Gemma 2B 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).
Gemma 2B:
Reasoning: (74 / 63) + (91 / 78) = (492/486) + (857/486) = 1349/486. Therefore, the sum is 1349/486.
Expected answer: 295/126
Correct? No
Problem: What is the result of adding 94/5 to 1/25?
Gemma 2B:
Reasoning: 94/5 + 1/25 = (94*25)/5 + 1*5 = 230/5 + 5 = 48. ### Answer: 48
Expected answer: 471/25
Correct? No
Problem: What is the result of subtracting 48/20 from 49/8? Answer as a simplified fraction.
Gemma 2B:
Reasoning: 49/8 - 48/20 = (49/8) * (20/48) = 49/48. ### Answer: 49/48
Expected answer: 149/40
Correct? No
Problem: Calculate the value of the expression ((45 / 5) - (6 / 47)).
Gemma 2B:
Reasoning: The expression can be simplified as follows: (45/5) - (6/47) = 9 - 0.13 = 8.87. Therefore, the final answer is 8.87.
Expected answer: 417/47
Correct? No
Problem: What is the sum of 22/49 and 72/35? Provide your answer as a simplified fraction.
Gemma 2B:
Reasoning: 22/49 = <<(22/49)*1=2/49>>2/49 and 72/35 = <<(72/35)*1=192/35>>192/35. The sum is 2/49 + 192/35 = (2+192)/49 = 194/49. ### Answer: 194/49
Expected answer: 614/245
Correct? No
Problem: What is the result of (39 / 9) - (44 / 69)?
Gemma 2B:
Reasoning: (39 / 9) - (44 / 69) = 4 - 6 = <<4-6= -2>>-2. The final answer is -2.
Expected answer: 85/23
Correct? No
Problem: Calculate the sum of 49/79 and 18/21.
Gemma 2B:
Reasoning: 49/79 = 0.61 and 18/21 = 0.82. The sum is 0.61 + 0.82 = 1.43. ### Answer: 1.43
Expected answer: 817/553
Correct? No
Problem: What is the sum of 95/46 and 65/31?
Gemma 2B:
Reasoning: 95/46 + 65/31 = (95*31 + 65*46) / (46*31) = 295 + 295 = 590. ### Answer: 590
Expected answer: 5935/1426
Correct? No
Problem: What is the sum of 25 over 63 and 74 over 6?
Gemma 2B:
Reasoning: 25/63 + 74/6 = (25*6)/63 + (74*6)/6 = 125/63 + 432/63 = 557/63. ### Answer: 557
Expected answer: 802/63
Correct? No
Problem: What is the sum of 79/91 and 100/47?
Gemma 2B:
Reasoning: 79/91 + 100/47 = (79*47 + 100*91) / (91*47) = 3413/4007. ### Answer: 3413/4007
Expected answer: 12813/4277
Correct? No
Problem: What is the result of ((55 / 47) + (72 / 21))?
Gemma 2B:
Reasoning: (55/47) + (72/21) = (55/47) + (36/47) = 91/47. ### Answer: 91/47
Expected answer: 1513/329
Correct? No
Problem: What is the sum of 86/62 and 99/41?
Gemma 2B:
Reasoning: 86/62 = <<86/62=1.5>>1.5 and 99/41 = <<99/41=2.44>>2.44. The sum is 1.5+2.44 = <<1.5+2.44=4>>4.
Expected answer: 4832/1271
Correct? No
Problem: Calculate the sum of 87/88 and 24/13.
Gemma 2B:
Reasoning: 87/88 = 0.98, and 24/13 = 1.82. Adding these two fractions, we get 0.98 + 1.82 = 2.80. ### Answer: 2.80
Expected answer: 3243/1144
Correct? No
Problem: Calculate ((68 / 33) + (70 / 25)). Write your answer in its simplest form.
Gemma 2B:
Reasoning: 68/33 = 2, and 70/25 = 2.8. Adding these two numbers together gives 2 + 2.8 = 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.
Gemma 2B:
Reasoning: 35/97 = 0.363 and 11/9 = 0.111. The sum is 0.363 + 0.111 = 0.474. ### Answer: 0.474
Expected answer: 1382/873
Correct? No
Problem: What is the result of subtracting 79/70 from 11/5?
Gemma 2B:
Reasoning: 11/5 - 79/70 = (11)(70) - (79)(5) = 770 - 395 = <<770-395=375>>375. ### Answer: 375
Expected answer: 15/14
Correct? No
Problem: What is the sum of 68/16 and 52/78?
Gemma 2B:
Reasoning: 68/16 = <<68/16=4>>4 and 52/78 = <<52/78=0.625>>0.625. The sum is 4+0.625 = <<4+0.625=4.625>>4.625. ### Answer: 4.625
Expected answer: 59/12
Correct? No
Problem: Find the sum of 21/75 and 44/47.
Gemma 2B:
Reasoning: 21/75 = <<(21/75)*100=28.00>>28% and 44/47 = <<(44/47)*100=100%. Therefore, 21/75 + 44/47 = 28% + 100% = 128%. ### Answer: 128
Expected answer: 1429/1175
Correct? No
Problem: Calculate the result of (77/5 + 4/11).
Gemma 2B:
Reasoning: (77/5 + 4/11) = (77/5) + (4/11) = (77/5) + (44/55) = (77/5) + (8/5) = (85/55). ### Answer: 85
Expected answer: 867/55
Correct? No
Problem: What's the sum of 60/48 and 37/47?
Gemma 2B:
Reasoning: 60/48 = <<60/48=1.25>>1.25 and 37/47 = <<37/47>>0.79. The sum is 1.25+0.79 = <<1.25+0.79=2>>2.
Expected answer: 383/188
Correct? No
Problem: Solve ((14 / 72) + (25 / 6)).
Gemma 2B:
Reasoning: (14 / 72) + (25 / 6) = (70/48) + (20/48) = 90/48 = 5/4. ### Answer: 5/4
Expected answer: 157/36
Correct? No
Problem: What is the sum of 84/97 and 25/2?
Gemma 2B:
Reasoning: 84/97 + 25/2 = (84*2)/(97*2) + (25*97)/(97*2) = 168/194 + 225/194 = 393/194. ### Answer: 393
Expected answer: 2593/194
Correct? No
Problem: What is the difference between the fractions 66/20 and 4/78?
Gemma 2B:
Reasoning: 66/20 = 33/10, which is equivalent to 0.33. 4/78 = 0.05. Therefore, the difference between the fractions is 0.33 - 0.05 = 0.28. ### Answer: 0.28
Expected answer: 1267/390
Correct? No
Problem: Calculate the expression: 83 divided by 37 minus 12 divided by 14.
Gemma 2B:
Reasoning: 83 divided by 37 minus 12 divided by 14 = 2.29 - 0.85 = 1.44. ### Answer: 1.44
Expected answer: 359/259
Correct? No
Problem: What is the sum of 95/57 and 28/80?
Gemma 2B:
Reasoning: 95/57 + 28/80 = <<(95/57)+(28/80)>> (95/57)+(28/80) = 1.79. ### Answer: 1.79
Expected answer: 121/60
Correct? No
Problem: Calculate the sum of 14/57 and 92/42.
Gemma 2B:
Reasoning: Convert the fractions to an equivalent fraction with a common denominator. 14/57 = 7/29 92/42 = 4/21 Add the fractions: 7/29 + 4/21 = (7)(3)/(29)(3) + (4)(7)/(21)(7) = 21/87. ### Answer: 21/87
Expected answer: 324/133
Correct? No
Problem: What is the result of ((77 / 55) + (6 / 5))?
Gemma 2B:
Reasoning: (77/55) + (6/5) = 1.4 + 1.2 = 2.6. ### Answer: 2.6
Expected answer: 13/5
Correct? Yes
Problem: Calculate the value of (56 / 8) + (90 / 86). How much does it equal?
Gemma 2B:
Reasoning: (56 / 8) + (90 / 86) = 7 + 10.2 = 17.2. ### Answer: 17.2
Expected answer: 346/43
Correct? No
Problem: What is the sum of 23/20 and 82/97?
Gemma 2B:
Reasoning: 23/20 = <<(23/20)*100=115>>115 and 82/97 = <<(82/97)*100=85.7>>85.7. The sum is 115+85.7 = <<115+85.7=200.7>>200.7.
Expected answer: 3871/1940
Correct? No
Problem: Calculate the sum of 54/88 and 28/10.
Gemma 2B:
Reasoning: 54/88 = <<54/88=0.6>>0.6 and 28/10 = <<28/10=2.8>>2.8. Adding 0.6 and 2.8 gives 3.4. ### Answer: 3.4
Expected answer: 751/220
Correct? No
Problem: What is the result of the following operation: 7 / 69 + 71 / 47?
Gemma 2B:
Reasoning: 7 / 69 + 71 / 47 = (7 * 47) / (69 * 47) + (71 * 69) / (69 * 47) = 349 / 3470 = 0.0102. ### Answer: 0.0102
Expected answer: 5228/3243
Correct? No
Problem: What is the sum of 15/32 and 65/15?
Gemma 2B:
Reasoning: 15/32 + 65/15 = (15)(15)/(32)(15) + (65)(32)/(15)(32) = 25/32. ### Answer: 25/32
Expected answer: 461/96
Correct? No
Problem: What is the sum of 4/31 and 76/11?
Gemma 2B:
Reasoning: 4/31 + 76/11 = (4)(11)/(31)(11) + (76)(3)/11 = 44/31 + 224/31 = 268/31. ### Answer: 268
Expected answer: 2400/341
Correct? No
Problem: What is the sum when you add 82/15 to 100/12?
Gemma 2B:
Reasoning: 82/15 + 100/12 = (82 x 12) / (15 x 12) + (100 x 15) / (15 x 12) = 936/1800 = 0.54. ### Answer: 0.54
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.
Gemma 2B:
Reasoning: (92/29) + (41/33) = (288/87) + (132/87) = 420/87 = 5.00. ### Answer: 5
Expected answer: 4225/957
Correct? No
Problem: What is the sum of 57/29 and 14/98?
Gemma 2B:
Reasoning: 57/29 + 14/98 = (57 x 98) / (29 x 98) = 546/2860. ### Answer: 0.194
Expected answer: 428/203
Correct? No
Problem: Solve the given expression: 70/25 + 83/28.
Gemma 2B:
Reasoning: 70/25 = <<70/25=2.8>>2.8 and 83/28 = <<83/28=3.06>>3.06. Adding 2.8 and 3.06, we get 5.86. ### Answer: 5.86
Expected answer: 807/140
Correct? No
Problem: What is the result of adding the fractions 50/73 and 20/23?
Gemma 2B:
Reasoning: We can add fractions with the same denominator by adding the numerators and keeping the denominator the same. 50/73 + 20/23 = (50*23) + (20*73) / (73*23) = 1250/1895 = 0.65. ### Answer: 0.65
Expected answer: 2610/1679
Correct? No
Problem: What is the value of ((49 / 57) + (89 / 99))?
Gemma 2B:
Reasoning: (49 / 57) + (89 / 99) = (49/57) + (88/99) = (49/57) + (88/99) = (49+88)/57 = 137/57 = 2.35. ### Answer: 2.35
Expected answer: 3308/1881
Correct? No
Problem: Calculate the result of 94 / 35 - 23 / 49. Report your answer as a simplified fraction.
Gemma 2B:
Reasoning: 94 / 35 - 23 / 49 = 2.74 - 0.48 = 2.26. The result of 94 / 35 - 23 / 49 is 2.26.
Expected answer: 543/245
Correct? No
Problem: Calculate the sum of 58/30 and 49/37 and leave your answer as a fraction.
Gemma 2B:
Reasoning: 58/30 = <<58/30=1.9>>1.9 and 49/37 = <<49/37=1.4>>1.4. Adding 1.9 and 1.4 gives 3.3. ### Answer: 3.3
Expected answer: 1808/555
Correct? No
Problem: Calculate the sum of 45/53 and 71/50.
Gemma 2B:
Reasoning: 45/53 + 71/50 = (45 x 50) + (71 x 53) / (53 x 50) = 2250 + 3615 / 2600 = 2515/2600. ### Answer: 2515/2600
Expected answer: 6013/2650
Correct? No
Problem: Calculate the sum of 36/72 and 49/1.
Gemma 2B:
Reasoning: 36/72 = 3/8 and 49/1 = 49. Therefore, 36/72 + 49/1 = 3/8 + 49 = 49/8. ### Answer: 49/8
Expected answer: 99/2
Correct? No
Problem: What is the sum of 61/20 and 29/15?
Gemma 2B:
Reasoning: 61/20 = <<61/20>> and 29/15 = <<29/15>>, so 61/20 + 29/15 = <<(61/20)+(29/15)>> = <<(61/20)+(29/15)>=(61+29)/20 = 80/20 = <<4>>4. ### Answer: 4
Expected answer: 299/60
Correct? No
Problem: Solve the expression ((33 / 90) + (77 / 79)). Give your answer as an unsimplified fraction.
Gemma 2B:
Reasoning: (33/90) + (77/79) = (33/90) + (99/90) = 132/90 = 1.4. ### Answer: 1.4
Expected answer: 3179/2370
Correct? No
Problem: What is the sum of 30/79 and 29/6? Give your answer as a fraction.
Gemma 2B:
Reasoning: 30/79 + 29/6 = (30*6)/(79*6) + (29*79)/(6*79) = 180/531 + 231/531 = 411/531. ### Answer: 411/531
Expected answer: 2471/474
Correct? No
Problem: What is the answer when you subtract 11/66 from 59/2?
Gemma 2B:
Reasoning: 59/2 - 11/66 = (59-11) / (66) = 48/66 = 8/3. ### Answer: 8/3
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?
Gemma 2B:
Reasoning: To add fractions with different denominators, we first need to rewrite them with a common denominator. The least common multiple of 23 and 26 is 60. 58/23 = 58 ÷ 60 = 0.9333... 25/26 = 25 ÷ 60 = 0.4166... Adding these fractions gives us 0.9333... + 0.4166... = 1.3499... Therefore, the sum of 58/23 and 25/26 is 1.3499...
Expected answer: 2083/598
Correct? No
Problem: Calculate the sum of the fractions 70/13 and 17/52.
Gemma 2B:
Reasoning: We can add the numerators and keep the denominator the same. 70/13 + 17/52 = 560/672 + 17/672 = 577/672. Therefore, the sum of the fractions is 577/672.
Expected answer: 297/52
Correct? No
Problem: What is the sum of 78/44 and 17/91?
Gemma 2B:
Reasoning: 78/44 = <<78/44=1.75>>1.75 and 17/91 = <<17/91=0.018>>0.018. The sum is 1.75 + 0.018 = <<1.75+0.018=1.76>>1.76. ### Answer: 1.76
Expected answer: 3923/2002
Correct? No
Problem: What is the sum of 43/4 and 71/4?
Gemma 2B:
Reasoning: 43/4 + 71/4 = (43+71)/4 = 114/4 = 28.5. ### Answer: 28.5
Expected answer: 57/2
Correct? Yes
Problem: What is the result of adding the fractions 17/74 and 53/27?
Gemma 2B:
Reasoning: We can add fractions with the same denominator by adding the numerators and keeping the denominator the same. 17/74 + 53/27 = (17+53)/74 = 70/74 = 5/4. ### Answer: 5/4
Expected answer: 4381/1998
Correct? No
Problem: Compute the value of (76/76) + (96/16).
Gemma 2B:
Reasoning: (76/76) + (96/16) = 1 + 6 = 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?
Gemma 2B:
### Answer: 152
Expected answer: 14
Correct? No
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?
Gemma 2B:
### Answer: 7
Expected answer: 43/11
Correct? No
Problem: What is the result of ((94 / 14) - (50 / 90))? Answer as a simplified fraction.
Gemma 2B:
Reasoning: (94/14)-(50/90) = (14)(94/14)-(10)(50/90) = 14-5 = <<14-5=9>>9. ### Answer: 9
Expected answer: 388/63
Correct? No
Problem: What is the result of subtracting twenty-nine seventy-ninths from thirty-three sevenths?
Gemma 2B:
Reasoning: Subtract 29/7 from 33/7 gives <<33/7-29/7=4>>4. Therefore, the result of subtracting 29/7 from 33/7 is 4.
Expected answer: 2404/553
Correct? No
Problem: What is the sum of 60/79 and 53/38?
Gemma 2B:
Reasoning: 60/79 + 53/38 = <<(60/79)+(53/38)>> = (60/79)*(38/53) = 160/401. ### Answer: 160/401
Expected answer: 6467/3002
Correct? No
Problem: Solve the following fraction equation: 39/48 + 19/84.
Gemma 2B:
Reasoning: Combine like fractions by finding a common denominator. The least common multiple of 48 and 84 is 336. 39/48 = 39/48, and 19/84 = 19/84. Combining like fractions, we have 39/48 + 19/84 = 39/48. ### Answer: 39/48
Expected answer: 349/336
Correct? No
Problem: What is the sum of 16/86 and 60/3?
Gemma 2B:
Reasoning: 16/86 = <<16/86=0.0183>>0.0183 and 60/3 = <<60/3=20>>20. The sum is 0.0183+20 = <<0.0183+20=20.0183>>20.0183. ### Answer: 20.0183
Expected answer: 868/43
Correct? No
Problem: Solve the following equation: ((95 / 69) + (67 / 9))
Gemma 2B:
Reasoning: First, we add the fractions by finding a common denominator. The least common multiple of 69 and 9 is 633. So, we rewrite the fractions with their equivalent fractions using the least common multiple: (95/69) = 15/17 (67/9) = 67/9 Adding the fractions: 15/17 + 67/9 = 15/17 + 7/9 = (15 + 7) / 17 = 22/17 ### Answer: 22/17
Expected answer: 1826/207
Correct? No
Problem: Calculate the result of 95 / 16 - 43 / 60.
Gemma 2B:
Reasoning: 95 / 16 - 43 / 60 = (95 * 60) / (16 * 60) - (43 * 16) / (60 * 16). = 5750/960 - 672/960 = 0.59 - 0.72 = 0.27. ### Answer: 0.27
Expected answer: 1253/240
Correct? No
Problem: What is the sum of the fractions 38/8 and 4/16?
Gemma 2B:
Reasoning: 38/8 = <<38/8>>19 and 4/16 = <<4/16>>1. The sum of the fractions is 19+1 = <<19+1=20>>20. ### Answer: 20
Expected answer: 5
Correct? No
Problem: Calculate the result of 67 / 15 - 27 / 12.
Gemma 2B:
Reasoning: 67/15 - 27/12 = 4.5 - 2.25 = 2.25. ### Answer: 2.25
Expected answer: 133/60
Correct? No
Problem: Calculate the sum of 38/59 and 80/94.
Gemma 2B:
Reasoning: 38/59 + 80/94 = (38/59) * (94/80) = 340/4760. ### Answer: 0.706
Expected answer: 4146/2773
Correct? No
Problem: Calculate the sum of 10/14 and 70/20. Report your answer as a decimal.
Gemma 2B:
Reasoning: 10/14 = <<10/14=0.7142857142...>>0.7143, and 70/20 = <<70/20=3.5>>3.5. Therefore, 10/14 + 70/20 = 0.7143 + 3.5 = 4.2143.
Expected answer: 59/14
Correct? No
Problem: What is the result of subtracting 19/44 from 33/5?
Gemma 2B:
Reasoning: 33/5 - 19/44 = (33*44)/(5*44) - (19*5)/(44*5) = 132/220 - 95/220 = 37/220. ### Answer: 37/220
Expected answer: 1357/220
Correct? No
Problem: Find the result for (97 / 13) + (62 / 22). Answer as a decimal to the nearest hundredth.
Gemma 2B:
Reasoning: (97 / 13) + (62 / 22) = 7.5 + 2.8 = 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?
Gemma 2B:
Reasoning: 78/35 = <<78/35=2.2>>2.2 and 30/60 = <<30/60=0.5>>0.5. The sum is 2.2+0.5 = <<2.2+0.5=2.7>>2.7.
Expected answer: 191/70
Correct? No
Problem: What is the sum of 49/75 and 88/58?
Gemma 2B:
Reasoning: 49/75 + 88/58 = (49/75) * (58/88) = 297/680. ### Answer: 297/680
Expected answer: 4721/2175
Correct? No
Problem: What is the result of ((50 / 2) - (50 / 32))?
Gemma 2B:
Reasoning: (50/2) - (50/32) = 25 - 1.25 = 23.75. ### Answer: 23.75
Expected answer: 375/16
Correct? No
Problem: What is the result of ((77 / 30) + (18 / 51))?
Gemma 2B:
Reasoning: (77 / 30) + (18 / 51) = (77/30) + (36/153) = (77/30) + (4/153) = (77 + 4)/30 = 81/30 = 3.07. ### Answer: 3.07
Expected answer: 1489/510
Correct? No
Problem: What is the result of (36 / 37) + (8 / 4)?
Gemma 2B:
Reasoning: (36 / 37) + (8 / 4) = 36/37 + 8/4 = (36 * 4)/(37 * 4) + (8 * 37)/(4 * 37) = 144/148 + 296/148 = 440/148 = 4.
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.
Gemma 2B:
Reasoning: (57 / 22) - (72 / 48) = (57/22) - (36/48) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57/22) - (9/16) = (57
Expected answer: 12/11
Correct? No
Problem: What is the sum of 48 divided by 16 and 12 divided by 29?
Gemma 2B:
Reasoning: 48/16 = <<48/16=3>>3 and 12/29 = <<12/29=0.41>>0.41. The sum is 3+0.41 = <<3+0.41=3.41>>3.41.
Expected answer: 99/29
Correct? No
Problem: What is the sum of 37/20 and 16/75? Write your answer as a simplified fraction.
Gemma 2B:
Reasoning: 37/20 = <<37/20>> and 16/75 = <<16/75>>. The sum is 37/20 + 16/75 = <<(37/20)+(16/75)>> = <<(37/20)+(16/75)>> = <<(37+16)/20>> = <<53/20>> = 265/1000.
Expected answer: 619/300
Correct? No
Problem: Calculate the summation: 83/40 + 6/8.
Gemma 2B:
Reasoning: 83/40 = 2.075 and 6/8 = 0.75. Adding these fractions, we get 2.075 + 0.75 = 2.825.
Expected answer: 113/40
Correct? Yes
Problem: Find the result of the addition of the fractions 37/69 and 67/61.
Gemma 2B:
Reasoning: We can find the least common multiple (LCM) of 69 and 61 to add the fractions. The LCM of 69 and 61 is 617. Then, we can rewrite the fractions with their equivalent fractions using the LCM as the denominator. 37/69 = 37/69 67/61 = 67/61 Adding the fractions: 37/69 + 67/61 = 37/69 + 67/61 = 104/69 = 1.44 ### Answer: 1.44
Expected answer: 6880/4209
Correct? No
Problem: What is the sum of 89/84 and 75/34?
Gemma 2B:
Reasoning: 89/84 = <<(89/84)*100=102.5>>102.5 and 75/34 = <<(75/34)*100=218.8>>218.8. The sum is 102.5+218.8 = <<102.5+218.8=321.3>>321.3.
Expected answer: 4663/1428
Correct? No
Problem: What is the result when you add 51/78 and 44/83?
Gemma 2B:
Reasoning: 51/78 + 44/83 = (51 x 83) + (44 x 78) / (78 x 83) = 4411/6594. ### Answer: 0.664
Expected answer: 2555/2158
Correct? No
Problem: Calculate the sum of the fractions 99/85 and 77/55.
Gemma 2B:
Reasoning: The least common multiple of 85 and 55 is 425. Then, the sum of the fractions is 99/85 + 77/55 = <<99/85+77/55=176/425>>176/425. ### Answer: 176
Expected answer: 218/85
Correct? No
Problem: What is the value of 97 / 56 - 31 / 52? Represent your answer as a simplified fraction.
Gemma 2B:
Reasoning: 97 / 56 - 31 / 52 = (97/56) - (31/52) = (97-31)/(56-52). The answer is 66/56 = 11/8.
Expected answer: 827/728
Correct? No
Problem: Calculate the result of the following fraction operation: (78 / 74) + (72 / 51).
Gemma 2B:
Reasoning: The fractions can be added by adding the numerators and keeping the denominator the same. (78 / 74) + (72 / 51) = 78/74 + 72/51 = (78 * 51)/(74 * 51) + (72 * 74)/(51 * 74) = 39/29. ### Answer: 39/29
Expected answer: 1551/629
Correct? No
Problem: What is the result of the operation (33 / 23) - (12 / 75)? Express your answer as a fraction.
Gemma 2B:
Reasoning: (33 / 23) - (12 / 75) = (33 * 75)/(23 * 75) - (12 * 23)/(75 * 23) = 2450/5250 - 296/1875 = 0.45 - 0.016 = 0.434. ### Answer: 0.434
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.
Gemma 2B:
Reasoning: 85/42 - 98/99 = (85/42) - (98/99) = (175/88) - (196/88) = (175-196)/88 = -21/88. The result is approximately -0.243.
Expected answer: 1433/1386
Correct? No
Problem: What is the sum of 19/30 and 75/77? Express your answer as a simplified fraction.
Gemma 2B:
Reasoning: 19/30 = <<19/30=0.6>>0.6, and 75/77 = <<75/77=0.94>>0.94. The sum is 0.6 + 0.94 = 1.54, which can be simplified as 1 34/70.
Expected answer: 3713/2310
Correct? No
Problem: What is the sum of 57/66 and 39/64? Please express your answer as a fraction.
Gemma 2B:
Reasoning: 57/66 + 39/64 = (57 x 64)/(66 x 64) + (39 x 66)/(66 x 64) = 3401/4088. ### Answer: 3401/4088
Expected answer: 1037/704
Correct? No
Problem: What is the sum of 80/13 and 2/48?
Gemma 2B:
Reasoning: 80/13 + 2/48 = (80*48)/(13*48) + (2*13)/(48*13) = 320/528 + 26/528 = 346/528. ### Answer: 346
Expected answer: 1933/312
Correct? No
Problem: Calculate the result of the operation ((55 / 30) - (1 / 72)).
Gemma 2B:
Reasoning: 55/30 = <<55/30=1.8>>1.8, and 1/72 = <<1/72=0.0125>>0.0125. Therefore, (55/30 - 1/72) = 1.8 - 0.0125 = <<1.8-0.0125=1.78>>1.78. ### Answer: 1.78
Expected answer: 131/72
Correct? No
Problem: Calculate the sum of the fractions 69/21 and 71/86.
Gemma 2B:
Reasoning: We can add the numerators and keep the denominator the same. 69/21 + 71/86 = (69 x 86) + (71 x 21) / (21 x 86) = 593 + 1515/1902 = 2108/1902. ### Answer: 2108/1902
Expected answer: 2475/602
Correct? No
Problem: What is the sum of 24/60 and 42/45? Answer as a simplified fraction.
Gemma 2B:
Reasoning: 24/60 = <<24/60=0.4>>0.4 and 42/45 = <<42/45=0.8>>0.8. The sum is 0.4+0.8 = 1.2, which is a simplified fraction of 12/15.
Expected answer: 4/3
Correct? No
Problem: What is the sum of 64/76 and 35/33?
Gemma 2B:
Reasoning: 64/76 + 35/33 = (64/76) * (33/35) = 192/260 = 0.76. ### Answer: 0.76
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.
Gemma 2B:
Reasoning: 47/16 = <<47/16>>1 and 96/10 = <<96/10>>1. The sum is 1+1 = <<1+1=2>>2. ### Answer: 2
Expected answer: 1003/80
Correct? No
Problem: What is the result of the operation (58 / 2) + (31 / 32)?
Gemma 2B:
Reasoning: (58 / 2) + (31 / 32) = 29 + 0.94 = 30.94. ### Answer: 30.94
Expected answer: 959/32
Correct? No
Problem: What is the sum of 26/90 and 50/26 when calculated as a fraction?
Gemma 2B:
Reasoning: 26/90 = <<(26/90) * (90/26) = 1>>1 50/26 = <<(50/26) * (26/50) = 1>>1 Therefore, 26/90 + 50/26 = 1 + 1 = 2. ### Answer: 2
Expected answer: 1294/585
Correct? No
Problem: Calculate the sum of 80/98 and 92/82.
Gemma 2B:
Reasoning: 80/98 = 0.81, and 92/82 = 0.99. Adding these fractions, we get 0.81 + 0.99 = 1.80. ### Answer: 1.80
Expected answer: 3894/2009
Correct? No
Problem: Calculate the sum of 89/44 and 69/5.
Gemma 2B:
Reasoning: 89/44 = <<89/44=2.04>>2.04 and 69/5 = <<69/5=13.8>>13.8. Adding 2.04 and 13.8 = <<2.04+13.8=15.8>>15.8. ### Answer: 15.8
Expected answer: 3481/220
Correct? No
Problem: Calculate the following expression: 79/32 - 52/55.
Gemma 2B:
Reasoning: Subtract the numerators from the denominators: 79/32 - 52/55 = (79)(55)/(32)(55) - (52)(32)/(55)(32). Simplify the fractions: 79/32 - 52/55 = 3955/1600 - 288/1600 = 1067/1600. ### Answer: 0.65
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?
Gemma 2B:
Reasoning: The piece they sold is 45/2 - 18/90 = <<45/2-18/90=30/90>>30/90 feet shorter than the usual length. ### Answer: 30/90
Expected answer: 223/10
Correct? No
Problem: What is the sum of 99/92 and 15/74 as a simplified fraction?
Gemma 2B:
Reasoning: 99/92 = <<99/92=1.0909...>>1.0909... and 15/74 = <<15/74=0.0204...>>0.0204... The sum is 1.0909... + 0.0204... = 1.1113... ### Answer: 1.1113
Expected answer: 4353/3404
Correct? No
Problem: Calculate the result of 54/1 + 62/30. Express your answer in simplest terms.
Gemma 2B:
Reasoning: 54/1 = 54, and 62/30 = 2. Therefore, 54/1 + 62/30 = 54 + 2 = 56. ### Answer: 56
Expected answer: 841/15
Correct? No
Problem: What value do you get by adding 85/29 and 47/7?
Gemma 2B:
Reasoning: 85/29 + 47/7 = (85/29) * (7/47) = 5.99. ### Answer: 5.99
Expected answer: 1958/203
Correct? No