacity to make 994 crayons in one operation. However, each box only holds 425 crayons. If they operate at full capacity, how many crayons will be left out of the boxes after the operation?
LLemma 34B:
Reasoning: 994-425 = <<994-425=569>>569 crayons will be left out of the boxes after the operation. ### Answer: 569
Expected answer: 144
Correct? No
Problem: A wildlife reserve has 740 tigers. The reserve is divided into different zones, and each zone can only hold up to 696 tigers. If tigers are distributed evenly among the zones, how many tigers will be left in the last zone?
LLemma 34B:
Reasoning: 740/696 = <<740/696=1>>1 zone will have 696 tigers. The last zone will have 740-696 = <<740-696=44>>44 tigers. ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: Consider the wildlife reserve again. This time, however, the zones have been expanded and each can now accommodate up to 908 tigers. If the 740 tigers are distributed evenly among the expanded zones, how many tigers will be left in the last zone?
LLemma 34B:
Reasoning: 740/908 = <<740/908=0>>0 zones will have 908 tigers. The last zone will have 740-0 = <<740-0=740>>740 tigers. ### Answer: 740
Expected answer: 740
Correct? Yes
Problem: A hat shop makes 830 hats every week. In order to make special edition boxes, the shop plans to put 421 hats in each box. If all the hats are evenly distributed among the boxes, how many hats will be left over?
LLemma 34B:
Reasoning: 830/421 = <<830/421=2>>2 boxes will be filled with 421 hats each. There will be 830-2*421 = <<830-2*421=109>>109 hats left over. ### Answer: 109
Expected answer: 409
Correct? No
Problem: There are 871 fish in a lake. A fisherman catches 575 fish every month. If the fish repopulate at the same rate that the fisherman is depleting them, how many fish will be left after a month?
LLemma 34B:
Reasoning: 871-575 = <<871-575=296>>296 fish will be left after a month. ### Answer: 296
Expected answer: 296
Correct? Yes
Problem: There are 891 beach balls, and every beach bag can fit 119 beach balls. If all the beach balls are evenly placed into the bags, how many beach balls will not fit and left over?
LLemma 34B:
Reasoning: 891/119 = <<891/119=7>>7 bags will be filled with 119 beach balls. There will be 891-7*119 = <<891-7*119=10>>10 beach balls left over. ### Answer: 10
Expected answer: 58
Correct? No
Problem: There are 544 stars in a particular constellation. These stars are grouped into smaller clusters of 446 stars each. If these clusters are evenly split, how many stars will remain ungrouped?
LLemma 34B:
Reasoning: 544/446 = <<544/446=1.22>>1.22 clusters of stars will remain ungrouped. 1.22 clusters of stars is 1.22*446 = <<1.22*446=549.52>>549.52 stars. ### Answer: 549.52
Expected answer: 98
Correct? No
Problem: A manufacturer produces 805 socks in one shift. They are packaged into sets of 132 each. After the packaging, how many socks will remain unpackaged?
LLemma 34B:
Reasoning: 805/132 = <<805/132=6>>6 sets of 132 socks can be packaged. 805-132*6 = <<805-132*6=11>>11 socks will remain unpackaged. ### Answer: 11
Expected answer: 13
Correct? No
Problem: An astronomy club has 759 members that want to view a rare celestial event through their club's telescope. However, the telescope can only handle 228 people viewing the event each night. If they distribute the viewing evenings evenly amongst all members, how many people will view the event on the final night?
LLemma 34B:
Reasoning: 759/228 = <<759/228=3.31>>3.31 people will view the event on the final night. ### Answer: 3.31
Expected answer: 75
Correct? No
Problem: A postman has to deliver 891 letters. Each mailbox can only hold 616 letters. If he puts equal numbers of letters in each mailbox, how many letters will remain in the last mailbox?
LLemma 34B:
Reasoning: 891/616 = <<891/616=1.45>>1.45 mailboxes will be filled. The last mailbox will have 891-1.45*616 = <<891-1.45*616=135>>135 letters. ### Answer: 135
Expected answer: 275
Correct? No
Problem: A total of 941 flies are jumping around the pond. Every time a frog jumps, it eats exactly 258 flies. After a series of jumps where each jump the frog eats the same number of flies, how many flies are left?
LLemma 34B:
Reasoning: The frog eats 941/258 = <<941/258=3.67>>3.67 times. There are 941-3.67*258 = <<941-3.67*258=1>>1 flies left. ### Answer: 1
Expected answer: 167
Correct? No
Problem: A large park has a capacity of 991 spaces for cars to park. If all the spaces are evenly distributed between 66 rows, how many spare spaces will be there in the last row after max spaces are filled?
LLemma 34B:
Reasoning: 991/6 = <<991/6=165>>165 spaces will be filled in each row. The last row will have 991-165*5 = <<991-165*5=161>>161 spare spaces. ### Answer: 161
Expected answer: 1
Correct? No
Problem: There are 193 liters of water that need to be divided evenly among 167 water bottles. If each bottle holds the same amount of water, how many liters overflows and can't be distributed to the bottles?
LLemma 34B:
Reasoning: 193/167 = <<193/167=1.15>>1.15 liters of water can be distributed to each bottle. <<193-167*1.15=1.15>>1.15 liters of water overflows and can't be distributed to the bottles. ### Answer: 1.15
Expected answer: 26
Correct? No
Problem: A dragon lays 996 jewel eggs in rows. Each row can hold 319 eggs. If the dragon distributes the eggs evenly among the rows, how many eggs would be left over to be put in the last row?
LLemma 34B:
Reasoning: 996/319 = <<996/319=3>>3 rows can be filled with 319*3 = <<319*3=957>>957 eggs. There would be 996-957 = <<996-957=39>>39 eggs left over to be put in the last row. ### Answer: 39
Expected answer: 39
Correct? Yes
Problem: Now, consider if the dragon had only laid 8 jewel eggs and continued to distribute them among rows that could hold 319 eggs. How many eggs would be left over to be put in the last row?
LLemma 34B:
Reasoning: 8/319 = <<8/319=0>>0 rows can be filled with 319*0 = <<319*0=0>>0 eggs. There would be 8-0 = <<8-0=8>>8 eggs left over to be put in the last row. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A lamp manufacturer produces 691 bulb units. If a pack includes 205 bulbs, how many bulbs would be left unpacked after filling as many packs as possible?
LLemma 34B:
Reasoning: 691/205 = <<691/205=3>>3 packs can be filled. 691-3*205 = <<691-3*205=101>>101 bulbs would be left unpacked. ### Answer: 101
Expected answer: 76
Correct? No
Problem: On a farm, there are 330 bales of hay to be stored evenly in barns. Each barn can store up to 259 bales. After filling up the barns as evenly as possible, how many bales of hay will be left for the last barn?
LLemma 34B:
Reasoning: 330/259 = <<330/259=1>>1 barn will be filled to capacity. The remaining 330-259 = <<330-259=71>>71 bales of hay will be left for the last barn. ### Answer: 71
Expected answer: 71
Correct? Yes
Problem: A construction company is installing 166 windows on a building. They have determined that one installation team can install 137 windows per day. If all windows are equally distributed amongst teams each day, how many windows will remain for the team to install on the next day?
LLemma 34B:
Reasoning: 166/137 = <<166/137=1.2>>1.2 teams will install the windows. 1.2*137 = <<1.2*137=164.4>>164.4 windows will remain for the team to install on the next day. ### Answer: 164.4
Expected answer: 29
Correct? No
Problem: There are 533 campers coming for a camping event at a park. Each tent can host 445 people. If the campers are evenly distributed among the tents, how many campers will be left over after all the tents are filled?
LLemma 34B:
Reasoning: 533/4 = <<533/4=133.25>>133.25 campers will be left over after all the tents are filled. ### Answer: 133.25
Expected answer: 88
Correct? No
Problem: There are 999 seashells collected from a beach. They are grouped in beach-themed souvenir sets, each containing 474 shells. After grouping, how many seashells will be left without a set?
LLemma 34B:
Reasoning: 999/47 = <<999/47=21>>21 sets of seashells can be made. There are 999-21*47 = <<999-21*47=1>>1 seashell left without a set. ### Answer: 1
Expected answer: 51
Correct? No
Problem: A tailor has 366 meters of fabric. If each skirt requires 160 meters of fabric, how many meters of fabric will be left after making as many skirts as possible?
LLemma 34B:
Reasoning: 366/160 = <<366/160=2.2875>>2.2875 skirts can be made. 2.2875 skirts is 2 skirts and 287.5% of a skirt. 287.5% of 160 meters is 47.25 meters. 47.25 meters of fabric will be left after making as many skirts as possible. ### Answer: 47.25
Expected answer: 46
Correct? No
Problem: A toymaker made 993 dolls to be packed in boxes for shipment. Each box can hold 327 dolls. How many dolls will she have left once all the boxes are packed to their capacities?
LLemma 34B:
Reasoning: 993/327 = <<993/327=3>>3 boxes can be packed. 993-3*327 = <<993-3*327=1>>1 doll will be left. ### Answer: 1
Expected answer: 12
Correct? No
Problem: A child has 964 stuffed animals that they want to divide equally among their 839 friends. If they distribute the stuffed animals evenly, how many will the child have left over?
LLemma 34B:
Reasoning: 964/839 = <<964/839=1.14>>1.14 stuffed animals will be left over. ### Answer: 1.14
Expected answer: 125
Correct? No
Problem: A toy factory produces 369 teddy bears in a day. The bears are packaged in boxes and each box can hold 270 teddy bears. How many teddy bears will be left if all the teddy bears are evenly packed in the boxes?
LLemma 34B:
Reasoning: 369/270 = <<369/270=1.3928571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428571428
Expected answer: 99
Correct? No
Problem: A village has a yearly tradition of building snowmen. This year, the villagers make 804 snowballs to build their snowmen. Each snowman needs exactly 184 snowballs. After all snowmen are built, how many snowballs are left leftover?
LLemma 34B:
Reasoning: 804/184 = <<804/184=4>>4 snowmen can be built. 4*184 = <<4*184=736>>736 snowballs are used to build the snowmen. 804-736 = <<804-736=68>>68 snowballs are left leftover. ### Answer: 68
Expected answer: 68
Correct? Yes
Problem: In the same village, another year, there were only 444 snowballs made to build the snowmen. If each snowman still requires exactly 184 snowballs, how many snowballs would be left over after as many complete snowmen as possible are built?
LLemma 34B:
Reasoning: 444/184 = <<444/184=2>>2 snowmen can be built. 2*184 = <<2*184=368>>368 snowballs are used to build the snowmen. 444-368 = <<444-368=76>>76 snowballs are left leftover. ### Answer: 76
Expected answer: 76
Correct? Yes
Problem: A jewelry store has 843 rings to be placed equally into 839 boxes. If each box is filled, how many rings will be left over?
LLemma 34B:
Reasoning: 843/839 = <<843/839=1>>1. There will be 1 ring left over. ### Answer: 1
Expected answer: 4
Correct? No
Problem: A fireplace manufacturing company has 819 bricks to build fireplaces, and each fireplace requires 583 bricks. If they build as many fireplaces as possible, how many bricks will they have left over?
LLemma 34B:
Reasoning: 819/583 = <<819/583=1.4>>1.4 fireplaces can be built. 819 - 583*1.4 = <<819-583*1.4=11>>11 bricks will be left over. ### Answer: 11
Expected answer: 236
Correct? No
Problem: A marshmallow factory produces 998 marshmallows per minute. However, the packaging machine can only hold 957 marshmallows at a time. What will be the number of marshmallows left un-packaged in a minute after all the packaging machines are filled?
LLemma 34B:
Reasoning: The packaging machine can hold 957 marshmallows. The factory produces 998 marshmallows per minute. 998-957 = <<998-957=41>>41 marshmallows will be left un-packaged in a minute after all the packaging machines are filled. ### Answer: 41
Expected answer: 41
Correct? Yes
Problem: The marshmallow factory upgraded its packaging machine and now it can hold 804 marshmallows at a time instead of 957. If the factory continues to produce 998 marshmallows per minute, what will be the number of marshmallows left un-packaged in a minute after all the packaging machines are filled with the new capacity?
LLemma 34B:
Reasoning: The packaging machine can hold 804 marshmallows. The factory produces 998 marshmallows per minute. 998-804 = <<998-804=194>>194 marshmallows will be left un-packaged in a minute after all the packaging machines are filled. ### Answer: 194
Expected answer: 194
Correct? Yes
Problem: There are 984 roses in the castle's garden. Princess likes to place 426 roses in every tribute for her loyal subjects. If she distributes roses evenly to create as many tributes as possible, how many roses will be left undistributed in the castle's garden?
LLemma 34B:
Reasoning: Princess can distribute 984/426 = <<984/426=2>>2 tributes. There will be 984-2*426 = <<984-2*426=112>>112 roses left undistributed in the castle's garden. ### Answer: 112
Expected answer: 132
Correct? No
Problem: A song has 334 words in it. If each line in the song has 23 words, how many words would be in the incomplete line at the end of the song?
LLemma 34B:
Reasoning: 334/23 = <<334/23=14.5>>14.5 lines of the song. The incomplete line has 334-14*23 = <<334-14*23=14>>14 words. ### Answer: 14
Expected answer: 12
Correct? No
Problem: A teacher has 928 pages of study materials that he wants to print for his students. His printer can only print 336 pages in one go. After filling the printer a number of times, how many pages will he have left over to print?
LLemma 34B:
Reasoning: The printer can print 928/336 = <<928/336=2.78>>2.78 times. The printer will have 928-2.78*336 = <<928-2.78*336=104>>104 pages left over to print. ### Answer: 104
Expected answer: 256
Correct? No
Problem: Scientists have spotted 972 sharks in an area. The scientists tag groups of 667 sharks each. How many sharks are left untagged after the scientists finish tagging as many complete groups as possible?
LLemma 34B:
Reasoning: The scientists can tag 972/667 = <<972/667=1>>1 group of 667 sharks. There are 972-667 = <<972-667=305>>305 sharks left untagged. ### Answer: 305
Expected answer: 305
Correct? Yes
Problem: Following up on the previous question, the scientists later spotted a new group of 758 sharks in a different area. Again, they were trying to tag the sharks in groups of 667. How many sharks were left untagged after all complete groups have been tagged in this new area?
LLemma 34B:
Reasoning: The scientists can tag 758/667 = <<758/667=1>>1 group of 667 sharks. There are 758-667 = <<758-667=91>>91 sharks left untagged. ### Answer: 91
Expected answer: 91
Correct? Yes
Problem: There are 686 blocks of cheese in the dairy shop. Each box can contain 349 blocks of cheese. If all the blocks of cheese are evenly distributed in the boxes, how many blocks of cheese would be left over after all the boxes are filled?
LLemma 34B:
Reasoning: 686/349 = <<686/349=2>>2 boxes can be filled. There would be 686-2*349 = <<686-2*349=1>>1 block of cheese left over. ### Answer: 1
Expected answer: 337
Correct? No
Problem: There were 513 centimeters of snowfall recorded this winter. A snowplow can clear up to 170 centimeters of snow at a time. If the snowplow runs continuously, how many centimeters of snow will be left over after the final pass?
LLemma 34B:
Reasoning: The snowplow can clear 170 centimeters of snow at a time. The snowplow will clear 513/170 = <<513/170=3>>3 times. The snowplow will clear 3*170 = <<3*170=510>>510 centimeters of snow. There will be 513-510 = <<513-510=3>>3 centimeters of snow left over after the final pass. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: Suppose that instead of 513 centimeters, there were 460 centimeters of snowfall this winter. If the same snowplow, which can clear up to 170 centimeters of snow at a time, runs continuously, how many centimeters of snow would then be left over after the final pass?
LLemma 34B:
Reasoning: The snowplow can clear 170 centimeters of snow at a time. The snowplow will clear 460/170 = <<460/170=2>>2 times. The snowplow will clear 2*170 = <<2*170=340>>340 centimeters of snow. There will be 460-340 = <<460-340=120>>120 centimeters of snow left over after the final pass. ### Answer: 120
Expected answer: 120
Correct? Yes
Problem: A compass maker has 661 needles to install in compasses. Each compass uses 510 needles. After installing as many full compasses as he can, how many needles will the compass maker have left?
LLemma 34B:
Reasoning: The compass maker can install 661/510 = <<661/510=1.282>>1.282 compasses. The compass maker will have 661-1.282*510 = <<661-1.282*510=11>>11 needles left. ### Answer: 11
Expected answer: 151
Correct? No
Problem: A furniture factory has manufactured 380 chairs to distribute to its retail shops. Each shop can only hold 310 chairs in its storage. If the factory evenly distributes all the chairs to the shops, how many chairs will be left at the factory?
LLemma 34B:
Reasoning: 380/310 = <<380/310=1.22>>1.22 shops can be filled with chairs. The remaining 0.22 shops can hold 0.22*310 = <<0.22*310=66.2>>66 chairs. ### Answer: 66
Expected answer: 70
Correct? No
Problem: A farmer has gathered 929 tomatoes from his field. He plans to sell them in boxes, with 154 tomatoes in each box. After packing them evenly in boxes, how many tomatoes will be left over?
LLemma 34B:
Reasoning: 929/154 = <<929/154=6>>6 boxes of tomatoes can be made. There will be 929-6*154 = <<929-6*154=18>>18 tomatoes left over. ### Answer: 18
Expected answer: 5
Correct? No
Problem: A sporting goods store has 454 pairs of ice skates in total. The store distributes the skates evenly among 128 boxes. How many pairs of ice skates will be left over after all the boxes are filled up equally?
LLemma 34B:
Reasoning: 454/128 = <<454/128=3.5>>3.5 pairs of ice skates will be left over after all the boxes are filled up equally. ### Answer: 3.5
Expected answer: 70
Correct? No
Problem: A windmill generates 506 units of power per day. Every day, a small village consumes power in increments of 385 units. At the end of the day, after the village has consumed as much power as it can in full increments, how much power is left over?
LLemma 34B:
Reasoning: The village consumes 506/385 = <<506/385=1>>1 full increment of power. There are 506-385 = <<506-385=121>>121 units of power left over. ### Answer: 121
Expected answer: 121
Correct? Yes
Problem: Following the scenario of the windmill and the small village, let's now consider that the windmill had a great day and managed to generate 506 units of power. However, due to development demands, the daily consumption of the village has increased to 920 units. At the end of the day, with the power being consumed in complete units, how much power is left over?
LLemma 34B:
Reasoning: The village consumes 506/920 = <<506/920=0>>0 full increments of power. There are 506-0*920 = <<506-0*920=506>>506 units of power left over. ### Answer: 506
Expected answer: 506
Correct? Yes
Problem: Superhero Blast Man has 338 energy units in his power cells. Each energy blast he fires uses 16 energy units. After using equal units of energy firing blasts, how many energy units will Blast Man have left in his power cells?
LLemma 34B:
Reasoning: Blast Man used 338/16 = <<338/16=21>>21 blasts. Blast Man has 338-21*16 = <<338-21*16=1>>1 energy unit left in his power cells. ### Answer: 1
Expected answer: 2
Correct? No
Problem: A school district has 530 students who need to be transported and each school bus can carry 144 students. If all students are equally spread across the buses, how many students will be on the last school bus?
LLemma 34B:
Reasoning: 530/144 = <<530/144=3.69>>3.69 students will be on the last school bus. ### Answer: 3.69
Expected answer: 98
Correct? No
Problem: A wizard has 999 spells in his book. He tries to distribute them equally among 951 apprentice wizards but they don't divide evenly. How many spells will the wizard have left after giving out as many as he can to his apprentices?
LLemma 34B:
Reasoning: 999/951 = <<999/951=1.05>>1.05 spells per apprentice. The wizard will have 999 - 951*1.05 = <<999-951*1.05=48.05>>48.05 spells left. ### Answer: 48.05
Expected answer: 48
Correct? No
Problem: A scooter manufacturing company has produced 767 scooters. Each delivery truck they use can carry 369 scooters. If they distribute the scooters evenly among the trucks, how many scooters will be left after all the trucks are loaded?
LLemma 34B:
Reasoning: 767/369 = <<767/369=2>>2 trucks will be loaded. 767-2*369 = <<767-2*369=1>>1 scooter will be left after all the trucks are loaded. ### Answer: 1
Expected answer: 29
Correct? No
Problem: There are 846 water droplets in a cloud. Each raindrop needs 722 droplets to form. If all droplets are used to form raindrops, how many droplets would be left unconverted in the cloud after reaching the maximum number of rain drops?
LLemma 34B:
Reasoning: 846/722 = <<846/722=1.17>>1.17 raindrops can be formed. 1.17*722 = <<1.17*722=845.44>>845.44 droplets would be left unconverted in the cloud after reaching the maximum number of rain drops. ### Answer: 845.44
Expected answer: 124
Correct? No
Problem: Unicorn Village, a magical place where 265 unicorns live, is divided into 146 equal sections where these magical creatures reside. If each section is occupied by an equal number of unicorns, how many unicorns will live in the last incomplete section?
LLemma 34B:
Reasoning: 265/146 = <<265/146=1.82>>1.82 unicorns will live in the last incomplete section. ### Answer: 1.82
Expected answer: 119
Correct? No
Problem: In a game, there are 923 players waiting to enter a match. Only 383 players can enter a match at a time. If players enter matches evenly, how many players will be left waiting after filling all the matches?
LLemma 34B:
Reasoning: 923/383 = <<923/383=2>>2 matches can be filled. There will be 923-2*383 = <<923-2*383=11>>11 players left waiting after filling all the matches. ### Answer: 11
Expected answer: 157
Correct? No
Problem: A pirate ship has 923 cannonballs on board. They want to equally disperse them between 499 different crates. After evenly distributing them as much as possible, how many cannonballs will be left uncrated?
LLemma 34B:
Reasoning: 923/499 = <<923/499=1.85>>1.85 cannonballs will be left uncrated. ### Answer: 1.85
Expected answer: 424
Correct? No
Problem: A kite store has 530 string spools to attach to their kites. They distribute them to 518 kites, each getting one string spool. After each kite gets a spool, how many spools are left in the store?
LLemma 34B:
Reasoning: 530-518 = <<530-518=12>>12 spools are left in the store. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: A dairy farm produces 913 gallons of milk in a day. If every milk jug holds 39 gallons, how many gallons will be left over after all the jugs are filled?
LLemma 34B:
Reasoning: 913/39 = <<913/39=23>>23 milk jugs will be filled. 913-23*39 = <<913-23*39=1>>1 gallon will be left over. ### Answer: 1
Expected answer: 16
Correct? No
Problem: A doll seller received a shipment of 603 new dolls to put on the shelves. She arranged all the dolls in rows, with 369 dolls in each row. After filling up the rows as much as possible, how many dolls were left unarranged?
LLemma 34B:
Reasoning: 603/369 = <<603/369=1.64>>1.64 rows can be filled up. There are 603-369*1.64 = <<603-369*1.64=101>>101 dolls left unarranged. ### Answer: 101
Expected answer: 234
Correct? No
Problem: A jewelry maker has 850 beads to make necklaces. They use 631 beads for each necklace. After using as many beads as possible, how many beads will the jewelry maker have left over?
LLemma 34B:
Reasoning: The jewelry maker can make 850/631 = <<850/631=1.34>>1.34 necklaces. The jewelry maker can use 631*1.34 = <<631*1.34=850.04>>850.04 beads. The jewelry maker has 850-850.04 = <<850-850.04=0.04>>0.04 beads left over. ### Answer: 0.04
Expected answer: 219
Correct? No
Problem: A gardener has 952 grapes that he wants to package into boxes. If each box can hold 380 grapes, how many grapes will be left after the gardener has filled as many boxes as possible?
LLemma 34B:
Reasoning: The gardener can fill 952/380 = <<952/380=2.5>>2.5 boxes. The gardener can fill 2 boxes. The gardener can put 2*380 = <<2*380=760>>760 grapes in the boxes. The gardener has 952-760 = <<952-760=192>>192 grapes left. ### Answer: 192
Expected answer: 192
Correct? Yes
Problem: The gardener's friend gave him an additional 183 grapes from his own garden. If the gardener decides to package these grapes as well into boxes with each box holding 380 grapes, how many grapes will remain after packaging the new grapes into as many boxes as possible?
LLemma 34B:
Reasoning: The gardener can fill 183/380 = <<183/380=0.5>>0.5 boxes. The gardener can fill 0 boxes. The gardener can put 0*380 = <<0*380=0>>0 grapes in the boxes. The gardener has 183-0 = <<183-0=183>>183 grapes left. ### Answer: 183
Expected answer: 183
Correct? Yes
Problem: On a treasure map, there are 236 steps mentioned on the guide. If every 44 steps I make leads me to a significant place or clue, how many steps will be left after I reach the last significant place or clue?
LLemma 34B:
Reasoning: 236/44 = <<236/44=5.4>>5.4 steps will be left after I reach the last significant place or clue. ### Answer: 5.4
Expected answer: 16
Correct? No
Problem: Sarah blew 932 bubbles using her new bubble machine. The machine is designed to form groups of 507 bubbles each before releasing them. After forming complete groups, how many bubbles does it make in its final, incomplete group?
LLemma 34B:
Reasoning: 932/507 = <<932/507=1.84>>1.84 groups of 507 bubbles. The machine makes 507*1.84 = <<507*1.84=931.98>>931.98 bubbles in its final, incomplete group. ### Answer: 931.98
Expected answer: 425
Correct? No
Problem: At the park, there are 931 kids who want to use the swings. Each swing set can accommodate 34 kids at a time. If all the swing sets are filled continuously, how many kids will be waiting for their turn after all the swing sets are occupied?
LLemma 34B:
Reasoning: 931/34 = <<931/34=27.35>>27.35 swing sets are needed. There will be 931-27*34 = <<931-27*34=1>>1 kids waiting for their turn after all the swing sets are occupied. ### Answer: 1
Expected answer: 13
Correct? No
Problem: John has 943 dollar bills in his possession. He tries to stuff them in wallets that can each contain 433 dollar bills. After fully loading as many wallets as he can, how many dollar bills does he have left?
LLemma 34B:
Reasoning: John can load 943/433 = <<943/433=2>>2 wallets. John has 943-2*433 = <<943-2*433=10>>10 dollar bills left. ### Answer: 10
Expected answer: 77
Correct? No
Problem: A helicopter pilot plans to transport 240 passengers over several trips. He can carry 177 passengers in one trip. How many passengers will be left behind after the helicopter makes the first full trip?
LLemma 34B:
Reasoning: The helicopter can carry 177 passengers in one trip. The helicopter will leave behind 240-177 = <<240-177=63>>63 passengers after the first full trip. ### Answer: 63
Expected answer: 63
Correct? Yes
Problem: A gardener has 982 flowers to plant in flowerbeds. Each flowerbed can fit 555 flowers. After filling up as many flowerbeds as possible, how many flowers will the gardener have left to plant?
LLemma 34B:
Reasoning: The gardener can fill 982/555 = <<982/555=1.77>>1.77 flowerbeds. The gardener will have 982-1.77*555 = <<982-1.77*555=112>>112 flowers left to plant. ### Answer: 112
Expected answer: 427
Correct? No
Problem: A farmer grows 203 strawberry plants. She wants to divide her plants into groups of 5 to sell. How many plants will be remaining if she divides them equally?
LLemma 34B:
Reasoning: 203/5 = <<203/5=40.6>>40.6 plants will be remaining if she divides them equally. ### Answer: 40.6
Expected answer: 3
Correct? No
Problem: A gardener has 355 carrots. He wants to create bundles of 16. After creating as many bundles as he can, how many carrots will he have left?
LLemma 34B:
Reasoning: 355/16 = <<355/16=21.9375>>21.9375 bundles of 16 carrots. 355 - 21.9375*16 = <<355-21.9375*16=1.9375>>1.9375 carrots left. ### Answer: 1.9375
Expected answer: 3
Correct? No
Problem: A total rainfall of 612 inches fell over a certain city in 29 consecutive days. If the rain fell in the same amount every day, how many inches of rain would be left to make the days evenly rainy?
LLemma 34B:
Reasoning: 612/29 = <<612/29=21>>21 inches of rain would be left to make the days evenly rainy. ### Answer: 21
Expected answer: 3
Correct? No
Problem: A truck company has got 514 boxes for delivery. Each truck can hold up to 371 boxes. If each truck is loaded to its full capacity, how many boxes will be left over?
LLemma 34B:
Reasoning: Each truck can hold 371 boxes. 514/371 = <<514/371=1>>1 truck can hold 371 boxes. There will be 514-371 = <<514-371=143>>143 boxes left over. ### Answer: 143
Expected answer: 143
Correct? Yes
Problem: In a large sandbox, children create 684 sandcastles over the summer. The sandcastles were grouped into sets of 230 for a photography contest. After all the sets were completed, how many sandcastles were left that didn't form a complete set?
LLemma 34B:
Reasoning: 684/230 = <<684/230=2>>2 sets of 230 sandcastles were created. 2*230 = <<2*230=460>>460 sandcastles were used in the photography contest. 684-460 = <<684-460=224>>224 sandcastles were left over. ### Answer: 224
Expected answer: 224
Correct? Yes
Problem: Continuing from the prior problem, suppose that in another large sandbox, children now create 533 sandcastles over the summer instead of 684. If they still group the sandcastles in sets of 230 for a photography contest, how many sandcastles will be left now that don't form a complete set?
LLemma 34B:
Reasoning: 533/230 = <<533/230=2>>2 sets of 230 sandcastles were created. 2*230 = <<2*230=460>>460 sandcastles were used in the photography contest. 533-460 = <<533-460=73>>73 sandcastles were left over. ### Answer: 73
Expected answer: 73
Correct? Yes
Problem: A toy manufacturer has a production run of 735 toy cars. They package the cars in packs of 348 for bulk shipments. If all the toy cars are divided equally among packs, how many toy cars will be left over after all full packs have been filled?
LLemma 34B:
Reasoning: 735/348 = <<735/348=2>>2 full packs of toy cars can be made. 735-2*348 = <<735-2*348=107>>107 toy cars will be left over. ### Answer: 107
Expected answer: 39
Correct? No
Problem: In a forest, there are 386 animals. Each woodlands territory can support 95 animals. If the existing animals are evenly distributed among the territories, how many animals will be left in the last not fully occupied territory?
LLemma 34B:
Reasoning: 386/95 = <<386/95=4>>4 territories will be fully occupied. The last territory will have 386 - 4*95 = <<386-4*95=16>>16 animals. ### Answer: 16
Expected answer: 6
Correct? No
Problem: A forest has 801 trees. A tree disease starts to spread and is expected to affect 646 trees. If all the diseased trees have to be cut down evenly, how many trees are likely to stay healthy after the disease has affected all possible trees?
LLemma 34B:
Reasoning: 801-646 = <<801-646=155>>155 trees are likely to stay healthy after the disease has affected all possible trees. ### Answer: 155
Expected answer: 155
Correct? Yes
Problem: A rope manufacturer has made a rope of 934 meters in length. This rope is supposed to be cut into smaller pieces, each piece being 902 meters in length. After cutting into the maximum possible number of equal pieces, how many meters will the last piece of the rope be?
LLemma 34B:
Reasoning: 934/902 = <<934/902=1>>1 piece of 902 meters in length. 934-902 = <<934-902=32>>32 meters will be the last piece of the rope. ### Answer: 32
Expected answer: 32
Correct? Yes
Problem: Continuing from the previous scenario, suppose that the manufacturer only made a rope of 202 meters in length initially. Applying the same method of cutting rope into pieces that are each 902 meters long, how many meters would the piece of the rope be now?
LLemma 34B:
Reasoning: 202/902 = <<202/902=0>>0 pieces of 902 meters in length. 202 meters would be the piece of the rope now. ### Answer: 202
Expected answer: 202
Correct? Yes
Problem: A dairy farm produces 561 liters of milk each day. The milk is packaged into 550-liter containers. How many liters of milk are left over each day after filling the containers?
LLemma 34B:
Reasoning: 561-550 = <<561-550=11>>11 liters of milk are left over each day after filling the containers. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: If the dairy farm increased its production and started producing 729 liters of milk each day instead of 561 liters, how many liters of milk would be left over each day after filling the 550-liter containers?
LLemma 34B:
Reasoning: 729-550 = <<729-550=179>>179 liters of milk would be left over each day after filling the 550-liter containers. ### Answer: 179
Expected answer: 179
Correct? Yes
Problem: Jon has 259 puzzle pieces. If each puzzle requires 258 pieces, how many pieces will be left over once he completes a full puzzle?
LLemma 34B:
Reasoning: Jon will have 259-258 = <<259-258=1>>1 piece left over. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: In the previous problem, Jon had 259 puzzle pieces and each puzzle requires 258 pieces. Suppose instead each puzzle needs 542 pieces. How many pieces would Jon have left over after finishing as many full puzzles as possible with his 259 pieces?
LLemma 34B:
Reasoning: Jon can make 259/542 = <<259/542=0>>0 puzzles. Jon will have 259-0*542 = <<259-0*542=259>>259 pieces left over. ### Answer: 259
Expected answer: 259
Correct? Yes
Problem: A jewelry maker has 673 beads. She plans to use exactly 49 beads for each bracelet. How many beads will she have left after creating as many bracelets as possible with the exact number of beads?
LLemma 34B:
Reasoning: 673/49 = <<673/49=13.777777777777778>>13.777777777777778 bracelets can be made. 673-13.777777777777778*49 = <<673-13.777777777777778*49=14>>14 beads will be left. ### Answer: 14
Expected answer: 36
Correct? No
Problem: A police station received 927 calls within a week. They have 311 operators who can handle the same number of calls each week. However, when the calls are divided equally, how many calls will the last operator handle?
LLemma 34B:
Reasoning: 927/311 = <<927/311=2.98>>2.98 calls per operator. The last operator will handle 2.98 calls. ### Answer: 2.98
Expected answer: 305
Correct? No
Problem: John has 764 pieces for his jigsaw puzzle, and every package should contain 589 pieces. If he separates these pieces into full packages, how many pieces will be left outside without a package?
LLemma 34B:
Reasoning: John can make 764/589 = <<764/589=1.3>>1.3 packages. John will have 764-1.3*589 = <<764-1.3*589=105>>105 pieces left outside without a package. ### Answer: 105
Expected answer: 175
Correct? No
Problem: A dressmaker has 984 meters of fabric. She uses 217 meters of fabric to make each dress. After using all the fabric she can to make as many dresses as possible, how many meters of fabric will she have left?
LLemma 34B:
Reasoning: 984/217 = <<984/217=4.5>>4.5 dresses can be made. 984 - 217*4.5 = <<984-217*4.5=102.5>>102.5 meters of fabric will be left. ### Answer: 102.5
Expected answer: 116
Correct? No
Problem: A company donates 639 sleeping bags for a camping event. Each campsite is supplied with 374 sleeping bags. If all the sleeping bags are divided equally among the campsites, how many sleeping bags will there be left?
LLemma 34B:
Reasoning: 639/374 = <<639/374=1.7>>1.7 campsites can be supplied with sleeping bags. There will be 639-1.7*374 = <<639-1.7*374=115>>115 sleeping bags left. ### Answer: 115
Expected answer: 265
Correct? No
Problem: A pizza restaurant made 620 pizzas today. They package up the pizzas in boxes that hold 578 each for delivery. If the pizzas are evenly distributed into these boxes, how many pizzas will be left over that don't fit into a box?
LLemma 34B:
Reasoning: 620/578 = <<620/578=1>>1 box will be filled to capacity. 620-578 = <<620-578=42>>42 pizzas will be left over. ### Answer: 42
Expected answer: 42
Correct? Yes
Problem: The owner of the pizza restaurant decides to make 74 more pizzas tomorrow, bringing the total to 694 pizzas. If they are again distributed into boxes that hold 578 pizzas each, how many pizzas will be left out without a box this time?
LLemma 34B:
Reasoning: 694/578 = <<694/578=1>>1 box will be filled to capacity. 694-578 = <<694-578=116>>116 pizzas will be left over. ### Answer: 116
Expected answer: 116
Correct? Yes
Problem: A factory made a total of 820 robots. It can store 684 robots in one storage unit. If the robots are evenly stored, how many robots will not fit and remain outside of the storage units?
LLemma 34B:
Reasoning: 820/684 = <<820/684=1.204>>1.204 storage units are needed. 1.204*684 = <<1.204*684=820.08>>820.08 robots fit in the storage units. 820-820.08 = <<820-820.08=0.08>>0.08 robots will not fit and remain outside of the storage units. ### Answer: 0.08
Expected answer: 136
Correct? No
Problem: A cloud changes its shape by reducing its water droplets. Initially, there were 516 droplets in the cloud. If the cloud loses water droplets at an equal rate and becomes entirely dry after every 289 droplets, how many droplets will be left when the cloud is dry after the final cycle?
LLemma 34B:
Reasoning: The cloud loses 289 droplets in each cycle. The cloud loses 516/289 = <<516/289=1.77>>1.77 cycles. The cloud loses 1.77*289 = <<1.77*289=511.43>>511.43 droplets. The cloud has 516-511.43 = <<516-511.43=4.57>>4.57 droplets left. ### Answer: 4.57
Expected answer: 227
Correct? No
Problem: A transport company needs to load 330 boxes into trucks. Each truck can hold exactly 4 boxes. After filling each truck to its full capacity, how many boxes will be left unloaded?
LLemma 34B:
Reasoning: 330/4 = <<330/4=82.5>>82.5 trucks can be filled. There will be 330-82.5*4 = <<330-82.5*4=10>>10 boxes left unloaded. ### Answer: 10
Expected answer: 2
Correct? No
Problem: A farmer harvested 649 potatoes this season. He decides to pack them into crates each containing 183 potatoes. How many potatoes will be left after all crates are filled to their maximum capacity?
LLemma 34B:
Reasoning: 649/183 = <<649/183=3.5>>3.5 crates can be filled. 3.5*183 = <<3.5*183=614.5>>614.5 potatoes will be left after all crates are filled to their maximum capacity. ### Answer: 614.5
Expected answer: 100
Correct? No
Problem: A t-shirt company has a batch of 258 shirts in production. Each box can pack 67 shirts. If all the shirts are evenly distributed in the boxes, how many shirts would be left outside the boxes?
LLemma 34B:
Reasoning: 258/67 = <<258/67=3.86>>3.86 boxes can be filled. There would be 258-3.86*67 = <<258-3.86*67=2.14>>2.14 shirts left outside the boxes. ### Answer: 2.14
Expected answer: 57
Correct? No
Problem: On a pirate ship, there are 995 gold coins that need to be evenly divided among the 267 pirates. If they split the gold up as evenly as possible, how many gold coins will be left over?
LLemma 34B:
Reasoning: 995/267 = <<995/267=3.722222222222222>>3.722222222222222 There will be 3.722222222222222 = <<3.722222222222222=3>>3 gold coins left over. ### Answer: 3
Expected answer: 194
Correct? No
Problem: There are 776 snails all lined up in a row. If you group them in bunches of 375 snails, how many snails will be left in the final group?
LLemma 34B:
Reasoning: 776/375 = <<776/375=2>>2 bunches of 375 snails. There will be 776-375*2 = <<776-375*2=25>>25 snails left in the final group. ### Answer: 25
Expected answer: 26
Correct? No
Problem: A pillow factory produces 589 pillows per day. They package these pillows in boxes, and each box holds 198 pillows. If they pack as many full boxes as possible, how many pillows will be left outside the boxes at the end of the day?
LLemma 34B:
Reasoning: 589/198 = <<589/198=3>>3 boxes will be filled. There will be 589-3*198 = <<589-3*198=19>>19 pillows left outside the boxes at the end of the day. ### Answer: 19
Expected answer: 193
Correct? No
Problem: A jewelry maker has 633 beads. If she uses beads to make necklaces, with each necklace using exactly 30 beads, how many beads will she have left after making as many necklaces as she can?
LLemma 34B:
Reasoning: 633/30 = <<633/30=21>>21 necklaces can be made. 633-21*30 = <<633-21*30=3>>3 beads will be left. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: The jewelry maker found an additional box of beads in her storage, increasing her total number of beads to 588. Now, if she uses these beads to make necklaces, with each necklace using exactly 30 beads, how many beads will she have left after making as many necklaces as she can?
LLemma 34B:
Reasoning: 588/30 = <<588/30=19>>19 necklaces can be made. 588-19*30 = <<588-19*30=8>>8 beads will be left. ### Answer: 8
Expected answer: 18
Correct? No
Problem: John has collected 365 coins. He decided to put equal numbers of them in his 140 wallets. However, he found out he would still have some coins left after evenly distributing them into these wallets. How many coins will John have left?
LLemma 34B:
Reasoning: John will have 365/140 = <<365/140=2.5>>2.5 coins left. ### Answer: 2.5
Expected answer: 85
Correct? No
Problem: A sock manufacturer produces 743 socks in a single production run. The socks are packed into cartons, each containing 451 socks. After filling up as many cartons as possible, how many socks are left unpacked?
LLemma 34B:
Reasoning: 743/451 = <<743/451=1>>1 carton is filled up. 743-451 = <<743-451=292>>292 socks are left unpacked. ### Answer: 292
Expected answer: 292
Correct? Yes
Problem: Now suppose the sock manufacturer changes their packaging method and each carton contains 179 socks instead of 451 socks. After filling up as many cartons as possible with 743 socks, how many socks are left unpacked?
LLemma 34B:
Reasoning: 743/179 = <<743/179=4>>4 cartons are filled up. 743-4*179 = <<743-4*179=1>>1 sock is left unpacked. ### Answer: 1
Expected answer: 27
Correct? No
Problem: A total of 923 children want to slide down a slide at an amusement park. If 771 children can go down the slide without rest, how many children will be left waiting for their turn?
LLemma 34B:
Reasoning: 923-771 = <<923-771=152>>152 children will be left waiting for their turn. ### Answer: 152
Expected answer: 152
Correct? Yes
Problem: After the first 771 children go down the slide, another wave of children arrives and now there are 923 children in total waiting again. If 881 children can go down the slide without any break this time, how many children will be left waiting for their turn?
LLemma 34B:
Reasoning: 923-881 = <<923-881=42>>42 children will be left waiting for their turn. ### Answer: 42
Expected answer: 42
Correct? Yes
Problem: Superhero Iron Punch has to save 442 people from a collapsing building. He can teleport a maximum of 104 people at a time to safety. After teleporting as many full groups as he can, how many people will be left in the building for his last round of rescue?
LLemma 34B:
Reasoning: Iron Punch can teleport 104 people at a time. Iron Punch can teleport 442/104 = <<442/104=4>>4 full groups of 104 people. Iron Punch will be left with 442-4*104 = <<442-4*104=2>>2 people in the building for his last round of rescue. ### Answer: 2
Expected answer: 26
Correct? No
Problem: A card game manufacturer creates a deck of cards with 569 cards. Each card pack has 68 cards. After creating as many packs as possible, how many cards will the manufacturer have left over?
LLemma 34B:
Reasoning: 569/68 = <<569/68=8>>8 packs can be created. 569-8*68 = <<569-8*68=1>>1 card will be left over. ### Answer: 1
Expected answer: 25
Correct? No
Problem: A stationery store received a shipment of 842 erasers. The store owner wants to display them in boxes, with each box containing 719 erasers. After filling as many boxes as possible, how many erasers will be left over?
LLemma 34B:
Reasoning: The store owner can fill 842/719 = <<842/719=1>>1 box with 719 erasers. There will be 842-719 = <<842-719=123>>123 erasers left over. ### Answer: 123
Expected answer: 123
Correct? Yes
Problem: Suppose the stationery store owner later decided to display the erasers in smaller boxes, with each box containing 420 erasers instead. After filling as many boxes as possible, how many erasers will be left over now?
LLemma 34B:
Reasoning: The store owner can fill 842/420 = <<842/420=2>>2 boxes with 420 erasers. There will be 842-420*2 = <<842-420*2=24>>24 erasers left over. ### Answer: 24
Expected answer: 2
Correct? No
Problem: A farmer harvested 461 carrots from his garden. He packs them into boxes, each box can hold up to 244 carrots. After packing as many full boxes as possible, how many carrots will be left unpacked?
LLemma 34B:
Reasoning: 461/244 = <<461/244=1>>1 full box can be packed. 461-244 = <<461-244=217>>217 carrots will be left unpacked. ### Answer: 217
Expected answer: 217
Correct? Yes
Problem: The farmer found out that he had initially miscounted and he actually only harvested 11 carrots. After he tries to pack these into the boxes which each can hold up to 244 carrots, how many carrots will be left unpacked now?
LLemma 34B:
Reasoning: 11/244 = <<11/244=0>>0 full boxes can be packed. 11 carrots will be left unpacked. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: A penguin scientist counts 309 penguins in a colony. She decides to tag them in groups of 293 for easier tracking. How many penguins will be in the final, possibly incomplete, group?
LLemma 34B:
Reasoning: 309/293 = <<309/293=1>>1 group of 293 penguins, and 16 penguins will be in the final, possibly incomplete, group. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: The penguin scientist realizes she made a mistake and there were actually only 262 penguins in each group. How many penguins will be in the final, possibly incomplete, group now?
LLemma 34B:
Reasoning: 309/262 = <<309/262=1>>1 group of 262 penguins, and 47 penguins will be in the final, possibly incomplete, group. ### Answer: 47
Expected answer: 47
Correct? Yes
Problem: A sandwich shop has 580 slices of bread. They use 18 slices of bread for each sandwich-making batch. After using up the bread in these batches, how many slices will they have left?
LLemma 34B:
Reasoning: 580/18 = <<580/18=32.22222222222222>>32.22222222222222 slices of bread will be used in the batches. 580-32.22222222222222 = <<580-32.22222222222222=547.7777777777778>>547.7777777777778 slices of bread will be left. ### Answer: 547.7777777777778
Expected answer: 4
Correct? No
Problem: A tailor has 925 meters of fabric. The tailor uses 529 meters of fabric to make each dress. If the tailor uses the fabric evenly for each dress, how many meters of fabric will be left over after completing the dresses?
LLemma 34B:
Reasoning: The tailor uses 529/925 = <<529/925=0.57>>0.57 meters of fabric to make each dress. The tailor uses 925/529 = <<925/529=1.74>>1.74 dresses of fabric. The tailor uses 925-1.74*529 = <<925-1.74*529=10.2>>10.2 meters of fabric will be left over after completing the dresses. ### Answer: 10.2
Expected answer: 396
Correct? No
Problem: There are 976 tourists wanting to explore a castle. Each tour group throughout the day accommodates up to 530 people. After all the groups have taken off, how many tourists will be left for the last group of the day?
LLemma 34B:
Reasoning: 976/530 = <<976/530=1.85>>1.85 groups of tourists can be accommodated. The last group of the day will have 976 - 1.85*530 = <<976-1.85*530=106>>106 tourists. ### Answer: 106
Expected answer: 446
Correct? No