LLemma 34B on 7.NS.A.1-fraction
Common Core Standard 7.NS.A.1-fraction
This standard covers the following:
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Problem: Math problem: Determine the value of the sum when adding (74 / 63) and (91 / 78).
LLemma 34B:
Reasoning: (74 / 63) + (91 / 78) = <<(74/63)+(91/78)=1.168>>1.168 ### Answer: 1.168
Expected answer: 295/126
Correct? No
Problem: What is the result of adding 94/5 to 1/25?
LLemma 34B:
Reasoning: 94/5 = <<94/5=18.8>>18.8 1/25 = <<1/25=0.04>>0.04 18.8+0.04 = <<18.8+0.04=18.84>>18.84 ### Answer: 18.84
Expected answer: 471/25
Correct? Yes
Problem: If the sum from the previous problem is then added to 73/89, what is the final result?
LLemma 34B:
Reasoning: 18.84+73/89 = <<18.84+73/89=18.84+0.82=27.06>>27.06 ### Answer: 27.06
Expected answer: 43744/2225
Correct? No
Problem: If instead of adding 94/5 you had added 94/89 to 1/25 in the previous problem, what would have been the result?
LLemma 34B:
Reasoning: 94/89 = <<94/89=1.0512820512820513>>1.0512820512820513 1/25 = <<1/25=0.04>>0.04 1.0512820512820513+0.04 = <<1.0512820512820513+0.04=1.0912820512820513>>1.0912820512820513 ### Answer: 1.0912820512820513
Expected answer: 2439/2225
Correct? No
Problem: What is the result of subtracting 48/20 from 49/8? Answer as a simplified fraction.
LLemma 34B:
Reasoning: 48/20 = <<48/20=2.4>>2.4 and 49/8 = <<49/8=6.125>>6.125. 2.4-6.125 = <<2.4-6.125=-3.725>>-3.725. ### Answer: -3.725
Expected answer: 149/40
Correct? No
Problem: Calculate the value of the expression ((45 / 5) - (6 / 47)).
LLemma 34B:
Reasoning: ((45 / 5) - (6 / 47)) = (<<45/5=9>>9 - (<<6/47=0.12766>>0.12766)) = (9 - 0.12766) = <<9-0.12766=8.87234>>8.87234 ### Answer: 8.87234
Expected answer: 417/47
Correct? No
Problem: What is the sum of 22/49 and 72/35? Provide your answer as a simplified fraction.
LLemma 34B:
Reasoning: 22/49 + 72/35 = <<22/49+72/35=104/84>>104/84 ### Answer: 104/84
Expected answer: 614/245
Correct? No
Problem: What is the result of (39 / 9) - (44 / 69)?
LLemma 34B:
Reasoning: (39 / 9) - (44 / 69) = (4.333333333333333 - 0.6333333333333333) = <<4.333333333333333-0.6333333333333333=3.7>>3.7 ### Answer: 3.7
Expected answer: 85/23
Correct? No
Problem: Calculate the sum of 49/79 and 18/21.
LLemma 34B:
Reasoning: 49/79 + 18/21 = <<49/79+18/21=117/79>>117/79 ### Answer: 117/79
Expected answer: 817/553
Correct? No
Problem: What is the sum of 95/46 and 65/31?
LLemma 34B:
Reasoning: 95/46 + 65/31 = <<95/46+65/31=160/77>>160/77 ### Answer: 160/77
Expected answer: 5935/1426
Correct? No
Problem: What is the sum of 25 over 63 and 74 over 6?
LLemma 34B:
Reasoning: 25/63 + 74/6 = <<25/63+74/6=109/63>>109/63 ### Answer: 109/63
Expected answer: 802/63
Correct? No
Problem: What is the sum of 79/91 and 100/47?
LLemma 34B:
Reasoning: 79/91 + 100/47 = <<79/91+100/47=179/138>>179/138 ### Answer: 179/138
Expected answer: 12813/4277
Correct? No
Problem: What is the result of ((55 / 47) + (72 / 21))?
LLemma 34B:
Reasoning: ((55 / 47) + (72 / 21)) = (1 + 3) = <<1+3=4>>4 ### Answer: 4
Expected answer: 1513/329
Correct? No
Problem: What is the sum of 86/62 and 99/41?
LLemma 34B:
Reasoning: 86/62 = <<86/62=1.38>>1.38 and 99/41 = <<99/41=2.44>>2.44. 1.38+2.44 = <<1.38+2.44=3.82>>3.82 ### Answer: 3.82
Expected answer: 4832/1271
Correct? No
Problem: Calculate the sum of 87/88 and 24/13.
LLemma 34B:
Reasoning: 87/88 + 24/13 = <<87/88+24/13=111/88>>111/88 ### Answer: 111/88
Expected answer: 3243/1144
Correct? No
Problem: Calculate ((68 / 33) + (70 / 25)). Write your answer in its simplest form.
LLemma 34B:
Reasoning: ((68 / 33) + (70 / 25)) = (2 + 2) = 4 ### Answer: 4
Expected answer: 802/165
Correct? No
Problem: What is the summation of 35/97 and 11/9? Express the result in simplest form.
LLemma 34B:
Reasoning: 35/97 + 11/9 = <<35/97+11/9=146/97>>146/97 ### Answer: 146/97
Expected answer: 1382/873
Correct? No
Problem: What is the result of subtracting 79/70 from 11/5?
LLemma 34B:
Reasoning: 11/5 - 79/70 = <<11/5-79/70=11/5-79/70>>11/5 - 79/70 = 11/5 - 1/5 = <<11/5-1/5=10/5>>10/5 = 2 ### Answer: 2
Expected answer: 15/14
Correct? No
Problem: What is the sum of 68/16 and 52/78?
LLemma 34B:
Reasoning: 68/16 = <<68/16=4.25>>4.25 and 52/78 = <<52/78=0.6666666666666666>>0.6666666666666666. The sum of 68/16 and 52/78 is 4.25+0.6666666666666666 = <<4.25+0.6666666666666666=4.916666666666666>>4.916666666666666. ### Answer: 4.916666666666666
Expected answer: 59/12
Correct? No
Problem: Find the sum of 21/75 and 44/47.
LLemma 34B:
Reasoning: 21/75 + 44/47 = <<21/75+44/47=105/322>>105/322 ### Answer: 105/322
Expected answer: 1429/1175
Correct? No
Problem: Calculate the result of (77/5 + 4/11).
LLemma 34B:
Reasoning: (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4
Expected answer: 867/55
Correct? Yes
Problem: After finding the result of (77/5 + 4/11), add that result to 94/60. What is the final answer?
LLemma 34B:
Reasoning: (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4
Expected answer: 5719/330
Correct? No
Problem: Instead of the original problem (77/5 + 4/11), consider a change such that now we are adding 77/5 and 4/79 instead. In the context of the previous word problem, if we were originally adding parts of a recipe, we could consider the change as modifying one part of the recipe. What happens if we modify the recipe in this way, by replacing the quantity we originally added with 4/79?
LLemma 34B:
Reasoning: (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4/11) = (77/5 + 4
Expected answer: 6103/395
Correct? No
Problem: What's the sum of 60/48 and 37/47?
LLemma 34B:
Reasoning: 60/48 = <<60/48=1.25>>1.25 and 37/47 = <<37/47=0.78975621890547>>0.78975621890547. 1.25+0.78975621890547 = <<1.25+0.78975621890547=2.03975621890547>>2.03975621890547 ### Answer: 2.03975621890547
Expected answer: 383/188
Correct? No
Problem: Solve ((14 / 72) + (25 / 6)).
LLemma 34B:
Reasoning: ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (25 / 6)) = ((14 / 72) + (
Expected answer: 157/36
Correct? No
Problem: What is the sum of 84/97 and 25/2?
LLemma 34B:
Reasoning: 84/97 + 25/2 = <<84/97+25/2=109/97>>109/97 ### Answer: 109/97
Expected answer: 2593/194
Correct? No
Problem: What is the difference between the fractions 66/20 and 4/78?
LLemma 34B:
Reasoning: 66/20 = <<66/20=3.3>>3.3 and 4/78 = <<4/78=0.05128205128205128>>0.05128205128205128. The difference is 3.3-0.05128205128205128 = <<3.3-0.05128205128205128=3.248717948717949>>3.248717948717949. ### Answer: 3.248717948717949
Expected answer: 1267/390
Correct? No
Problem: Calculate the expression: 83 divided by 37 minus 12 divided by 14.
LLemma 34B:
Reasoning: 83/37 - 12/14 = <<83/37-12/14=1.7027>>1.7027 ### Answer: 1.7027
Expected answer: 359/259
Correct? No
Problem: What is the sum of 95/57 and 28/80?
LLemma 34B:
Reasoning: 95/57 = <<95/57=1.6666666666666667>>1.6666666666666667 28/80 = <<28/80=0.35>>0.35 1.6666666666666667+0.35 = <<1.6666666666666667+0.35=1.9999999999999998>>1.9999999999999998 ### Answer: 1.9999999999999998
Expected answer: 121/60
Correct? No
Problem: Calculate the sum of 14/57 and 92/42.
LLemma 34B:
Reasoning: 14/57 = <<14/57=0.244898>>0.244898 and 92/42 = <<92/42=2.190476>>2.190476. 14/57 + 92/42 = <<14/57+92/42=2.435374>>2.435374 ### Answer: 2.435374
Expected answer: 324/133
Correct? No
Problem: What is the result of ((77 / 55) + (6 / 5))?
LLemma 34B:
Reasoning: ((77 / 55) + (6 / 5)) = (1 + 1) = 2 ### Answer: 2
Expected answer: 13/5
Correct? No
Problem: Calculate the value of (56 / 8) + (90 / 86). How much does it equal?
LLemma 34B:
Reasoning: (56 / 8) + (90 / 86) = <<56/8+90/86=7.5+1.036=8.536>>8.536 ### Answer: 8.536
Expected answer: 346/43
Correct? No
Problem: What is the sum of 23/20 and 82/97?
LLemma 34B:
Reasoning: 23/20 + 82/97 = <<23/20+82/97=105/97>>105/97 ### Answer: 105/97
Expected answer: 3871/1940
Correct? No
Problem: Calculate the sum of 54/88 and 28/10.
LLemma 34B:
Reasoning: 54/88 = <<54/88=0.61728395>>0.61728395 and 28/10 = <<28/10=2.8>>2.8. 0.61728395 + 2.8 = <<0.61728395+2.8=3.41728395>>3.41728395 ### Answer: 3.41728395
Expected answer: 751/220
Correct? No
Problem: What is the result of the following operation: 7 / 69 + 71 / 47?
LLemma 34B:
Reasoning: 7 / 69 + 71 / 47 = 7/69 + 71/47 = <<7/69+71/47=1/9+1/4=5/36>>5/36 ### Answer: 5/36
Expected answer: 5228/3243
Correct? No
Problem: What is the sum of 15/32 and 65/15?
LLemma 34B:
Reasoning: 15/32 + 65/15 = <<15/32+65/15=103/15>>103/15 ### Answer: 103/15
Expected answer: 461/96
Correct? No
Problem: What is the sum of 4/31 and 76/11?
LLemma 34B:
Reasoning: 4/31 = <<4/31=0.129>>0.129 and 76/11 = <<76/11=6.909>>6.909. 4/31 + 76/11 = <<4/31+76/11=7.038>>7.038 ### Answer: 7.038
Expected answer: 2400/341
Correct? No
Problem: What is the sum when you add 82/15 to 100/12?
LLemma 34B:
Reasoning: 82/15 + 100/12 = <<82/15+100/12=104/15>>104/15 ### Answer: 104/15
Expected answer: 69/5
Correct? No
Problem: Calculate the result of the expression ((92 / 29) + (41 / 33)). Write your answer as a simplified fraction or a whole number.
LLemma 34B:
Reasoning: ((92 / 29) + (41 / 33)) = (3 + (41 / 33)) = (3 + 1) = 4 ### Answer: 4
Expected answer: 4225/957
Correct? No
Problem: What is the sum of 57/29 and 14/98?
LLemma 34B:
Reasoning: 57/29 = <<57/29=1.96551724137931>>1.96551724137931 14/98 = <<14/98=0.142857142857143>>0.142857142857143 57/29 + 14/98 = <<57/29+14/98=2.10837438423645>>2.10837438423645 ### Answer: 2.10837438423645
Expected answer: 428/203
Correct? No
Problem: Solve the given expression: 70/25 + 83/28.
LLemma 34B:
Reasoning: 70/25 = <<70/25=2.8>>2.8 and 83/28 = <<83/28=2.93>>2.93. 2.8 + 2.93 = <<2.8+2.93=5.73>>5.73 ### Answer: 5.73
Expected answer: 807/140
Correct? No
Problem: What is the result of adding the fractions 50/73 and 20/23?
LLemma 34B:
Reasoning: 50/73 + 20/23 = <<50/73+20/23=1230/1619>>1230/1619 ### Answer: 1230/1619
Expected answer: 2610/1679
Correct? No
Problem: What is the value of ((49 / 57) + (89 / 99))?
LLemma 34B:
Reasoning: ((49 / 57) + (89 / 99)) = <<(49/57)+(89/99)=0.87>>0.87 ### Answer: 0.87
Expected answer: 3308/1881
Correct? No
Problem: Calculate the result of 94 / 35 - 23 / 49. Report your answer as a simplified fraction.
LLemma 34B:
Reasoning: 94 / 35 = <<94/35=2.6857142857142857>>2.6857142857142857 23 / 49 = <<23/49=0.4693877551020408>>0.4693877551020408 2.6857142857142857 - 0.4693877551020408 = <<2.6857142857142857-0.4693877551020408=2.2163265306122445>>2.2163265306122445 ### Answer: 2.2163265306122445
Expected answer: 543/245
Correct? No
Problem: Calculate the sum of 58/30 and 49/37 and leave your answer as a fraction.
LLemma 34B:
Reasoning: 58/30 = <<58/30=19/10>>19/10 and 49/37 = <<49/37=7/4>>7/4. 19/10 + 7/4 = <<19/10+7/4=113/20>>113/20 ### Answer: 113/20
Expected answer: 1808/555
Correct? No
Problem: Calculate the sum of 45/53 and 71/50.
LLemma 34B:
Reasoning: 45/53 + 71/50 = <<45/53+71/50=116/263>>116/263 ### Answer: 116/263
Expected answer: 6013/2650
Correct? No
Problem: Calculate the sum of 36/72 and 49/1.
LLemma 34B:
Reasoning: 36/72 = <<36/72=1/2>>1/2 and 49/1 = <<49/1=49>>49. 1/2 + 49 = <<1/2+49=50>>50 ### Answer: 50
Expected answer: 99/2
Correct? No
Problem: What is the sum of 61/20 and 29/15?
LLemma 34B:
Reasoning: 61/20 = <<61/20=3.05>>3.05 and 29/15 = <<29/15=1.9333333333333333>>1.9333333333333333. 3.05+1.9333333333333333 = <<3.05+1.9333333333333333=4.983333333333333>>4.983333333333333 ### Answer: 4.983333333333333
Expected answer: 299/60
Correct? Yes
Problem: After finding the sum of 61/20 and 29/15, add that result to 58/31. What is the final answer?
LLemma 34B:
Reasoning: 61/20 = <<61/20=3.05>>3.05 and 29/15 = <<29/15=1.9333333333333333>>1.9333333333333333. 3.05+1.9333333333333333 = <<3.05+1.9333333333333333=4.983333333333333>>4.983333333333333 4.983333333333333+58/31 = <<4.983333333333333+58/31=10.983333333333334>>10.983333333333334 ### Answer: 10.983333333333334
Expected answer: 12749/1860
Correct? No
Problem: Previously you found the sum of 61/20 and 29/15. Now let's change the 15 in the denominator of the second fraction to 67, so that we are adding 61/20 and 29/67. What will the new sum be?
LLemma 34B:
Reasoning: 61/20 = <<61/20=3.05>>3.05 and 29/67 = <<29/67=0.4339622641509434>>0.4339622641509434. 3.05+0.4339622641509434 = <<3.05+0.4339622641509434=3.4839622641509434>>3.4839622641509434 ### Answer: 3.4839622641509434
Expected answer: 4667/1340
Correct? No
Problem: Solve the expression ((33 / 90) + (77 / 79)). Give your answer as an unsimplified fraction.
LLemma 34B:
Reasoning: ((33 / 90) + (77 / 79)) = <<(33/90)+(77/79)=(33*79+77*90)/(90*79)=1157/7110>>1157/7110 ### Answer: 1157/7110
Expected answer: 3179/2370
Correct? No
Problem: What is the sum of 30/79 and 29/6? Give your answer as a fraction.
LLemma 34B:
Reasoning: 30/79 + 29/6 = <<30/79+29/6=119/474>>119/474 ### Answer: 119/474
Expected answer: 2471/474
Correct? No
Problem: What is the answer when you subtract 11/66 from 59/2?
LLemma 34B:
Reasoning: 11/66 = <<11/66=1/6>>1/6. 59/2 - 1/6 = <<59/2-1/6=59/2-1/6=295/12=24 5/12>>24 5/12. ### Answer: 24 5/12
Expected answer: 88/3
Correct? No
Problem: Consider these two fractions: 58/23 and 25/26. What is the sum when those two fractions are added together?
LLemma 34B:
Reasoning: 58/23 + 25/26 = <<58/23+25/26=103/49>>103/49 ### Answer: 103/49
Expected answer: 2083/598
Correct? No
Problem: Calculate the sum of the fractions 70/13 and 17/52.
LLemma 34B:
Reasoning: 70/13 + 17/52 = <<70/13+17/52=107/65>>107/65 ### Answer: 107/65
Expected answer: 297/52
Correct? No
Problem: What is the sum of 78/44 and 17/91?
LLemma 34B:
Reasoning: 78/44 = <<78/44=1.7727272727272727>>1.7727272727272727 17/91 = <<17/91=0.18686868686868687>>0.18686868686868687 78/44 + 17/91 = <<78/44+17/91=1.9595959595959596>>1.9595959595959596 ### Answer: 1.9595959595959596
Expected answer: 3923/2002
Correct? No
Problem: What is the sum of 43/4 and 71/4?
LLemma 34B:
Reasoning: 43/4 + 71/4 = <<43/4+71/4=114/4>>114/4 ### Answer: 114/4
Expected answer: 57/2
Correct? Yes
Problem: What is the sum of 43/4 and 71/4 plus 92/79?
LLemma 34B:
Reasoning: 43/4 + 71/4 + 92/79 = <<43/4+71/4+92/79=114/4+92/79>>114/4 + 92/79 ### Answer: 114/4 + 92/79
Expected answer: 4687/158
Correct? Yes
Problem: What if instead of adding 71/4, we added 71/89 to 43/4? What would be the new total?
LLemma 34B:
Reasoning: 43/4 + 71/89 = <<43/4+71/89=114/89>>114/89 ### Answer: 114/89
Expected answer: 4111/356
Correct? No
Problem: What is the result of adding the fractions 17/74 and 53/27?
LLemma 34B:
Reasoning: 17/74 + 53/27 = <<17/74+53/27=100/74>>100/74 ### Answer: 100/74
Expected answer: 4381/1998
Correct? No
Problem: Compute the value of (76/76) + (96/16).
LLemma 34B:
Reasoning: (76/76) + (96/16) = 1 + 6 = <<1+6=7>>7. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: After finding the value of (76/76) + (96/16), what is the result when you add the solution to itself?
LLemma 34B:
Reasoning: 7 + 7 = <<7+7=14>>14. ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: You originally calculated (76/76) + (96/16). Now reconsider your thought, what would be the new total if the second fraction was 96/33 instead of 96/16?
LLemma 34B:
Reasoning: (76/76) + (96/33) = 1 + (96/33) = <<1+(96/33)=1+3>>1+3 = <<1+3=4>>4. ### Answer: 4
Expected answer: 43/11
Correct? No
Problem: What is the result of ((94 / 14) - (50 / 90))? Answer as a simplified fraction.
LLemma 34B:
Reasoning: ((94 / 14) - (50 / 90)) = ((94 / 14) - (1 / 2)) = (7 - (1 / 2)) = (7 - 0.5) = 6.5 ### Answer: 6.5
Expected answer: 388/63
Correct? No
Problem: What is the result of subtracting twenty-nine seventy-ninths from thirty-three sevenths?
LLemma 34B:
Reasoning: 29/79 = <<29/79=0.369>>0.369 and 33/7 = <<33/7=4.714>>4.714. 0.369 - 4.714 = <<0.369-4.714=-4.345>>-4.345 ### Answer: -4.345
Expected answer: 2404/553
Correct? No
Problem: What is the sum of 60/79 and 53/38?
LLemma 34B:
Reasoning: 60/79 + 53/38 = <<60/79+53/38=113/79>>113/79 ### Answer: 113/79
Expected answer: 6467/3002
Correct? No
Problem: Solve the following fraction equation: 39/48 + 19/84.
LLemma 34B:
Reasoning: 39/48 + 19/84 = <<39/48+19/84=1>>1 ### Answer: 1
Expected answer: 349/336
Correct? No
Problem: What is the sum of 16/86 and 60/3?
LLemma 34B:
Reasoning: 16/86 = <<16/86=1/5>>1/5 and 60/3 = <<60/3=20>>20. 1/5 + 20 = <<1/5+20=20 1/5>>20 1/5. ### Answer: 20 1/5
Expected answer: 868/43
Correct? No
Problem: Solve the following equation: ((95 / 69) + (67 / 9))
LLemma 34B:
Reasoning: ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (67 / 9)) = ((95 / 69) + (
Expected answer: 1826/207
Correct? No
Problem: Calculate the result of 95 / 16 - 43 / 60.
LLemma 34B:
Reasoning: 95 / 16 = <<95/16=5.9375>>5.9375 and 43 / 60 = <<43/60=0.7166666666666666>>0.7166666666666666. 5.9375 - 0.7166666666666666 = <<5.9375-0.7166666666666666=5.220833333333333>>5.220833333333333 ### Answer: 5.220833333333333
Expected answer: 1253/240
Correct? Yes
Problem: After finding the result of 95 / 16 - 43 / 60, add the result to 80 / 79. What is the final answer?
LLemma 34B:
Reasoning: 80 / 79 = <<80/79=1.0126582278481013>>1.0126582278481013. 5.220833333333333 + 1.0126582278481013 = <<5.220833333333333+1.0126582278481013=6.233491561696434>>6.233491561696434 ### Answer: 6.233491561696434
Expected answer: 118187/18960
Correct? No
Problem: After finding the result of 95 / 16 - 43 / 60 in the previous problem, let's change it a bit. What if instead of 95/16, you had 91/16 and you subtracted 43/60 from it? What would the new result be?
LLemma 34B:
Reasoning: 91/16 = <<91/16=5.6875>>5.6875 and 43/60 = <<43/60=0.7166666666666666>>0.7166666666666666. 5.6875 - 0.7166666666666666 = <<5.6875-0.7166666666666666=4.970833333333333>>4.970833333333333 ### Answer: 4.970833333333333
Expected answer: 1193/240
Correct? No
Problem: What is the sum of the fractions 38/8 and 4/16?
LLemma 34B:
Reasoning: 38/8 = <<38/8=4.75>>4.75 and 4/16 = <<4/16=0.25>>0.25. 4.75+0.25 = <<4.75+0.25=5>>5. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: Recalling the fraction calculation from the previous problem (38/8 and 4/16), what is the new total if you were to add 32/64 to this sum?
LLemma 34B:
Reasoning: 32/64 = <<32/64=0.5>>0.5. 5+0.5 = <<5+0.5=5.5>>5.5. ### Answer: 5.5
Expected answer: 11/2
Correct? Yes
Problem: In the previous problem, we considered the sum of the fractions 38/8 and 4/16 and then added 32/64. Now, instead of 38/8, let's consider 12/8. What would be the new sum if you added 12/8 and 4/16 together?
LLemma 34B:
Reasoning: 12/8 = <<12/8=1.5>>1.5 and 4/16 = <<4/16=0.25>>0.25. 1.5+0.25 = <<1.5+0.25=1.75>>1.75. ### Answer: 1.75
Expected answer: 7/4
Correct? Yes
Problem: Calculate the result of 67 / 15 - 27 / 12.
LLemma 34B:
Reasoning: 67 / 15 = <<67/15=4.466666666666667>>4.466666666666667 27 / 12 = <<27/12=2.25>>2.25 67 / 15 - 27 / 12 = <<67/15-27/12=2.213333333333333>>2.213333333333333 ### Answer: 2.213333333333333
Expected answer: 133/60
Correct? No
Problem: Calculate the sum of 38/59 and 80/94.
LLemma 34B:
Reasoning: 38/59 + 80/94 = <<38/59+80/94=118/153>>118/153 ### Answer: 118/153
Expected answer: 4146/2773
Correct? No
Problem: Calculate the sum of 10/14 and 70/20. Report your answer as a decimal.
LLemma 34B:
Reasoning: 10/14 = <<10/14=0.7142857142857143>>0.7142857142857143 and 70/20 = <<70/20=3.5>>3.5. 10/14 + 70/20 = <<10/14+70/20=4.214285714285714>>4.214285714285714 ### Answer: 4.214285714285714
Expected answer: 59/14
Correct? Yes
Problem: After calculating the sum of 10/14 and 70/20, add this result to 100/20. What is the new total?
LLemma 34B:
Reasoning: 100/20 = <<100/20=5>>5. 10/14 + 70/20 + 100/20 = <<10/14+70/20+100/20=9.214285714285714>>9.214285714285714 ### Answer: 9.214285714285714
Expected answer: 129/14
Correct? No
Problem: After reviewing your previous calculation, you realize that the first fraction was not 10/14 but actually 10/18. Now find the sum of the corrected fraction, 10/18 and the same second fraction, 70/20. What is the revised total?
LLemma 34B:
Reasoning: 10/18 = <<10/18=0.5555555555555556>>0.5555555555555556 and 70/20 = <<70/20=3.5>>3.5. 10/18 + 70/20 = <<10/18+70/20=4.055555555555555>>4.055555555555555 ### Answer: 4.055555555555555
Expected answer: 73/18
Correct? No
Problem: What is the result of subtracting 19/44 from 33/5?
LLemma 34B:
Reasoning: 33/5 - 19/44 = <<33/5-19/44=11/4>>11/4 ### Answer: 11/4
Expected answer: 1357/220
Correct? No
Problem: Find the result for (97 / 13) + (62 / 22). Answer as a decimal to the nearest hundredth.
LLemma 34B:
Reasoning: (97 / 13) + (62 / 22) = (97 / 13) + (62 / 22) = <<97/13+62/22=7.5+2.8=10.3>>10.3 ### Answer: 10.3
Expected answer: 1470/143
Correct? No
Problem: What is the sum of 78 divided by 35 and 30 divided by 60?
LLemma 34B:
Reasoning: 78/35 = <<78/35=2.2285714285714285714285714285714>>2.2285714285714285714285714285714 30/60 = <<30/60=0.5>>0.5 2.2285714285714285714285714285714+0.5 = <<2.2285714285714285714285714285714+0.5=2.7285714285714285714285714285714>>2.7285714285714285714285714285714 ### Answer: 2.7285714285714285714285714285714
Expected answer: 191/70
Correct? Yes
Problem: What is the sum of 49/75 and 88/58?
LLemma 34B:
Reasoning: 49/75 + 88/58 = <<49/75+88/58=137/135>>137/135 ### Answer: 137/135
Expected answer: 4721/2175
Correct? No
Problem: What is the result of ((50 / 2) - (50 / 32))?
LLemma 34B:
Reasoning: 50/2 = <<50/2=25>>25 and 50/32 = <<50/32=1.5625>>1.5625. 25 - 1.5625 = <<25-1.5625=23.4375>>23.4375. ### Answer: 23.4375
Expected answer: 375/16
Correct? Yes
Problem: Following up on our previous question, what is the result when you add (72 / 81) to the difference between (50 / 2) and (50 / 32)?
LLemma 34B:
Reasoning: 72/81 = <<72/81=0.888888888888889>>0.888888888888889. 50/2 = <<50/2=25>>25 and 50/32 = <<50/32=1.5625>>1.5625. 25 - 1.5625 = <<25-1.5625=23.4375>>23.4375. 23.4375 + 0.888888888888889 = <<23.4375+0.888888888888889=24.32647222222222>>24.32647222222222. ### Answer: 24.32647222222222
Expected answer: 3503/144
Correct? No
Problem: Following the previous problem, consider this change, what would the result be if instead of dividing by 32, you divide 50 by 91? What would be the new result for ((50 / 2) - (50 / 91))?
LLemma 34B:
Reasoning: 50/2 = <<50/2=25>>25 and 50/91 = <<50/91=0.550561797752809>>0.550561797752809. 25 - 0.550561797752809 = <<25-0.550561797752809=24.44943820224719>>24.44943820224719. ### Answer: 24.44943820224719
Expected answer: 2225/91
Correct? No
Problem: What is the result of ((77 / 30) + (18 / 51))?
LLemma 34B:
Reasoning: ((77 / 30) + (18 / 51)) = (<<77/30=2.5666666666666665>>2.5666666666666665 + (<<18/51=0.3529411764705882>>0.3529411764705882)) = (2.5666666666666665 + 0.3529411764705882) = <<2.5666666666666665+0.3529411764705882=2.9196078421172543>>2.9196078421172543 ### Answer: 2.9196078421172543
Expected answer: 1489/510
Correct? No
Problem: What is the result of (36 / 37) + (8 / 4)?
LLemma 34B:
Reasoning: (36 / 37) + (8 / 4) = <<36/37+8/4=1.025>>1.025 ### Answer: 1.025
Expected answer: 110/37
Correct? No
Problem: Calculate the result of (57 / 22) - (72 / 48) expressing your answer as a fraction in the simplest form.
LLemma 34B:
Reasoning: (57 / 22) - (72 / 48) = (57 / 22) - (2 * 72 / 2 * 48) = (57 / 22) - (72 / 96) = (57 * 96 / 22 * 96) - (72 / 96) = (5184 / 2016) - (72 / 96) = (5184 - 72) / 2016 = 5112 / 2016 = 2556 / 1008 = 1278 / 504 = 639 / 252 = 213 / 84 = 213 / (2 * 42) = 106 / 42 = 53 / 21 = 17 / 7 ### Answer: 17/7
Expected answer: 12/11
Correct? No
Problem: What is the sum of 48 divided by 16 and 12 divided by 29?
LLemma 34B:
Reasoning: 48/16 = <<48/16=3>>3 and 12/29 = <<12/29=0.4137931034>>0.4137931034. 3+0.4137931034 = <<3+0.4137931034=3.4137931034>>3.4137931034 ### Answer: 3.4137931034
Expected answer: 99/29
Correct? No
Problem: What is the sum of 37/20 and 16/75? Write your answer as a simplified fraction.
LLemma 34B:
Reasoning: 37/20 = <<37/20=1.85>>1.85 and 16/75 = <<16/75=0.21333333333333334>>0.21333333333333334. 1.85+0.21333333333333334 = <<1.85+0.21333333333333334=2.0633333333333335>>2.0633333333333335. ### Answer: 2.0633333333333335
Expected answer: 619/300
Correct? Yes
Problem: In addition to the previously computed sum of 37/20 and 16/75, now add the fraction 61/80 to this sum. What is the total when all three fractions are added together?
LLemma 34B:
Reasoning: 61/80 = <<61/80=0.7625>>0.7625. 2.0633333333333335+0.7625 = <<2.0633333333333335+0.7625=2.8258333333333335>>2.8258333333333335. ### Answer: 2.8258333333333335
Expected answer: 3391/1200
Correct? No
Problem: If there originally were 60/20 portions of a cake and you added 16/75 portions of another cake to it, how much cake would you have in total? Please write your answer as a simplified fraction.
LLemma 34B:
Reasoning: 60/20 = <<60/20=3>>3 and 16/75 = <<16/75=0.21333333333333334>>0.21333333333333334. 3+0.21333333333333334 = <<3+0.21333333333333334=3.2133333333333335>>3.2133333333333335. ### Answer: 3.2133333333333335
Expected answer: 241/75
Correct? No
Problem: Calculate the summation: 83/40 + 6/8.
LLemma 34B:
Reasoning: 83/40 = <<83/40=2.075>>2.075 and 6/8 = <<6/8=0.75>>0.75. 2.075 + 0.75 = <<2.075+0.75=2.825>>2.825 ### Answer: 2.825
Expected answer: 113/40
Correct? Yes
Problem: After finding the result of 83/40 + 6/8, subtract 24/64 from it. What do you get?
LLemma 34B:
Reasoning: 83/40 + 6/8 = <<83/40+6/8=2.825>>2.825. 2.825 - 24/64 = <<2.825-24/64=2.75>>2.75 ### Answer: 2.75
Expected answer: 49/20
Correct? No
Problem: After adjusting our original calculation, we now have 83/18 instead of 83/40. So now, what is the result of 83/18 + 6/8?
LLemma 34B:
Reasoning: 83/18 = <<83/18=4.555555555555555>>4.555555555555555 and 6/8 = <<6/8=0.75>>0.75. 4.555555555555555 + 0.75 = <<4.555555555555555+0.75=5.305555555555555>>5.305555555555555 ### Answer: 5.305555555555555
Expected answer: 193/36
Correct? No
Problem: Find the result of the addition of the fractions 37/69 and 67/61.
LLemma 34B:
Reasoning: 37/69 + 67/61 = <<37/69+67/61=104/130>>104/130 ### Answer: 104/130
Expected answer: 6880/4209
Correct? No
Problem: What is the sum of 89/84 and 75/34?
LLemma 34B:
Reasoning: 89/84 + 75/34 = <<89/84+75/34=164/84>>164/84 ### Answer: 164/84
Expected answer: 4663/1428
Correct? No
Problem: What is the result when you add 51/78 and 44/83?
LLemma 34B:
Reasoning: 51/78 + 44/83 = <<51/78+44/83=105/161>>105/161 ### Answer: 105/161
Expected answer: 2555/2158
Correct? No
Problem: Calculate the sum of the fractions 99/85 and 77/55.
LLemma 34B:
Reasoning: 99/85 + 77/55 = <<99/85+77/55=176/175>>176/175 ### Answer: 176/175
Expected answer: 218/85
Correct? No
Problem: What is the value of 97 / 56 - 31 / 52? Represent your answer as a simplified fraction.
LLemma 34B:
Reasoning: 97/56 = <<97/56=1.7142857142857142>>1.7142857142857142 31/52 = <<31/52=0.5961538461538461>>0.5961538461538461 1.7142857142857142 - 0.5961538461538461 = <<1.7142857142857142-0.5961538461538461=0.8294151915191519>>0.8294151915191519 ### Answer: 0.8294151915191519
Expected answer: 827/728
Correct? No
Problem: Calculate the result of the following fraction operation: (78 / 74) + (72 / 51).
LLemma 34B:
Reasoning: (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 74) + (72 / 51) = (78 / 7
Expected answer: 1551/629
Correct? No
Problem: What is the result of the operation (33 / 23) - (12 / 75)? Express your answer as a fraction.
LLemma 34B:
Reasoning: (33 / 23) - (12 / 75) = (33 / 23) - (12 / 75) = (33 * 75) / (23 * 75) - (12 * 23) / (75 * 23) = <<33*75=2555>>2555 / <<23*75=1725>>1725 - <<12*23=276>>276 / <<75*23=1725>>1725 = <<2555/1725=1.485>>1.485 ### Answer: 1.485
Expected answer: 733/575
Correct? No
Problem: What is the result of the operation 85/42 - 98/99? Simplify your answer to the nearest hundredth.
LLemma 34B:
Reasoning: 85/42 - 98/99 = <<85/42-98/99=0.01>>0.01 ### Answer: 0.01
Expected answer: 1433/1386
Correct? No
Problem: What is the sum of 19/30 and 75/77? Express your answer as a simplified fraction.
LLemma 34B:
Reasoning: 19/30 + 75/77 = <<19/30+75/77=104/231>>104/231 ### Answer: 104/231
Expected answer: 3713/2310
Correct? No
Problem: What is the sum of 57/66 and 39/64? Please express your answer as a fraction.
LLemma 34B:
Reasoning: 57/66 + 39/64 = <<57/66+39/64=103/130>>103/130 ### Answer: 103/130
Expected answer: 1037/704
Correct? No
Problem: What is the sum of 80/13 and 2/48?
LLemma 34B:
Reasoning: 80/13 = <<80/13=6>>6 and 2/48 = <<2/48=1/24>>1/24. 6+1/24 = <<6+1/24=25/24>>25/24. ### Answer: 25/24
Expected answer: 1933/312
Correct? No
Problem: Calculate the result of the operation ((55 / 30) - (1 / 72)).
LLemma 34B:
Reasoning: ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (1 / 72)) = ((55 / 30) - (
Expected answer: 131/72
Correct? Yes
Problem: In the previous problem, you calculated the result of the operation ((55 / 30) - (1 / 72)). What would be the result if you added the fraction (73 / 92) to your answer?
LLemma 34B:
Reasoning: ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30) - (1 / 72)) + (73 / 92) = ((55 / 30)
Expected answer: 4327/1656
Correct? No
Problem: In the previous problem, we started with the operation ((55 / 30) - (1 / 72)). Suppose now that we started with 80 instead of 55 in the first fraction. How will the result change when you calculate the new operation ((80 / 30) - (1 / 72))?
LLemma 34B:
Reasoning: ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (1 / 72)) = ((80 / 30) - (
Expected answer: 191/72
Correct? No
Problem: Calculate the sum of the fractions 69/21 and 71/86.
LLemma 34B:
Reasoning: 69/21 = <<69/21=3.2857142857142856>>3.2857142857142856 and 71/86 = <<71/86=0.8173076923076923>>0.8173076923076923. 3.2857142857142856+0.8173076923076923 = <<3.2857142857142856+0.8173076923076923=4.1030219776219775>>4.1030219776219775 ### Answer: 4.1030219776219775
Expected answer: 2475/602
Correct? No
Problem: What is the sum of 24/60 and 42/45? Answer as a simplified fraction.
LLemma 34B:
Reasoning: 24/60 = <<24/60=2/5>>2/5 and 42/45 = <<42/45=8/15>>8/15. 2/5 + 8/15 = <<2/5+8/15=10/15>>10/15 = <<10/15=2/3>>2/3. ### Answer: 2/3
Expected answer: 4/3
Correct? No
Problem: What is the sum of 64/76 and 35/33?
LLemma 34B:
Reasoning: 64/76 = <<64/76=0.8392857142857143>>0.8392857142857143 35/33 = <<35/33=1.0545454545454546>>1.0545454545454546 64/76 + 35/33 = <<64/76+35/33=1.893831168724271>>1.893831168724271 ### Answer: 1.893831168724271
Expected answer: 1193/627
Correct? No
Problem: What is the sum of 47/16 and 96/10? Please, express your answer as a mixed fraction if necessary.
LLemma 34B:
Reasoning: 47/16 + 96/10 = 47/16 + 960/100 = 470/1600 + 960/1000 = 1430/1600 = 143/160 = 7/8 + 12/10 = 7/8 + 6/5 = 35/40 + 48/40 = 83/40 = 2 + 1/40 = 2 1/40 ### Answer: 2 1/40
Expected answer: 1003/80
Correct? No
Problem: What is the result of the operation (58 / 2) + (31 / 32)?
LLemma 34B:
Reasoning: (58 / 2) + (31 / 32) = (29 + 0.96875) = 29.96875 ### Answer: 29.96875
Expected answer: 959/32
Correct? Yes
Problem: After you have calculated the result of the operation (58 / 2) + (31 / 32), subtract 90 / 58 from your answer. What is the final result?
LLemma 34B:
Reasoning: (58 / 2) + (31 / 32) = (29 + 0.96875) = 29.96875 29.96875 - (90 / 58) = 29.96875 - 1.551724 = 28.416976 ### Answer: 28.416976
Expected answer: 26371/928
Correct? No
Problem: In the problem of adding (58 / 2) + (31 / 32), what would the result be if we originally had (58 / 2) + (10 / 32) instead? Now, compute the value.
LLemma 34B:
Reasoning: (58 / 2) + (10 / 32) = (29 + 0.3125) = 29.3125 ### Answer: 29.3125
Expected answer: 469/16
Correct? No
Problem: What is the sum of 26/90 and 50/26 when calculated as a fraction?
LLemma 34B:
Reasoning: 26/90 = <<26/90=1/3>>1/3 and 50/26 = <<50/26=5/2>>5/2. 1/3 + 5/2 = <<1/3+5/2=11/6>>11/6. ### Answer: 11/6
Expected answer: 1294/585
Correct? No
Problem: Calculate the sum of 80/98 and 92/82.
LLemma 34B:
Reasoning: 80/98 = <<80/98=0.81795>>0.81795 and 92/82 = <<92/82=1.12245>>1.12245. 0.81795+1.12245 = <<0.81795+1.12245=2.0>>2.0 ### Answer: 2.0
Expected answer: 3894/2009
Correct? No
Problem: Calculate the sum of 89/44 and 69/5.
LLemma 34B:
Reasoning: 89/44 = <<89/44=2.0454545454545454545454545454545>>2.0454545454545454545454545454545 69/5 = <<69/5=13.8>>13.8 89/44 + 69/5 = <<89/44+69/5=15.8454545454545454545454545454545>>15.8454545454545454545454545454545 ### Answer: 15.8454545454545454545454545454545
Expected answer: 3481/220
Correct? No
Problem: Calculate the following expression: 79/32 - 52/55.
LLemma 34B:
Reasoning: 79/32 - 52/55 = <<79/32-52/55=1/32>>1/32 ### Answer: 1/32
Expected answer: 2681/1760
Correct? No
Problem: If Wooden Treasures, a furniture workshop, cuts a log into pieces. Each piece is 45/2 feet long. If they sell a piece of wood that is 18/90 feet shorter than the usual length, how long is the piece they sold?
LLemma 34B:
Reasoning: The usual length of a piece of wood is 45/2 feet. The piece they sold is 18/90 feet shorter than the usual length. The piece they sold is 45/2 - 18/90 = <<45/2-18/90=22.5/90=1/4>>1/4 feet long. ### Answer: 1/4
Expected answer: 223/10
Correct? No
Problem: What is the sum of 99/92 and 15/74 as a simplified fraction?
LLemma 34B:
Reasoning: 99/92 + 15/74 = <<99/92+15/74=114/92>>114/92 ### Answer: 114/92
Expected answer: 4353/3404
Correct? No
Problem: Calculate the result of 54/1 + 62/30. Express your answer in simplest terms.
LLemma 34B:
Reasoning: 54/1 + 62/30 = <<54/1+62/30=54+62/30=116/30>>116/30 ### Answer: 116/30
Expected answer: 841/15
Correct? No
Problem: What value do you get by adding 85/29 and 47/7?
LLemma 34B:
Reasoning: 85/29 + 47/7 = <<85/29+47/7=132/29>>132/29 ### Answer: 132/29
Expected answer: 1958/203
Correct? No