LLemma 7B 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 7B:
Reasoning: (74 / 63) = <<74/63=1.15>>1.15 (91 / 78) = <<91/78=1.17>>1.17 1.15 + 1.17 = <<1.15+1.17=2.32>>2.32 ### Answer: 2.32
Expected answer: 295/126
Correct? No
Problem: What is the result of adding 94/5 to 1/25?
LLemma 7B:
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 7B:
Reasoning: 18.84+73/89 = <<18.84+73/89=18.84+0.82=19.66>>19.66 ### Answer: 19.66
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 7B:
Reasoning: 94/89 = <<94/89=1.05>>1.05 1/25 = <<1/25=0.04>>0.04 1.05+0.04 = <<1.05+0.04=1.09>>1.09 ### Answer: 1.09
Expected answer: 2439/2225
Correct? No
Problem: What is the result of subtracting 48/20 from 49/8? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 48/20 = <<48/20=3/1>>3/1 and 49/8 = <<49/8=7/2>>7/2. 3/1 - 7/2 = <<3/1-7/2=1/2>>1/2 ### Answer: 1/2
Expected answer: 149/40
Correct? No
Problem: Calculate the value of the expression ((45 / 5) - (6 / 47)).
LLemma 7B:
Reasoning: 45/5 = <<45/5=9>>9, 6/47 = <<6/47=0.127>>0.127 (9 - 0.127) = <<9-0.127=8.873>>8.873 ### Answer: 8.873
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 7B:
Reasoning: 22/49 + 72/35 = <<22/49 + 72/35>> = <<(22*35)/(49*35) + (72*49)/(35*49)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 + 72*49)/(49*35)>> = <<(22*35 +
Expected answer: 614/245
Correct? No
Problem: What is the result of (39 / 9) - (44 / 69)?
LLemma 7B:
Reasoning: 39/9 = <<39/9=4.2222222222222224>>4.2222222222222224 4.2222222222222224 - 44/69 = <<4.2222222222222224-44/69=0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Expected answer: 85/23
Correct? No
Problem: Calculate the sum of 49/79 and 18/21.
LLemma 7B:
Reasoning: 49/79 + 18/21 = <<49/79 + 18/21 = 1.25>>1.25 ### Answer: 1.25
Expected answer: 817/553
Correct? No
Problem: What is the sum of 95/46 and 65/31?
LLemma 7B:
Reasoning: 95/46 = <<95/46=2>>2 65/31 = <<65/31=2>>2 2+2 = <<2+2=4>>4 ### Answer: 4
Expected answer: 5935/1426
Correct? No
Problem: What is the sum of 25 over 63 and 74 over 6?
LLemma 7B:
Reasoning: 25/63 + 74/6 = <<25/63+74/6=11/2>>11/2 ### Answer: 11/2
Expected answer: 802/63
Correct? No
Problem: What is the sum of 79/91 and 100/47?
LLemma 7B:
Reasoning: 79/91 is approximately 0.8428571428571429 and 100/47 is approximately 2.1212121212121214. The sum of 79/91 and 100/47 is approximately 3.963679367936794. ### Answer: 3.963679367936794
Expected answer: 12813/4277
Correct? No
Problem: What is the result of ((55 / 47) + (72 / 21))?
LLemma 7B:
Reasoning: 55/47 = <<55/47=1.176470588235294>> 72/21 = <<72/21=3.470588235294118>> ((55 / 47) + (72 / 21)) = <<1.176470588235294+3.470588235294118=4.64705882352941>> ### Answer: 4.64705882352941
Expected answer: 1513/329
Correct? No
Problem: What is the sum of 86/62 and 99/41?
LLemma 7B:
Reasoning: 86/62 = <<86/62=1.4150943396226415>>1.4150943396226415 99/41 = <<99/41=2.435897435897436>>2.435897435897436 1.4150943396226415 + 2.435897435897436 = <<1.4150943396226415+2.435897435897436=3.850991775519077>>3.850991775519077 ### Answer: 3.850991775519077
Expected answer: 4832/1271
Correct? No
Problem: Calculate the sum of 87/88 and 24/13.
LLemma 7B:
Reasoning: 87/88 + 24/13 = <<87/88 + 24/13 = 115/109>>115/109 ### Answer: 115/109
Expected answer: 3243/1144
Correct? No
Problem: Calculate ((68 / 33) + (70 / 25)). Write your answer in its simplest form.
LLemma 7B:
Reasoning: 68/33 = <<68/33=2>>2 70/25 = <<70/25=2.8>>2.8 2+2.8 = <<2+2.8=4.8>>4.8 ### Answer: 4.8
Expected answer: 802/165
Correct? No
Problem: What is the summation of 35/97 and 11/9? Express the result in simplest form.
LLemma 7B:
Reasoning: 35/97 + 11/9 = <<35/97 + 11/9>> = <<(35*9 + 11*97)/(97*9)>> = <<(35*9 + 11*97)/(97*9)>> = <<(315 + 1063)/(943)>> = <<1378/943>> = <<1378/943>> ### Answer: 1378/943
Expected answer: 1382/873
Correct? No
Problem: What is the result of subtracting 79/70 from 11/5?
LLemma 7B:
Reasoning: 11/5 - 79/70 = <<11/5 - 79/70 = 11/5 - 79/70 = 11/5 * 70/79 = 11*70/5*79 = 77/395>>77/395 ### Answer: 77/395
Expected answer: 15/14
Correct? No
Problem: What is the sum of 68/16 and 52/78?
LLemma 7B:
Reasoning: 68/16 = <<68/16=4.25>>4.25 and 52/78 = <<52/78=0.66>>0.66. 4.25 + 0.66 = <<4.25+0.66=4.91>>4.91 ### Answer: 4.91
Expected answer: 59/12
Correct? No
Problem: Find the sum of 21/75 and 44/47.
LLemma 7B:
Reasoning: 21/75 = <<21/75=0.28>>0.28 and 44/47 = <<44/47=0.92>>0.92. 0.28+0.92 = <<0.28+0.92=1.19>>1.19 ### Answer: 1.19
Expected answer: 1429/1175
Correct? No
Problem: Calculate the result of (77/5 + 4/11).
LLemma 7B:
Reasoning: 77/5 = <<77/5=15.4>>15.4 4/11 = <<4/11=0.36>>0.36 15.4 + 0.36 = <<15.4+0.36=15.76>>15.76 ### Answer: 15.76
Expected answer: 867/55
Correct? No
Problem: What's the sum of 60/48 and 37/47?
LLemma 7B:
Reasoning: 60/48 = <<60/48=1.25>>1.25 and 37/47 = <<37/47=0.7894736842105263>>0.7894736842105263. 1.25+0.7894736842105263 = <<1.25+0.7894736842105263=2.0394736842105263>>2.0394736842105263 ### Answer: 2.0394736842105263
Expected answer: 383/188
Correct? No
Problem: Solve ((14 / 72) + (25 / 6)).
LLemma 7B:
Reasoning: 14/72 = <<14/72=0.2>>0.2 25/6 = <<25/6=4.166666666666667>>4.166666666666667 ((14 / 72) + (25 / 6)) = <<0.2+4.166666666666667=4.366666666666667>>4.366666666666667 ### Answer: 4.366666666666667
Expected answer: 157/36
Correct? No
Problem: What is the sum of 84/97 and 25/2?
LLemma 7B:
Reasoning: 84/97 = <<84/97=0.8620689655>>0.8620689655 and 25/2 = <<25/2=12.5>>12.5 0.8620689655 + 12.5 = <<0.8620689655+12.5=13.3620689655>>13.3620689655 ### Answer: 13.3620689655
Expected answer: 2593/194
Correct? No
Problem: What is the difference between the fractions 66/20 and 4/78?
LLemma 7B:
Reasoning: 66/20 = <<66/20=3.3>>3.3 and 4/78 = <<4/78=0.05>>0.05. 3.3 - 0.05 = <<3.3-0.05=3.25>>3.25 ### Answer: 3.25
Expected answer: 1267/390
Correct? No
Problem: Calculate the expression: 83 divided by 37 minus 12 divided by 14.
LLemma 7B:
Reasoning: 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided by 37 minus 12 divided by 14 = <<83/37-12/14>> 83 divided
Expected answer: 359/259
Correct? No
Problem: What is the sum of 95/57 and 28/80?
LLemma 7B:
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=1.9666666666666667>>1.9666666666666667 ### Answer: 1.9666666666666667
Expected answer: 121/60
Correct? No
Problem: Calculate the sum of 14/57 and 92/42.
LLemma 7B:
Reasoning: 14/57 + 92/42 = <<14/57+92/42=14/57+18/42=14/57+9/21=7/57+9/21=7/57+3/21=1/57+3/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1/21=1/57+1
Expected answer: 324/133
Correct? No
Problem: What is the result of ((77 / 55) + (6 / 5))?
LLemma 7B:
Reasoning: 77/55 = <<77/55=1.4>>1.4 6/5 = <<6/5=1.2>>1.2 1.4 + 1.2 = <<1.4+1.2=2.6>>2.6 ### Answer: 2.6
Expected answer: 13/5
Correct? Yes
Problem: If we add the previously calculated result to 39/64, what fraction do we get?
LLemma 7B:
Reasoning: 39/64 = <<39/64=0.6125>>0.6125 2.6 + 0.6125 = <<2.6+0.6125=3.2125>>3.2125 ### Answer: 3.2125
Expected answer: 1027/320
Correct? No
Problem: Let's change the previous problem a bit. Instead of adding 6/5, what if we added 6/79 to 77/55? What fraction would we get then?
LLemma 7B:
Reasoning: 77/55 = <<77/55=1.4>>1.4 6/79 = <<6/79=0.077>>0.077 1.4 + 0.077 = <<1.4+0.077=1.477>>1.477 ### Answer: 1.477
Expected answer: 583/395
Correct? No
Problem: Calculate the value of (56 / 8) + (90 / 86). How much does it equal?
LLemma 7B:
Reasoning: 56/8 = <<56/8=7>>7 and 90/86 = <<90/86=1>>1. (56 / 8) + (90 / 86) = <<7+1=8>>8. ### Answer: 8
Expected answer: 346/43
Correct? No
Problem: What is the sum of 23/20 and 82/97?
LLemma 7B:
Reasoning: 23/20 + 82/97 = <<23/20 + 82/97>> ### Answer: 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Expected answer: 3871/1940
Correct? No
Problem: Calculate the sum of 54/88 and 28/10.
LLemma 7B:
Reasoning: 54/88 + 28/10 = <<54/88+28/10=1.25>>1.25 ### Answer: 1.25
Expected answer: 751/220
Correct? No
Problem: What is the result of the following operation: 7 / 69 + 71 / 47?
LLemma 7B:
Reasoning: 7 / 69 + 71 / 47 = <<7/69+71/47>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+(71*69)/(69*47)>> = <<(7*47)+
Expected answer: 5228/3243
Correct? No
Problem: What is the sum of 15/32 and 65/15?
LLemma 7B:
Reasoning: 15/32 + 65/15 = <<15/32 + 65/15>> ### Answer: 111/16
Expected answer: 461/96
Correct? No
Problem: What is the sum of 4/31 and 76/11?
LLemma 7B:
Reasoning: 4/31 + 76/11 = <<4/31 + 76/11 = 120/341>>120/341 ### Answer: 120/341
Expected answer: 2400/341
Correct? No
Problem: What is the sum when you add 82/15 to 100/12?
LLemma 7B:
Reasoning: 82/15 + 100/12 = <<82/15+100/12=100/3>>100/3 ### Answer: 100/3
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 7B:
Reasoning: 92/29 = <<92/29=3>>3 41/33 = <<41/33=1>>1 3+1 = <<3+1=4>>4 ### Answer: 4
Expected answer: 4225/957
Correct? No
Problem: What is the sum of 57/29 and 14/98?
LLemma 7B:
Reasoning: 57/29 = <<57/29=2>>2 and 14/98 = <<14/98=1/7>>1/7. 2+1/7 = <<2+1/7=15/7>>15/7. ### Answer: 15/7
Expected answer: 428/203
Correct? No
Problem: Solve the given expression: 70/25 + 83/28.
LLemma 7B:
Reasoning: 70/25 = <<70/25=2.8>>2.8 and 83/28 = <<83/28=2.925>>2.925. 70/25 + 83/28 = 2.8 + 2.925 = <<2.8+2.925=5.725>>5.725 ### Answer: 5.725
Expected answer: 807/140
Correct? No
Problem: What is the result of adding the fractions 50/73 and 20/23?
LLemma 7B:
Reasoning: 50/73 + 20/23 = <<50/73+20/23=100/96=50/48=25/24=5/4>>5/4 ### Answer: 5/4
Expected answer: 2610/1679
Correct? No
Problem: What is the value of ((49 / 57) + (89 / 99))?
LLemma 7B:
Reasoning: 49/57 = <<49/57=0.8421052631578947368421052631579>> 89/99 = <<89/99=0.89>> ((49 / 57) + (89 / 99)) = <<0.8421052631578947368421052631579 + 0.89 = 1.7321052631578947368421052631579>> ### Answer: 1.7321052631578947368421052631579
Expected answer: 3308/1881
Correct? No
Problem: Calculate the result of 94 / 35 - 23 / 49. Report your answer as a simplified fraction.
LLemma 7B:
Reasoning: 94 / 35 - 23 / 49 = <<94/35-23/49>> = <<(94*49-23*35)/(35*49)>> = <<(4506-795)/1685>> = <<3711/1685>> ### Answer: 21/13
Expected answer: 543/245
Correct? No
Problem: Calculate the sum of 58/30 and 49/37 and leave your answer as a fraction.
LLemma 7B:
Reasoning: 58/30 + 49/37 = <<58/30 + 49/37>> ### Answer: 117/111
Expected answer: 1808/555
Correct? No
Problem: Calculate the sum of 45/53 and 71/50.
LLemma 7B:
Reasoning: 45/53 = <<45/53=0.84210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526315789473684210526
Expected answer: 6013/2650
Correct? No
Problem: Calculate the sum of 36/72 and 49/1.
LLemma 7B:
Reasoning: 36/72 = <<36/72=0.5>>0.5 and 49/1 = <<49/1=49>>49. The sum of 36/72 and 49/1 is <<0.5+49=49.5>>49.5. ### Answer: 49.5
Expected answer: 99/2
Correct? Yes
Problem: After calculating the sum of 36/72 and 49/1, subtract 48/10 from the result. What is the final answer?
LLemma 7B:
Reasoning: 48/10 = <<48/10=4.8>>4.8. The final answer is <<49.5-4.8=44.7>>44.7. ### Answer: 44.7
Expected answer: 447/10
Correct? No
Problem: Earlier, you calculated the sum of 36/72 and 49/1. But what if instead of adding 49/1, you only added 14/1? What would be the new sum?
LLemma 7B:
Reasoning: 36/72 = <<36/72=0.5>>0.5 and 14/1 = <<14/1=14>>14. The sum of 36/72 and 14/1 is <<0.5+14=14.5>>14.5. ### Answer: 14.5
Expected answer: 29/2
Correct? No
Problem: What is the sum of 61/20 and 29/15?
LLemma 7B:
Reasoning: 61/20 + 29/15 = <<61/20 + 29/15>> ### Answer: 11/4
Expected answer: 299/60
Correct? No
Problem: Solve the expression ((33 / 90) + (77 / 79)). Give your answer as an unsimplified fraction.
LLemma 7B:
Reasoning: 33/90 + 77/79 = <<33/90 + 77/79>> ### Answer: 1107/6930
Expected answer: 3179/2370
Correct? No
Problem: What is the sum of 30/79 and 29/6? Give your answer as a fraction.
LLemma 7B:
Reasoning: 30/79 + 29/6 = <<30/79 + 29/6 = 1131/474>>1131/474 ### Answer: 1131/474
Expected answer: 2471/474
Correct? No
Problem: What is the answer when you subtract 11/66 from 59/2?
LLemma 7B:
Reasoning: 59/2 - 11/66 = <<59/2 - 11/66 = 131/66>>131/66 ### Answer: 131/66
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 7B:
Reasoning: 58/23 + 25/26 = <<58/23 + 25/26>> ### Answer: 103/23
Expected answer: 2083/598
Correct? No
Problem: Calculate the sum of the fractions 70/13 and 17/52.
LLemma 7B:
Reasoning: 70/13 + 17/52 = <<70/13 + 17/52 = 119/66>>119/66 ### Answer: 119/66
Expected answer: 297/52
Correct? No
Problem: What is the sum of 78/44 and 17/91?
LLemma 7B:
Reasoning: 78/44 = <<78/44=1.75>>1.75 and 17/91 = <<17/91=0.186>>0.186. 1.75 + 0.186 = <<1.75+0.186=1.936>>1.936 ### Answer: 1.936
Expected answer: 3923/2002
Correct? No
Problem: What is the sum of 43/4 and 71/4?
LLemma 7B:
Reasoning: 43/4 + 71/4 = <<43/4+71/4=114/4=28.5>>28.5 ### Answer: 28.5
Expected answer: 57/2
Correct? Yes
Problem: What is the sum of 43/4 and 71/4 plus 92/79?
LLemma 7B:
Reasoning: 43/4 + 71/4 + 92/79 = <<43/4+71/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79=114/4+92/79
Expected answer: 4687/158
Correct? No
Problem: What if instead of adding 71/4, we added 71/89 to 43/4? What would be the new total?
LLemma 7B:
Reasoning: 43/4 + 71/89 = <<43/4+71/89=114/89=1.25>>1.25 ### Answer: 1.25
Expected answer: 4111/356
Correct? No
Problem: What is the result of adding the fractions 17/74 and 53/27?
LLemma 7B:
Reasoning: 17/74 + 53/27 = <<17/74 + 53/27 = 17/74 + 53/27 = 17*27/74*27 + 53*74/27*74 = 459/1978 + 3782/1978 = 459+3782/1978 = 4241/1978 = 21/119>>21/119 ### Answer: 21/119
Expected answer: 4381/1998
Correct? No
Problem: Compute the value of (76/76) + (96/16).
LLemma 7B:
Reasoning: 76/76 = 1 and 96/16 = 6. (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 7B:
Reasoning: 76/76 = 1 and 96/16 = 6. (76/76) + (96/16) = 1 + 6 = <<1+6=7>>7 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 7B:
Reasoning: 96/33 = 3. (76/76) + (96/33) = 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 7B:
Reasoning: 94/14 = <<94/14=7>>7, 50/90 = <<50/90=1/18>>1/18. ((94 / 14) - (50 / 90)) = <<(94/14)-(50/90)>>((7)-(1/18)) = <<7-1/18>>(7-1/18) = <<7*18-1>>(126-1) = <<7*18-1>>125 = <<7*18-1>>125 ### Answer: 125
Expected answer: 388/63
Correct? No
Problem: What is the result of subtracting twenty-nine seventy-ninths from thirty-three sevenths?
LLemma 7B:
Reasoning: 33/7 - 29/70 = <<33/7 - 29/70 = 33/7 - 29/70 * 7/7 = (33-29)/70 = 4/70 = 2/35>>2/35 ### Answer: 2/35
Expected answer: 2404/553
Correct? No
Problem: What is the sum of 60/79 and 53/38?
LLemma 7B:
Reasoning: 60/79 + 53/38 = <<60/79 + 53/38 = 1001/311 = 3.21>>3.21 ### Answer: 3.21
Expected answer: 6467/3002
Correct? No
Problem: Solve the following fraction equation: 39/48 + 19/84.
LLemma 7B:
Reasoning: 39/48 + 19/84 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 39/48 + 19/42 = 3
Expected answer: 349/336
Correct? No
Problem: What is the sum of 16/86 and 60/3?
LLemma 7B:
Reasoning: 16/86 = <<16/86=0.185185185185185>>0.185185185185185 and 60/3 = <<60/3=20>>20. The sum of 16/86 and 60/3 is <<0.185185185185185+20=20.185185185185185>>20.185185185185185. ### Answer: 20.185185185185185
Expected answer: 868/43
Correct? No
Problem: Solve the following equation: ((95 / 69) + (67 / 9))
LLemma 7B:
Reasoning: 95/69 = <<95/69=1.35>>1.35 67/9 = <<67/9=7.44>>7.44 1.35 + 7.44 = <<1.35+7.44=8.79>>8.79 ### Answer: 8.79
Expected answer: 1826/207
Correct? No
Problem: Calculate the result of 95 / 16 - 43 / 60.
LLemma 7B:
Reasoning: 95 / 16 - 43 / 60 = <<95/16-43/60>> = <<(95*60-43*16)/(16*60)>> = <<(5670-688)/960>> = <<5670-688/960>> = <<5670/960-688/960>> = <<567/96-688/96>> = <<567-688/96>> = <<-121/96>> = <<-121/96*100/100>> = <<-12100/9600>> = <<-121/96>> ### Answer: -121/96
Expected answer: 1253/240
Correct? No
Problem: What is the sum of the fractions 38/8 and 4/16?
LLemma 7B:
Reasoning: 38/8 = <<38/8=9/2>>9/2 and 4/16 = <<4/16=1/4>>1/4 9/2 + 1/4 = <<9/2+1/4=19/4>>19/4 ### Answer: 19/4
Expected answer: 5
Correct? No
Problem: Calculate the result of 67 / 15 - 27 / 12.
LLemma 7B:
Reasoning: 67 / 15 - 27 / 12 = <<67/15-27/12>> = <<(67*12-27*15)/(15*12)>> = <<(744-405)/(180)>> = <<339/180>> = <<189/90>> = <<21/10>> = <<2.1>> ### Answer: 2.1
Expected answer: 133/60
Correct? No
Problem: Calculate the sum of 38/59 and 80/94.
LLemma 7B:
Reasoning: 38/59 + 80/94 = <<38/59 + 80/94 = 118/59>>118/59 ### Answer: 118/59
Expected answer: 4146/2773
Correct? No
Problem: Calculate the sum of 10/14 and 70/20. Report your answer as a decimal.
LLemma 7B:
Reasoning: 10/14 + 70/20 = <<10/14 + 70/20 = 1.15>>1.15 ### Answer: 1.15
Expected answer: 59/14
Correct? No
Problem: What is the result of subtracting 19/44 from 33/5?
LLemma 7B:
Reasoning: 33/5 - 19/44 = <<33/5 - 19/44 = 131/20>>131/20 ### Answer: 131/20
Expected answer: 1357/220
Correct? No
Problem: Find the result for (97 / 13) + (62 / 22). Answer as a decimal to the nearest hundredth.
LLemma 7B:
Reasoning: 97/13 = <<97/13=7.461538461538461538461538461538>> 62/22 = <<62/22=2.772727272727272727272727272727>> (97 / 13) + (62 / 22) = <<97/13=7.461538461538461538461538461538>> + <<62/22=2.772727272727272727272727272727>> = <<97/13=7.461538461538461538461538461538>> + <<62/22=2.772727272727272727272727272727>> = <<12.234353846153846153846153846154>> ### Answer: 12.23
Expected answer: 1470/143
Correct? No
Problem: What is the sum of 78 divided by 35 and 30 divided by 60?
LLemma 7B:
Reasoning: 78/35 = <<78/35=2.12>>2.12 30/60 = <<30/60=0.5>>0.5 2.12+0.5 = <<2.12+0.5=2.62>>2.62 ### Answer: 2.62
Expected answer: 191/70
Correct? No
Problem: What is the sum of 49/75 and 88/58?
LLemma 7B:
Reasoning: 49/75 = <<49/75=0.64>>0.64 and 88/58 = <<88/58=1.5>>1.5. 0.64+1.5 = <<0.64+1.5=2.1>>2.1 ### Answer: 2.1
Expected answer: 4721/2175
Correct? No
Problem: What is the result of ((50 / 2) - (50 / 32))?
LLemma 7B:
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 7B:
Reasoning: 72/81 = <<72/81=0.8771929824561403>>0.8771929824561403, 50/2 = <<50/2=25>>25, 50/32 = <<50/32=1.5625>>1.5625. 25 - 1.5625 = <<25-1.5625=23.4375>>23.4375. 0.8771929824561403 + 23.4375 = <<0.8771929824561403+23.4375=24.31468590697755>>24.31468590697755. ### Answer: 24.31468590697755
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 7B:
Reasoning: 50/2 = <<50/2=25>>25 and 50/91 = <<50/91=0.548611111111111>>0.548611111111111. 25 - 0.548611111111111 = <<25-0.548611111111111=24.45138888888889>>24.45138888888889. ### Answer: 24.45138888888889
Expected answer: 2225/91
Correct? No
Problem: What is the result of ((77 / 30) + (18 / 51))?
LLemma 7B:
Reasoning: 77/30 = <<77/30=2.56>>2.56 18/51 = <<18/51=0.34>>0.34 2.56 + 0.34 = <<2.56+0.34=2.89>>2.89 ### Answer: 2.89
Expected answer: 1489/510
Correct? No
Problem: What is the result of (36 / 37) + (8 / 4)?
LLemma 7B:
Reasoning: 36/37 = <<36/37=0.9615384615384615>> 8/4 = <<8/4=2>>2 0.9615384615384615 + 2 = <<0.9615384615384615+2=2.9615384615384615>>2.9615384615384615
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 7B:
Reasoning: 57/22 = <<57/22=2.5>>2.5 72/48 = <<72/48=1.5>>1.5 2.5 - 1.5 = <<2.5-1.5=1>>1 ### Answer: 1/2
Expected answer: 12/11
Correct? No
Problem: What is the sum of 48 divided by 16 and 12 divided by 29?
LLemma 7B:
Reasoning: 48/16 = <<48/16=3>>3 12/29 = <<12/29=0.4137931034482758620689655172413793>>0.4137931034482758620689655172413793 3+0.4137931034482758620689655172413793 = <<3+0.4137931034482758620689655172413793=3.4137931034482758620689655172413793>>3.4137931034482758620689655172413793 ### Answer: 3.4137931034482758620689655172413793
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 7B:
Reasoning: 37/20 + 16/75 = <<37/20 + 16/75 = 1093/150>>1093/150 ### Answer: 1093/150
Expected answer: 619/300
Correct? No
Problem: Calculate the summation: 83/40 + 6/8.
LLemma 7B:
Reasoning: 83/40 + 6/8 = (83+15)/(40+10) = 98/50 = 19/10 = 1.9 ### Answer: 1.9
Expected answer: 113/40
Correct? No
Problem: Find the result of the addition of the fractions 37/69 and 67/61.
LLemma 7B:
Reasoning: 37/69 + 67/61 = <<37/69 + 67/61>> ### Answer: 104/130
Expected answer: 6880/4209
Correct? No
Problem: What is the sum of 89/84 and 75/34?
LLemma 7B:
Reasoning: 89/84 + 75/34 = <<89/84+75/34=1.01>>1.01 ### Answer: 1.01
Expected answer: 4663/1428
Correct? No
Problem: What is the result when you add 51/78 and 44/83?
LLemma 7B:
Reasoning: 51/78 + 44/83 = <<51/78 + 44/83 = 115/657>>115/657 ### Answer: 115/657
Expected answer: 2555/2158
Correct? No
Problem: Calculate the sum of the fractions 99/85 and 77/55.
LLemma 7B:
Reasoning: 99/85 + 77/55 = <<99/85 + 77/55 = 176/445>>176/445 ### Answer: 176/445
Expected answer: 218/85
Correct? No
Problem: What is the value of 97 / 56 - 31 / 52? Represent your answer as a simplified fraction.
LLemma 7B:
Reasoning: 97 / 56 - 31 / 52 = <<97/56-31/52>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*52-31*56)/(56*52)>> = <<(97*
Expected answer: 827/728
Correct? Yes
Problem: After finding the value of 97 / 56 - 31 / 52, what is the result of adding it to 100 / 25? Write your final answer as a simplified fraction.
LLemma 7B:
Reasoning: 100 / 25 + 97 / 56 - 31 / 52 = <<100/25+97/56-31/52>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(100*56*52+97*25*52-31*25*56)/(25*56*52)>> = <<(
Expected answer: 3739/728
Correct? No
Problem: If instead of 31/52 in the previous problem you had 26/52 to subtract from 97/56, what would the new result be? Please express your answer as a simplified fraction.
LLemma 7B:
Reasoning: 97 / 56 - 26 / 52 = <<97/56-26/52>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97*52-26*56)/(56*52)>> = <<(97
Expected answer: 69/56
Correct? No
Problem: Calculate the result of the following fraction operation: (78 / 74) + (72 / 51).
LLemma 7B:
Reasoning: 78/74 = <<78/74=1>>1, 72/51 = <<72/51=1>>1. (78 / 74) + (72 / 51) = <<1+1=2>>2 ### Answer: 2
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 7B:
Reasoning: 33/23 = <<33/23=1.3461538461538461>> 1.3461538461538461 - 12/75 = <<1.3461538461538461-12/75=0.0112>>0.0112 ### Answer: 0.0112
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 7B:
Reasoning: 85/42 - 98/99 = <<85/42 - 98/99>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(42*99)>> = <<(85*99 - 98*42)/(
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 7B:
Reasoning: 19/30 + 75/77 = <<19/30 + 75/77>> = <<(19*77+75*30)/(30*77)>> = <<(1413+2250)/2310>> = <<3663/2310>> = <<1821/1155>> ### Answer: 1821/1155
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 7B:
Reasoning: 57/66 + 39/64 = <<57/66 + 39/64>> ### Answer: 115/132
Expected answer: 1037/704
Correct? No
Problem: What is the sum of 80/13 and 2/48?
LLemma 7B:
Reasoning: 80/13 + 2/48 = <<80/13+2/48=1.05>>1.05 ### Answer: 1.05
Expected answer: 1933/312
Correct? No
Problem: Calculate the result of the operation ((55 / 30) - (1 / 72)).
LLemma 7B:
Reasoning: 55/30 = <<55/30=1.8333333333333333>>1.8333333333333333 1/72 = <<1/72=0.01388888888888889>>0.01388888888888889 ((55 / 30) - (1 / 72)) = <<1.8333333333333333-0.01388888888888889=1.8194444444444444>>1.8194444444444444 ### Answer: 1.8194444444444444
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 7B:
Reasoning: 73/92 = <<73/92=0.7791666666666667>>0.7791666666666667 ((55 / 30) - (1 / 72)) + (73 / 92) = <<1.8194444444444444+0.7791666666666667=2.598611111111111>>2.598611111111111 ### Answer: 2.598611111111111
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 7B:
Reasoning: 80/30 = <<80/30=2.6666666666666665>>2.6666666666666665 1/72 = <<1/72=0.01388888888888889>>0.01388888888888889 ((80 / 30) - (1 / 72)) = <<2.6666666666666665-0.01388888888888889=2.6527777777777775>>2.6527777777777775 ### Answer: 2.6527777777777775
Expected answer: 191/72
Correct? No
Problem: Calculate the sum of the fractions 69/21 and 71/86.
LLemma 7B:
Reasoning: 69/21 + 71/86 = <<69/21 + 71/86 = 1103/1806>>1103/1806 ### Answer: 1103/1806
Expected answer: 2475/602
Correct? No
Problem: What is the sum of 24/60 and 42/45? Answer as a simplified fraction.
LLemma 7B:
Reasoning: 24/60 = <<24/60=1/5>>1/5 and 42/45 = <<42/45=14/15>>14/15. 1/5 + 14/15 = <<1/5+14/15=19/15>>19/15. ### Answer: 19/15
Expected answer: 4/3
Correct? No
Problem: What is the sum of 64/76 and 35/33?
LLemma 7B:
Reasoning: 64/76 + 35/33 = <<64/76+35/33=1.0000000000000001>>1.0000000000000001 ### Answer: 1.0000000000000001
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 7B:
Reasoning: 47/16 + 96/10 = <<47/16 + 96/10>> = <<(47*5)/(16*5) + (96*8)/(10*8)>> = <<235/80 + 768/80>> = <<235 + 768>>/80 = <<993/80>> = <<11.9875>> ### Answer: 11.9875
Expected answer: 1003/80
Correct? No
Problem: What is the result of the operation (58 / 2) + (31 / 32)?
LLemma 7B:
Reasoning: 58/2 = <<58/2=29>>29 and 31/32 = <<31/32=0.96875>>0.96875. 29 + 0.96875 = <<29+0.96875=29.96875>>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 7B:
Reasoning: 90/58 = <<90/58=1.5>>1.5 29.96875 - 1.5 = <<29.96875-1.5=28.46875>>28.46875 ### Answer: 28.46875
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 7B:
Reasoning: 58/2 = <<58/2=29>>29 and 10/32 = <<10/32=0.3125>>0.3125. 29 + 0.3125 = <<29+0.3125=29.3125>>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 7B:
Reasoning: 26/90 = <<26/90=1/3>>1/3 and 50/26 = <<50/26=20/13>>20/13. 1/3 + 20/13 = <<1/3+20/13=23/13>>23/13 ### Answer: 23/13
Expected answer: 1294/585
Correct? No
Problem: Calculate the sum of 80/98 and 92/82.
LLemma 7B:
Reasoning: 80/98 + 92/82 = <<80/98 + 92/82>> ### Answer: 1.7
Expected answer: 3894/2009
Correct? No
Problem: Calculate the sum of 89/44 and 69/5.
LLemma 7B:
Reasoning: 89/44 + 69/5 = <<89/44+69/5=117/20>>117/20 ### Answer: 117/20
Expected answer: 3481/220
Correct? No
Problem: Calculate the following expression: 79/32 - 52/55.
LLemma 7B:
Reasoning: 79/32 - 52/55 = <<79/32 - 52/55>> ### Answer: 1/10
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 7B:
Reasoning: 45/2 = <<45/2=22.5>>22.5 feet is the length of the log. 18/90 = <<18/90=0.2>>0.2 feet is the difference between the length of the log and the length of the piece they sold. 22.5 - 0.2 = <<22.5-0.2=22.3>>22.3 feet is the length of the piece they sold. ### Answer: 22.3
Expected answer: 223/10
Correct? Yes
Problem: Now, suppose Wooden Treasures had initially cut their log into piece of lengths (45/2) feet. After, they sold a piece that was 62/90 feet shorter than the standard length. How long was the piece they sold this time?
LLemma 7B:
Reasoning: 45/2 = <<45/2=22.5>>22.5 feet is the length of the log. 62/90 = <<62/90=0.7>>0.7 feet is the difference between the length of the log and the length of the piece they sold. 22.5 - 0.7 = <<22.5-0.7=21.8>>21.8 feet is the length of the piece they sold. ### Answer: 21.8
Expected answer: 1963/90
Correct? No
Problem: What is the sum of 99/92 and 15/74 as a simplified fraction?
LLemma 7B:
Reasoning: 99/92 + 15/74 = <<99/92 + 15/74>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(92*74)>> = <<(99*74 + 15*92)/(
Expected answer: 4353/3404
Correct? No
Problem: Calculate the result of 54/1 + 62/30. Express your answer in simplest terms.
LLemma 7B:
Reasoning: 54/1 = <<54/1=54>>54 and 62/30 = <<62/30=2.1>>2.1 54/1 + 62/30 = <<54/1+62/30=54+2.1=56.1>>56.1 ### Answer: 56.1
Expected answer: 841/15
Correct? No
Problem: What value do you get by adding 85/29 and 47/7?
LLemma 7B:
Reasoning: 85/29 + 47/7 = <<85/29 + 47/7>> ### Answer: 1.2
Expected answer: 1958/203
Correct? No