Mixtral 8x7B 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).
Mixtral 8x7B:
Reasoning: To add the fractions (74 / 63) and (91 / 78), we first need to find a common denominator for the two fractions. The least common multiple of 63 and 78 is 513. So, we convert (74 / 63) to have a denominator of 513 by multiplying both the numerator and denominator by 8: (74 x 8) / (63 x 8) = 592 / 504 We also convert (91 / 78) to have a denominator of 513 by multiplying both the numerator and denominator by 7: (91 x 7) / (78 x 7) = 637 / 546 Now, we can add the two fractions: 592 / 504 + 637 / 546 = (592 x 546) / (504 x 546) + (637 x 504) / (546 x 504) = (592 x 546 + 637 x 504) / 277728 = 1229 / 277728 ### Answer: The sum of (74 / 63) and (91 / 78) is 1229 / 277728.
Expected answer: 295/126
Correct? No
Problem: What is the result of adding 94/5 to 1/25?
Mixtral 8x7B:
Reasoning: To add the fractions 94/5 and 1/25, we need to get them to have a common denominator. The least common multiple of 5 and 25 is 50, so we convert 94/5 to 94*10/50 = 188/50 and 1/25 to 1*2/50 = 2/50. Then, we add the fractions: 188/50 + 2/50 = (188+2)/50 = 190/50. Finally, we simplify the fraction: 190/50 = 19/5. ### Answer: 19/5
Expected answer: 471/25
Correct? No
Problem: What is the result of subtracting 48/20 from 49/8? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, we calculate the value of 48/20, which simplifies to 12/5. Then, we calculate the value of 49/8. To subtract these two fractions, we need to find a common denominator, which is 40 in this case. So, we convert 49/8 to 195/40 and 12/5 to 48/40. Now, we can subtract the fractions: 195/40 - 48/40 = 147/40. We simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 7: 147/7 = 21 and 40/7 = 5.6. ### Answer: 21/5
Expected answer: 149/40
Correct? No
Problem: Calculate the value of the expression ((45 / 5) - (6 / 47)).
Mixtral 8x7B:
Reasoning: First, perform the division operations inside the parentheses: (9 - (6 / 47)) Then, perform the remaining division: (9 - 0.12766) Lastly, perform the subtraction: 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.
Mixtral 8x7B:
Reasoning: To add the fractions 22/49 and 72/35, we need to find a common denominator. The least common multiple of 49 and 35 is 3990. So, we convert 22/49 to 110/3990 and 72/35 to 2052/3990. Then, we add the fractions: 110/3990 + 2052/3990 = 2162/3990. Finally, we simplify the fraction: 2162/3990 simplifies to 1081/1995. ### Answer: 1081/1995
Expected answer: 614/245
Correct? No
Problem: What is the result of (39 / 9) - (44 / 69)?
Mixtral 8x7B:
Reasoning: First, we need to calculate the value of (39 / 9) which is equal to 39 / 9 = <<39/9=4.33333333333>>4.33333333333 (rounded to 11 decimal places). Next, we need to calculate the value of (44 / 69) which is equal to 44 / 69 = <<44/69=0.63768115942>>0.63768115942 (rounded to 11 decimal places). Finally, we need to subtract the second result from the first one: 4.33333333333 - 0.63768115942 = <<4.33333333333-0.63768115942=3.69565217391>>3.69565217391 (rounded to 11 decimal places). ### Answer: 3.69565217391
Expected answer: 85/23
Correct? No
Problem: Calculate the sum of 49/79 and 18/21.
Mixtral 8x7B:
Reasoning: To add the fractions 49/79 and 18/21, we need to find a common denominator. The least common multiple (LCM) of 79 and 21 is 1629. 49/79 = 49 * (1629 / 79) / 1629 = 657/1629 18/21 = 18 * (1629 / 21) / 1629 = 1212/1629 Now, we can add the fractions: 657/1629 + 1212/1629 = (657 + 1212) / 1629 = 1869 / 1629 ### Answer: 1869/1629
Expected answer: 817/553
Correct? No
Problem: What is the sum of 95/46 and 65/31?
Mixtral 8x7B:
Reasoning: To add the fractions 95/46 and 65/31, we need to get them over a common denominator. The least common multiple of 46 and 31 is 1406. So, convert each fraction to have this common denominator. 95/46 = (95 \* 31) / (46 \* 31) = 2955/1406 65/31 = (65 \* 46) / (31 \* 46) = 2990/1406 Now, add the two fractions: 2955/1406 + 2990/1406 = (2955 + 2990) / 1406 = 5945/1406 The fraction 5945/1406 is greater than 4, so we can simplify it to a mixed number: 5945/1406 = 4 1/1406. However, since the question asks for the sum, and 1/1406 is not a simplified fraction, we will leave the answer as an improper fraction: ### Answer: 5945/1406
Expected answer: 5935/1426
Correct? No
Problem: What is the sum of 25 over 63 and 74 over 6?
Mixtral 8x7B:
Reasoning: To add the fractions 25/63 and 74/6, we need to find a common denominator. The least common multiple of 63 and 6 is 6 * 63 = <<6*63=378>>378. So, we convert 25/63 to 25 * 6 / 63 = 150 / 378 and 74/6 to 74 * 63 / 6 = 4662 / 378. Now, we can add the fractions: 150 / 378 + 4662 / 378 = (150 + 4662) / 378 = 4812 / 378. ### Answer: 4812 / 378 or approximately 12.73 (when simplified to a decimal)
Expected answer: 802/63
Correct? Yes
Problem: If you subtract 9 over 47 from the result obtained from summing 25 over 63 and 74 over 6, what new value do you get?
Mixtral 8x7B:
Reasoning: We first found the sum of 25/63 and 74/6 to be 4812 / 378. Now, we subtract 9/47 from it: (4812 / 378) - (9 / 47) To subtract the fractions, we need a common denominator. The least common multiple of 378 and 47 is 378 * 47. So, we convert 9/47 to 9 * 378 / 47 = 3402 / 378. Now, we can subtract the fractions: (4812 / 378) - (3402 / 378) = (4812 - 3402) / 378 = 1410 / 378. ### Answer: 1410 / 378 or approximately 3.73 (when simplified to a decimal)
Expected answer: 37127/2961
Correct? No
Problem: What would be the new sum if we change the previous problem of adding 25 over 63 and 74 over 6 to now adding 25 over 63 and 6 over 6 instead?
Mixtral 8x7B:
Reasoning: To add the fractions 25/63 and 6/6, we need to make sure both fractions have the same denominator. Since 6 is already equal to 6/1, we can rewrite 6/6 as 6/1 * 63/63 = 378/63. Now, we can add the fractions: 25 / 63 + 378 / 63 = (25 + 378) / 63 = 403 / 63. ### Answer: 403 / 63 or approximately 6.40 (when simplified to a decimal)
Expected answer: 88/63
Correct? No
Problem: What is the sum of 79/91 and 100/47?
Mixtral 8x7B:
Reasoning: To add the fractions 79/91 and 100/47, we need to find a common denominator. The least common multiple of 91 and 47 is 4187. So, we convert the fractions to have this common denominator: 79/91 = (79 \* 47) / 4187 = 3743 / 4187 100/47 = (100 \* 91) / 4187 = 9100 / 4187 Then, we add the fractions: 3743 / 4187 + 9100 / 4187 = (3743 + 9100) / 4187 = 12843 / 4187 ### Answer: 12843 / 4187
Expected answer: 12813/4277
Correct? No
Problem: What is the result of ((55 / 47) + (72 / 21))?
Mixtral 8x7B:
Reasoning: First, we need to perform the division operations inside the parentheses: (1.1702127659574468 + 3.428571428571429) = 4.6 ### Answer: 4.6
Expected answer: 1513/329
Correct? No
Problem: What is the sum of 86/62 and 99/41?
Mixtral 8x7B:
Reasoning: To add the fractions 86/62 and 99/41, we need to find a common denominator. The least common multiple of 62 and 41 is 2530. So, we convert the fractions to have this common denominator: 86/62 becomes (86 \* 41) / 2530 = 3536/2530 and 99/41 becomes (99 \* 62) / 2530 = 6118/2530. Now, we can add the fractions: 3536/2530 + 6118/2530 = (3536 + 6118) / 2530 = 9654/2530. ### Answer: 9654/2530
Expected answer: 4832/1271
Correct? No
Problem: Calculate the sum of 87/88 and 24/13.
Mixtral 8x7B:
Reasoning: To add the fractions 87/88 and 24/13, we need to find a common denominator. The least common multiple of 88 and 13 is 1128. So, we convert both fractions to have this common denominator: 87/88 = (87 \* 13) / 1128 = 1131/1128 24/13 = (24 \* 88) / 1128 = 2112/1128 Now, we can add the fractions: 1131/1128 + 2112/1128 = (1131 + 2112) / 1128 = 3243/1128 ### Answer: 3243/1128
Expected answer: 3243/1144
Correct? No
Problem: Calculate ((68 / 33) + (70 / 25)). Write your answer in its simplest form.
Mixtral 8x7B:
Reasoning: To simplify the expression, first, calculate the value of each fraction: (68 / 33) = 2.06060606061 (rounded to 11 decimal places) (70 / 25) = 2.8 Then, add the simplified fractions: 2.06060606061 + 2.8 = 4.86060606061 (rounded to 11 decimal places) To express the result in its simplest form, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 486060606061 and 10 is 1. Therefore, the simplified form of the expression is 4.86060606061 or 4 48/625 in mixed number form. ### Answer: 4 48/625
Expected answer: 802/165
Correct? No
Problem: What is the summation of 35/97 and 11/9? Express the result in simplest form.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. The least common multiple of 97 and 9 is
Expected answer: 1382/873
Correct? No
Problem: What is the result of subtracting 79/70 from 11/5?
Mixtral 8x7B:
Reasoning: To subtract two fractions, we need to get a common denominator. In this case, the common denominator of 70 and 5 is 350. So, we convert 11/5 to 11 \* 70/5 \* 70 = 494/350 and 79/70 to 79 \* 5/70 \* 5 = 395/350. Now, we can subtract 395/350 from 494/350, which is equal to (494-395)/350 = 99/350. ### Answer: 99/350
Expected answer: 15/14
Correct? No
Problem: What is the sum of 68/16 and 52/78?
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have the same denominator. The least common denominator of 16 and 78 is 1224. 68/16 = (68 \* 78) / 16 / 78 = 544/1224 52/78 = (52 \* 16) / 78 / 16 = 832/1224 Then, we add the fractions: 544/1224 + 832/1224 = (544 + 832) / 1224 = 1376/1224 Now, we simplify the fraction: 1376/1224 = 344/306 ### Answer: 344/306 or 1.12424 (rounded to 8 decimal places)
Expected answer: 59/12
Correct? No
Problem: Find the sum of 21/75 and 44/47.
Mixtral 8x7B:
Reasoning: The sum of two fractions can be found by finding a common denominator and adding the numerators. The least common multiple of 75 and 47 is 3525. So, (21/75) + (44/47) = (21*47)/(75*47) + (44*75)/(47*75) = 987/3525 + 3300/3525 = 4287/3525. ### Answer: 4287/3525 or about 1.217 (rounded to three decimal places)
Expected answer: 1429/1175
Correct? Yes
Problem: Now that you calculated the sum of 21/75 and 44/47, can you find out what would be the total of two such sums added together?
Mixtral 8x7B:
Yes, if you have two sums, say A + B and C + D, and you have already calculated A + B to be equal to X, then the total of A + B and C + D would be X + C + D. If A + B = X and C + D = Y, then A + B + C + D = X + Y. So, if you have already calculated the sum of 21/75 and 44/47 to be 4287/3525, and you have another sum Z = E + F, then the total of the two sums would be 4287/3525 + Z. ### Answer: The total of the two sums would be 4287/3525 + Z, where Z is the value of the second sum.
Expected answer: 2858/1175
Correct? No
Problem: Previously, you computed the sum of 21/75 and 44/47. Now, imagine instead that the fraction was 21/63 rather than 21/75. What would the sum of 21/63 and 44/47 be?
Mixtral 8x7B:
Reasoning: The sum of two fractions can be found by finding a common denominator and adding the numerators. The least common multiple of 63 and 47 is 2919. So, (21/63) + (44/47) = (21*47)/(63*47) + (44*63)/(47*63) = 987/2919 + 2788/2919 = 3775/2919. ### Answer: 3775/2919 or about 1.294 (rounded to three decimal places)
Expected answer: 179/141
Correct? No
Problem: Calculate the result of (77/5 + 4/11).
Mixtral 8x7B:
Reasoning: To add the fractions 77/5 and 4/1
Expected answer: 867/55
Correct? No
Problem: What's the sum of 60/48 and 37/47?
Mixtral 8x7B:
Reasoning: To add the fractions 60/48 and 37/47, we need to get them over a common denominator. The least common multiple of 48 and 47 is 2256. So, we convert 60/48 to 75/64 and 37/47 to 84/64. Then, we add the fractions: 75/64 + 84/64 = 159/64. ### Answer: 159/64
Expected answer: 383/188
Correct? No
Problem: Solve ((14 / 72) + (25 / 6)).
Mixtral 8x7B:
Reasoning: First, find the common denominator of 72 and 6, which is 72. Then, convert 25/6 to have a denominator of 72: 25/6 = (25 \* 12) / 72 = 300 / 72. Now, add the fractions: (14 / 72) + (300 / 72) = (14 + 300) / 72 = 314 / 72. ### Answer: 314 / 72.
Expected answer: 157/36
Correct? Yes
Problem: In addition to the calculation you did in the last question, let's add another operation. Solve ((14 / 24) + ((14 / 72) + (25 / 6))).
Mixtral 8x7B:
Reasoning: First, find the common denominator of 24 and 72, which is 72. Then, convert 14/24 to have a denominator of 72: 14/24 = (14 \* 3) / 72 = 42 / 72. Now, add the fractions: (42 / 72) + ((14 / 72) + (300 / 72)) = (42 + 14 + 300) / 72 = 356 / 72. ### Answer: 356 / 72. (Note: The answer from the previous question is included in this answer, as the problem asked to add another operation to the previous calculation.)
Expected answer: 89/18
Correct? Yes
Problem: In the previous problem, we calculated the sum ((14 / 72) + (25 / 6)). But what if we made a mistake and it wasn't 25/6 of something added, but it was actually 90/6? Given this new information, what would be the new value of ((14 / 72) + (90 / 6))?
Mixtral 8x7B:
Reasoning: First, find the common denominator of 72 and 6, which is 72. Then, convert 90/6 to have a denominator of 72: 90/6 = (90 \* 12) / 72 = 1080 / 72. Now, add the fractions: (14 / 72) + (1080 / 72) = (14 + 1080) / 72 = 1094 / 72. ### Answer: 1094 / 72. (Note: The original answer was incorrect due to the incorrect value given for the second fraction. The answer has been updated based on the new information provided.)
Expected answer: 547/36
Correct? Yes
Problem: What is the sum of 84/97 and 25/2?
Mixtral 8x7B:
Reasoning: To add the fractions 84/97 and 25/2, we need to find a common denominator. The least common multiple of 97 and 2 is 97*2 = <<97*2=194>>194. So, we convert 25/2 to 25*(97)/(2*97) = 2425/194. Then, we add the fractions: 84/97 + 2425/194 = (84 + 2425)/194 = 2509/194. ### Answer: 2509/194
Expected answer: 2593/194
Correct? No
Problem: What is the difference between the fractions 66/20 and 4/78?
Mixtral 8x7B:
Reasoning: To find the difference between two fractions, we need to get them over a common denominator. The least common multiple of 20 and 78 is 1560. So, we convert 66/20 to 198/1560 and 4/78 to 50/1560. The difference between 198/1
Expected answer: 1267/390
Correct? No
Problem: Calculate the expression: 83 divided by 37 minus 12 divided by 14.
Mixtral 8x7B:
Reasoning: First, perform the division operations: 83/37 = 2.24324324 and 12/14 = 0.857142857. Then, subtract the second result from the first: 2.24324324 - 0.857142857 = <<2.24324324-0.857142857=1.386090383>>1.386090383. ### Answer: 1.386090383 (rounded to 9 decimal places)
Expected answer: 359/259
Correct? No
Problem: What is the sum of 95/57 and 28/80?
Mixtral 8x7B:
Reasoning: To add the fractions 95/57 and 28/80, we need to find a common denominator. The least common multiple (LCM) of 57 and 80 is 4560. So, convert each fraction to have this common denominator: 95/57 = (95 \* 80) / 57 / 80 = 15200 / 4560 28/80 = 28 \* 57 / 80 \* 57 = 1596 / 4560 Now, add the two fractions: 15200 / 4560 + 1596 / 4560 = (15200 + 1596) / 4560 = 16796 / 4560 Simplify the fraction: 16796 / 4560 = 4.123595505617978 (rounded to 8 decimal places) ### Answer: The sum of 95/57 and 28/80 is 4.12359551 (rounded to 7 decimal places).
Expected answer: 121/60
Correct? No
Problem: Calculate the sum of 14/57 and 92/42.
Mixtral 8x7B:
Reasoning: To add the fractions 14/57 and 92/42, we need to find a common denominator. The least common multiple of 57 and 42 is 6210. So, we convert 14/57 to 14*10/57*10 = 140/570 and 92/42 to 92*135/42*135 = 12360/5670. Then, we add the two fractions: 140/570 + 12360/5670 = 13760/5670. ### Answer: 13760/5670 or 1.935 (rounded to three decimal places)
Expected answer: 324/133
Correct? No
Problem: What is the result of ((77 / 55) + (6 / 5))?
Mixtral 8x7B:
Reasoning: First, perform the division operations inside the parentheses: (1.4 + 1.2) Then, add the results: 1.4 + 1.2 = 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?
Mixtral 8x7B:
Reasoning: First, calculate the value of 39/64, which is approximately equal to 0.609. Then, add this value to the previously calculated result: 2.6 + 0.609 = 3.209 ### Answer: 3.209
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?
Mixtral 8x7B:
Reasoning: First, perform the division operations inside the parentheses: (77 / 55) + (6 / 79) Then, add the results: 1.4 + 0.07594936708860759 = 1.4759493670886076 ### Answer: 1.4759493670886076 (Note: This is the exact value. The decimal representation can be rounded to a desired number of decimal places as needed.)
Expected answer: 583/395
Correct? No
Problem: Calculate the value of (56 / 8) + (90 / 86). How much does it equal?
Mixtral 8x7B:
Reasoning: (56 / 8) = 7 and (90 / 86) ≈ 1.047. So, (56 / 8) + (90 / 86) = 7 + 1.047 = 8.047. ### Answer: 8.047
Expected answer: 346/43
Correct? No
Problem: What is the sum of 23/20 and 82/97?
Mixtral 8x7B:
Reasoning: To add two fractions, we need to have the same denominator. The least common denominator of 20 and 97 is 1940. So, convert each fraction to have this denominator: 23/20 = (23 \* 97) / (20 \* 97) = 2231 / 1940 82/97 = (82 \* 20) / (97 \* 20) = 1640 / 1940 Now, add the fractions: 2231 / 1940 + 1640 / 1940 = (2231 + 1640) / 1940 = 3871 / 1940 Simplify the fraction: 3871 / 1940 = 1 1/20 + 82/97 = 1 19/194 ### Answer: 1 19/194
Expected answer: 3871/1940
Correct? No
Problem: Calculate the sum of 54/88 and 28/10.
Mixtral 8x7B:
Reasoning: To add the fractions 54/88 and 28/10, we need to find a common denominator. The least common multiple of 88 and 10 is 440. So, we convert 54/88 to 54*5/88*5 = 270/440 and 28/10 to 28*44/10*44 = 1232/440. Then, we add the two fractions: 270/440 + 1232/440 = (270 + 1232)/440 = 1502/440. Finally, we simplify the fraction: 1502/440 = 751/220. ### Answer: 751/220
Expected answer: 751/220
Correct? Yes
Problem: After finding the sum of 54/88 and 28/10, add this to 21/13 and find the resulting value.
Mixtral 8x7B:
Reasoning: We found in the previous question that the sum of 54/88 and 28/10 is 751/220. Now, we need to add this fraction to 21/13. To do this, we need to find a common denominator. The least common multiple of 220 and 13 is 2860. So, we convert 751/220 to 751*13/220*13 = 9763/2860 and 21/13 to 21*220/13*220 = 4820/2860. Then, we add the two fractions: 9763/2860 + 4820/2860 = (9763 + 4820)/2860 = 14583/2860. ### Answer: 14583/2860 or approximately 5.10 when expressed as a decimal.
Expected answer: 14383/2860
Correct? No
Problem: What is the result of the following operation: 7 / 69 + 71 / 47?
Mixtral 8x7B:
Reasoning: First, we need to perform the division operations: 7 / 69 ≈ 0.10149 and 71 / 47 ≈ 1.51064. Then, we add the results: 0.10149 + 1.51064 = 1.61213. ### Answer: 1.61213
Expected answer: 5228/3243
Correct? No
Problem: What is the sum of 15/32 and 65/15?
Mixtral 8x7B:
Reasoning: To add the fractions 15/32 and 65/15, we need to find a common denominator. The least common multiple of 32 and 15 is 480. So, we convert each fraction to an equivalent fraction with denominator 480. 15/32 = (15 \* 15) / (32 \* 15) = 225/480 65/15 = (65 \* 32) / (15 \* 32) = 2080/480 Now, we can add the fractions: 225/480 + 2080/480 = (225 + 2080) / 480 = 2305/480 To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 5: 2305 / 5 = 461 and 480 / 5 = 96 ### Answer: The sum of 15/32 and 65/15 is 461/96.
Expected answer: 461/96
Correct? Yes
Problem: What is the sum of 87/26 and the result of the previous problem ((15/32) + (65/15))?
Mixtral 8x7B:
Reasoning: We first need to find the sum of 15/32 and 65/15, which we found in the previous problem to be 461/96. Now, we need to find the sum of 87/26 and 461/96. To do this, we need to find a common denominator. The least common multiple of 26 and 96 is 2448. So, we convert each fraction to an equivalent fraction with denominator 2448. 87/26 = (87 \* 93) / (26 \* 93) = 8081/2448 461/96 = (461 \* 25) / (96 \* 25) = 11525/2448 Now, we can add the fractions: 8081/2448 + 11525/2448 = (8081 + 11525) / 2448 = 19606/2448 To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2: 19606 / 2 = 9803 and 2448 / 2 = 1224 ### Answer: The sum of 87/26 and the result of the previous problem ((15/32) + (65/15)) is 9803/1224.
Expected answer: 10169/1248
Correct? No
Problem: What is the sum of 4/31 and 76/11?
Mixtral 8x7B:
Reasoning: To add the fractions 4/31 and 76/11, we need to find a common denominator. The least common multiple of 31 and 11 is 341. So, we convert 4/31 to 4\*11/31\*11 = 44/341 and 76/1
Expected answer: 2400/341
Correct? No
Problem: What is the sum when you add 82/15 to 100/12?
Mixtral 8x7B:
Reasoning: To add the fractions 82/15 and 100/12, we need to find a common denominator. The least common multiple of 15 and 12 is 60, so we convert both fractions to have this common denominator: 82/15 becomes (82 \* 4) / 60 = 328/60 100/12 becomes (100 \* 5) / 60 = 500/60 Now, we can add the fractions: 328/60 + 500/60 = 828/60 We simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2: 828/60 = 414/30 Finally, we simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 6: 414/30 = 7/5 + 68/5 = 73/5 ### Answer: The sum is 73/5 or 14 2/5 when expressed as a mixed number.
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.
Mixtral 8x7B:
Reasoning: Calculate the result of the two divisions: 92 / 29 = 3 remainder 1 41 / 33 = about 1.24, but as a remainder it is 41 - (33 \* 1) = 8 Now, add the whole numbers and divide the sum of the remainders by the common denominator: 3 + 1 + 8 / 29 = 4 + 8 / 29 = 4 remainder 8 So, the result is 4 and 8/29 as an improper fraction: 4 + 29/29 = 4 1/29 ### Answer: 4 1/29
Expected answer: 4225/957
Correct? No
Problem: What is the sum of 57/29 and 14/98?
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have the same denominator. The least common multiple of 29 and 98 is 2638. So, (57/29) = (57\*34)/2638 = 1953/2638 and (14/98) = (14\*14)/2638 = 196/2638 Then, (1953/2638) + (196/2638) = (1953+196)/2638 = 2149/2638 ### Answer: 2149/2638 or 57/29 + 14/98 = 2149/2638
Expected answer: 428/203
Correct? No
Problem: Solve the given expression: 70/25 + 83/28.
Mixtral 8x7B:
Reasoning: To add the given fractions, we need to get their common denominator. The least common multiple (LCM) of 25 and 28 is 25*4=100 and 28*3=84, so the LCM is 2100. Then, we convert 70/25 to 70*4/25*4=280/100 and 83/28 to 83*3/28*3=249/84. Now, we can add the fractions: 280/100 + 249/84 = (280*84+249*100)/100*84 = 51720/8400 = 2586/420 = 13/2 + 3/42 = 13/2 + 0 + 3/42 = 13/2. ### Answer: 13/2
Expected answer: 807/140
Correct? No
Problem: What is the result of adding the fractions 50/73 and 20/23?
Mixtral 8x7B:
Reasoning: To add the fractions 50/73 and 20/23, we first need to find a common denominator. The least common multiple (LCM) of 73 and 23 is 1699. Then, convert each fraction to have this common denominator: 50/73 = (50 \* 23) / 1699 = 1150 / 1699 20/23 = (20 \* 73) / 1699 = 1460 / 1699 Now, add the fractions: 1150 / 1699 + 1460 / 1699 = (1150 + 1460) / 1699 = 2610 / 1699 Simplify the fraction: 2610 / 1699 is already in simplest form. ### Answer: 2610/1699
Expected answer: 2610/1679
Correct? No
Problem: What is the value of ((49 / 57) + (89 / 99))?
Mixtral 8x7B:
Reasoning: First, we need to calculate the value of (49 / 57) and (89 / 99). (49 / 57) ≈ 0.85965 and (89 / 99) ≈ 0.89899. Then, we add these values: 0.85965 + 0.89899 = 1.75864. ### Answer: 1.75864 or approximately 1.76 when rounded to two decimal places.
Expected answer: 3308/1881
Correct? No
Problem: Calculate the result of 94 / 35 - 23 / 49. Report your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, calculate the two division problems: 94 / 35 ≈ 2.6857 and 23 / 49 ≈ 0.4694 Then, subtract the two decimal numbers: 2.6857 - 0.4694 = 2.2163 Finally, convert the decimal number to a fraction: 2.2163 = 22163 / 10000 = 29/125 (simplified) ### Answer: 29/125
Expected answer: 543/245
Correct? No
Problem: Calculate the sum of 58/30 and 49/37 and leave your answer as a fraction.
Mixtral 8x7B:
To find the sum of 58/30 and
Expected answer: 1808/555
Correct? No
Problem: Calculate the sum of 45/53 and 71/50.
Mixtral 8x7B:
Reasoning: To add the fractions 45/53 and 71/50, we need to find a common denominator. The least common multiple of 53 and 50 is 2650. So, convert each fraction to have this common denominator: 45/53 * 50/50 = 2250/2650 and 71/50 * 53/53 = 3743/2650 Now, add the two fractions: 2250/2650 + 3743/2650 = 6093/2650 ### Answer: 6093/2650
Expected answer: 6013/2650
Correct? No
Problem: Calculate the sum of 36/72 and 49/1.
Mixtral 8x7B:
Reasoning: To add the fractions 36/72 and 49/1, we need to have the same denominator. The least common denominator of 72 and 1 is 72. So, we convert 49/1 to 49/1 * 72/72 = 336/72. Then, we add the fractions: 36/72 + 336/72 = 372/72. ### Answer: 372/72 or 1 3/2 (simplified form)
Expected answer: 99/2
Correct? No
Problem: What is the sum of 61/20 and 29/15?
Mixtral 8x7B:
Reasoning: To add the fractions 61/20 and 29/15, we need to find a common denominator. The least common multiple of 20 and 15 is 60. So, we convert both fractions to have this common denominator: 61/20 = (61 \* 3)/(20 \* 3) = 183/60 29/15 = (29 \* 4)/(15 \* 4) = 116/60 Now, we can add the fractions: 183/60 + 116/60 = (183 + 116)/60 = 309/60 To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 3: 309/60 = 103/20 ### Answer: The sum of 61/20 and 29/15 is 103/20.
Expected answer: 299/60
Correct? No
Problem: Solve the expression ((33 / 90) + (77 / 79)). Give your answer as an unsimplified fraction.
Mixtral 8x7B:
Reasoning: First, we need to calculate the value of (33 / 90) and (77 / 79) separately. (33 / 90) = 11 / 30 (simplified) (77 / 79) is already in simplest form. Now, we add the two results: (11 / 30) + (77 / 79) To add the fractions, we need to have the same denominator. The least common multiple of 30 and 79 is 2370. (11 * 79) / 2370 + (77 * 30) / 2370 1069 / 2370 + 2310 / 2370 Now, we can add the fractions: (1069 + 2310) / 2370 3379 / 2370 ### Answer: 3379 / 2370
Expected answer: 3179/2370
Correct? No
Problem: What is the sum of 30/79 and 29/6? Give your answer as a fraction.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have the same denominator. The least common multiple of 79 and 6 is 474. So, we convert 30/79 to 30*6/79*6 = 180/474 and 29/6 to 29*79/6*79 = 2291/474. Then, we add the fractions: 180/474 + 2291/474 = (180+2291)/474 = 2471/474. ### Answer: 2471/474
Expected answer: 2471/474
Correct? Yes
Problem: After finding the sum of 30/79 and 29/6, subtract 44/75 from it. What is the result?
Mixtral 8x7B:
Reasoning: We found that the sum of 30/79 and 29/6 is 2471/474. To subtract 44/75 from 2471/474, we need to have the same denominator. The least common multiple of 474 and 75 is 143250. So, we convert 2471/474 to 2471*300/474*300 = 741300/143250 and 44/75 to 44*1904/75*1904 = 80256/143250. Then, we subtract the fractions: 741300/143250 - 80256/143250 = (741300-80256)/143250 = 661044/143250. ### Answer: 661044/143250
Expected answer: 54823/11850
Correct? No
Problem: After recalculating, you realized you had 30/97 instead of 30/79. Now, add that to 29/6. What is the new result?
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have the same denominator. The least common multiple of 97 and 6 is 582. So, we convert 30/97 to 30*6/97*6 = 180/582 and 29/6 to 29*97/6*97 = 2813/582. Then, we add the fractions: 180/582 + 2813/582 = (180+2813)/582 = 2993/582. ### Answer: 2993/582
Expected answer: 2993/582
Correct? Yes
Problem: What is the answer when you subtract 11/66 from 59/2?
Mixtral 8x7B:
Reasoning: To subtract a fraction from another fraction, we need to get a common denominator. The common denominator of 66 and 2 is 66. So, we first write 59/2 as 177/66. Then, we subtract 11/66 from 177/66 to get (177-11)/66 = 166/66. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2, to get 83/33. ### Answer: 83/33
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?
Mixtral 8x7B:
Reasoning: To add the fractions 58/23 and 25/26, we need to get them over a common denominator. The least common multiple of 23 and 26 is 598. 58/23 + 25/26 = (58*26)/598 + (25*23)/598 = 1508/598 + 575/598 = 2083/598 ### Answer: 2083/598 or 3.48 (rounded to two decimal places)
Expected answer: 2083/598
Correct? Yes
Problem: We previously calculated the sum of the fractions 58/23 and 25/26. Now, suppose we had started with 45/23 instead of 58/23. How does the sum of 45/23 and 25/26 compare to the original calculation?
Mixtral 8x7B:
Reasoning: To add the fractions 45/23 and 25/26, we need to get them over a common denominator. The least common multiple of 23 and 26 is 598. 45/23 + 25/26 = (45*26)/598 + (25*23)/598 = 1170/598 + 575/598 = 1745/598 The original calculation was 2083/598, and 1745/598 is less than 2083/598. ### Answer: 1745/598 is less than 2083/598.
Expected answer: 1745/598
Correct? Yes
Problem: Calculate the sum of the fractions 70/13 and 17/52.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have the same denominator. The least common multiple of 13 and 52 is 52. 70/13 + 17/52 = 70/13 + 17/((13*4)) = (70*4)/(13*4) + 17/52 = 280/52 + 17/52 = 297/52 = 99/17 + 17/52 = 99/17 + 1/32 = (99*32 + 17)/(17*32) = 3135/544. ### Answer: 3135/544
Expected answer: 297/52
Correct? No
Problem: What is the sum of 78/44 and 17/91?
Mixtral 8x7B:
Reasoning: To add the fractions 78/44 and 17/91, we need to get them over a common denominator. The least common multiple of 44 and 91 is 3994. So, we convert the fractions to have this common denominator: 78/44 = (78 \* 91) / (44 \* 91) = 7053/3994 17/91 = (17 \* 44) / (91 \* 44) = 748/3994 Now, we can add the fractions: 7053/3994 + 748/3994 = (7053 + 748) / 3994 = 7801/3994 ### Answer: The sum of 78/44 and 17/91 is 7801/3994.
Expected answer: 3923/2002
Correct? No
Problem: What is the sum of 43/4 and 71/4?
Mixtral 8x7B:
Reasoning: Both fractions have the same denominator (the bottom number), so we can add the numerators (the top numbers) and keep the denominator the same: 43/4 + 71/4 = (43+71)/4 = 114/4. We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4: 114 ÷ 4 / 4 ÷ 4 = 28.5 / 1 = 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?
Mixtral 8x7B:
Reasoning: First, we need to find the sum of 43/4 and 71/4, which is (43+71)/4 = 114/4 = 28.5. Then, we add 92/79 to 28.5, but we can't add a fraction to a decimal number directly. We need to convert 28.5 to a fraction, which is 28.5 = 285/10. Now, we can add the two fractions: 285/10 + 92/79 = (285*79) / (10*79) + (92*10) / (79*10) = (285*79) / (79*10) + (92*10) / (79*10) = (285+92) / 10 = 377 / 10 = 37.7. ### Answer: 37.7 (Note: The final answer is rounded to one decimal place.)
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?
Mixtral 8x7B:
Reasoning: The fractions have different denominators, so we need to find a common denominator to add them. The least common multiple of 4 and 89 is 89*4 = 356. We can convert 43/4 to 43*(89/89) / 4 = (43*89)/356 = 3807/356. We can convert 71/89 to 71*4/89*4 = 284/356. Now we can add the fractions: 3807/356 + 284/356 = (3807+284)/356 = 4091/356. ### Answer: 4091/356 or approximately 11.5 (when rounded to two decimal places)
Expected answer: 4111/356
Correct? No
Problem: What is the result of adding the fractions 17/74 and 53/27?
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. In this case, the least common multiple of 74 and 27 is 2054. So, we convert the fractions to have this common denominator: 17/74 = (17 \* 27) / 2054 = 459 / 2054 53/27 = (53 \* 74) / 2054 = 3922 / 2054 Now, we can add the fractions: 459 / 2054 + 3922 / 2054 = (459 + 3922) / 2054 = 4381 / 2054 The fraction 4381/2054 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 19: 4381 / 2054 = 233 / 108 ### Answer: The result of adding the fractions 17/74 and 53/27 is 233/108.
Expected answer: 4381/1998
Correct? No
Problem: Compute the value of (76/76) + (96/16).
Mixtral 8x7B:
Reasoning: (76/76) + (96/16) = 1 + 6 = 7. ### Answer: 7 Note: The expression (76/76) simplifies to 1, and (96/16) simplifies to 6.
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?
Mixtral 8x7B:
Reasoning: We previously found that (76/76) + (96/16) = 7. So, adding the solution to itself gives: 7 + 7 = 14. ### Answer: 14 Note: This is equivalent to calculating (76/76) + (96/16) + (76/76) + (96/16).
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?
Mixtral 8x7B:
Reasoning: (76/76) + (96/33) cannot be simplified further. ### Answer: 76/76 + 96/33 ≈ 2.0303 + 2.9091 ≈ 5.9494
Expected answer: 43/11
Correct? No
Problem: What is the result of ((94 / 14) - (50 / 90))? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: Calculate the two expressions in parentheses: 94 / 14 = 47 / 7 50 / 90 = 5 / 9 Now, subtract the two simplified fractions: (47 / 7) - (5 / 9) To subtract fractions, the denominators must be the same. Find the least common multiple (LCM) of 7 and 9, which is 63. Multiply both the numerator and the denominator of (47 / 7) by 9 to get 423 / 63. Multiply both the numerator and the denominator of (5 / 9) by 7 to get 35 / 63. Now, subtract the two fractions: 423 / 63 - 35 / 63 = (423 - 35) / 63 = 388 / 63 Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4: 388 / 4 = 97 63 / 4 = 15.75 ### Answer: 97 / 15.75
Expected answer: 388/63
Correct? Yes
Problem: After calculating the result of ((94 / 14) - (50 / 90)), reconsider the calculation by replacing (50 / 90) with (50 / 19) instead. What is the result of ((94 / 14) - (50 / 19))? What is the final result as a simplified fraction?
Mixtral 8x7B:
Reasoning: Calculate the two expressions in parentheses: 94 / 14 = 47 / 7 50 / 19 is already in its simplified form. Now, subtract the two fractions: (47 / 7) - (50 / 19) To subtract fractions, the denominators must be the same. Find the least common multiple (LCM) of 7 and 19, which is 133. Multiply both the numerator and the denominator of (47 / 7) by 19 to get 893 / 133. Multiply both the numerator and the denominator of (50 / 19) by 7 to get 350 / 133. Now, subtract the two fractions: 893 / 133 - 350 / 133 = (893 - 350) / 133 = 543 / 133 Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3: 543 / 3 = 181 133 / 3 = 44.33333333333 ### Answer: 181 / 44.33333333333 (Note: The answer is expressed as a simplified fraction, but the decimal equivalent is also provided for clarity.)
Expected answer: 543/133
Correct? No
Problem: What is the result of subtracting twenty-nine seventy-ninths from thirty-three sevenths?
Mixtral 8x7B:
To subtract twenty-nine seventy-ninths from thirty-three sevenths, we first need to convert both numbers to a common denominator. The least common multiple of 79 and 7 is 553. Thirty-three sevenths is equal to 33*7/7 = 231/7 = 231/553. Twenty-nine seventy-ninths is equal to 29*553/79/553 = 16477/553. Now, we can subtract: 231/553 - 16477/553 = (231-16477)/553 = -16246/553. ### Answer: The result of subtracting twenty-nine seventy-ninths from thirty-three sevenths is -16246/553.
Expected answer: 2404/553
Correct? No
Problem: What is the sum of 60/79 and 53/38?
Mixtral 8x7B:
Reasoning: To add the fractions 60/79 and 53/38, we need to find a common denominator. The least common multiple (LCM) of 79 and 38 is 2932. Then, convert 60/79 to have a denominator of 2932: (60/79)\*(2932/2932) = 147280/2932. Similarly, convert 53/38 to have a denominator of 2932: (53/38)\*(2932/2932) = 202876/2932. Now, add the fractions: 147280/2932 + 202876/2932 = (147280 + 202876)/2932 = 350156/2932. ### Answer: 350156/2932 or approximately 120.05 (when rounded to two decimal places)
Expected answer: 6467/3002
Correct? No
Problem: Solve the following fraction equation: 39/48 + 19/84.
Mixtral 8x7B:
Reasoning: To solve this fraction equation, we need to find a common denominator for the fractions 39/48 and 19/84. The least common multiple of 48 and 84 is 252, so we convert both fractions to have this common denominator: 39/48 = (39 \* 5) / (48 \* 5) = 195 / 252 19/84 = (19 \* 3) / (84 \* 3) = 57 / 252 Now, we can add the fractions: 195 / 252 + 57 / 252 = (195 + 57) / 252 = 252 / 252 ### Answer: 1
Expected answer: 349/336
Correct? No
Problem: What is the sum of 16/86 and 60/3?
Mixtral 8x7B:
Reasoning: To add two fractions, we need to have the same denominator. The least common denominator of 86 and 3 is 258. So, we convert 16/86 to 16*3/86*3 = 48/258 and 60/3 to 60*86/3*86 = 1560/258. Then, we add the two fractions: 48/258 + 1560/258 = (48+1560)/258 = 1608/258. ### Answer: 1608/258 or 6.236641604026846 (rounded to 12 decimal places)
Expected answer: 868/43
Correct? No
Problem: Solve the following equation: ((95 / 69) + (67 / 9))
Mixtral 8x7B:
Reasoning: First, we need to perform the operations inside the parentheses: (1.3768 + 7.4444) = 8.8212 ### Answer: 8.8212
Expected answer: 1826/207
Correct? No
Problem: Calculate the result of 95 / 16 - 43 / 60.
Mixtral 8x7B:
Reasoning: First, we need to perform the division operations: 95 / 16 = 5.9375 43 / 60 = 0.7166666666666667 Then, we subtract the results: 5.9375 - 0.7166666666666667 = 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?
Mixtral 8x7B:
Reasoning: We first found that 95 / 16 - 43 / 60 = 5.220833333333333. Then, we calculate 80 / 79 = 1.012658227848101. Finally, we add the two results: 5.220833333333333 + 1.012658227848101 = 6.233491561181434 ### Answer: 6.233491561181434
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?
Mixtral 8x7B:
Reasoning: First, we need to perform the division operations: 91 / 16 = 5.6875 43 / 60 = 0.7166666666666667 Then, we subtract the results: 5.6875 - 0.7166666666666667 = 4.970833333333333 ### Answer: 4.970833333333333 In this case, the result is different because we changed the dividend in the first division operation from 95 to 91.
Expected answer: 1193/240
Correct? No
Problem: What is the sum of the fractions 38/8 and 4/16?
Mixtral 8x7B:
Reasoning: The fraction 38/8 can be simplified to 19/4. The sum of 19/4 and 4/1
Expected answer: 5
Correct? No
Problem: Calculate the result of 67 / 15 - 27 / 12.
Mixtral 8x7B:
Reasoning: First, we need to perform the division operations: 67/15 = 4.46666666667 and 27/12 = 2.25. Then, we subtract the results: 4.46666666667 - 2.25 = 2.21666666667. ### Answer: 2.21666666667 (when rounded to 14 decimal places) or approximately 2.22 (when rounded to two decimal places).
Expected answer: 133/60
Correct? No
Problem: Calculate the sum of 38/59 and 80/94.
Mixtral 8x7B:
Reasoning: To add the fractions 38/59 and 80/94, we need to find a common denominator. The least common multiple (LCM) of 59 and 94 is 5022. So, convert 38/59 to have a denominator of 5022: 38/59 \* (5022/5022) = 2217/5022 Convert 80/94 to have a denominator of 5022: 80/94 \* (5022/5022) = 4176/5022 Now, add the fractions: 2217/5022 + 4176/5022 = (2217 + 4176)/5022 = 6393/5022 ### Answer: 6393/5022
Expected answer: 4146/2773
Correct? No
Problem: Calculate the sum of 10/14 and 70/20. Report your answer as a decimal.
Mixtral 8x7B:
Reasoning: To calculate the sum of 10/14 and 70/20, we first need to get a common denominator. The common denominator of 14 and 20 is 140. So, we convert 10/14 to 10*10/14*10 = 100/140 and 70/20 to 70*7/20*7 = 490/140. Then, we add the two fractions: 100/140 + 490/140 = 590/140. Finally, we simplify the fraction: 590/140 = 59/14 = 4.21428571429. ### Answer: 4.21428571429
Expected answer: 59/14
Correct? No
Problem: What is the result of subtracting 19/44 from 33/5?
Mixtral 8x7B:
Reasoning: To subtract a fraction from another fraction, we need to get a common denominator first. The common denominator of 44 and 5 is 220. So, we convert 33/5 to 33*(44/5) / (44/1) = 323.2/5 and 19/44 to 19/44. Then, we subtract 19/44 from 323.2/5 to get (323.2 - 19)/5 = 304.2/5 = 60.84. ### Answer: 60.84
Expected answer: 1357/220
Correct? No
Problem: Find the result for (97 / 13) + (62 / 22). Answer as a decimal to the nearest hundredth.
Mixtral 8x7B:
Reasoning: First, we need to calculate the value of the two fractions: 97 / 13 ≈ 7.4615 62 / 22 ≈ 2.8182 Then, we add the two decimal values: 7.4615 + 2.8182 ≈ 10.2797 Finally, we round this value to the nearest hundredth: 10.28 ### Answer: 10.28
Expected answer: 1470/143
Correct? No
Problem: What is the sum of 78 divided by 35 and 30 divided by 60?
Mixtral 8x7B:
Reasoning: First, we need to perform the division operations: 78 divided by 35 is approximately 2.23 (when rounded to two decimal places). 30 divided by 60 is approximately 0.5 (when rounded to one decimal place). Then, we add the results: 2.23 + 0.5 = 2.73. ### Answer: 2.73
Expected answer: 191/70
Correct? No
Problem: What is the sum of 49/75 and 88/58?
Mixtral 8x7B:
Reasoning: To add the fractions 49/75 and 88/58, we need to find a common denominator. The least common multiple (LCM) of 75 and 58 is 4350. 49/75 = (49 \* 60) / 4350 = 2940 / 4350 88/58 = (88 \* 75) / 4350 = 6600 / 4350 Now, we can add the fractions: 2940 / 4350 + 6600 / 4350 = (2940 + 6600) / 4350 = 9540 / 4350 Simplifying the fraction: 9540 / 4350 = 318 / 145 ### Answer: 318 / 145
Expected answer: 4721/2175
Correct? No
Problem: What is the result of ((50 / 2) - (50 / 32))?
Mixtral 8x7B:
Reasoning: First, perform the division operations inside the parentheses: (25 - 1.5625) Then, subtract: 25 - 1.5625 = 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)?
Mixtral 8x7B:
Reasoning: First, calculate the difference between (50 / 2) and (50 / 32): 25 - 1.5625 = 23.4375 Then, calculate (72 / 81): 72 / 81 = 0.8888888888888888 Finally, add the two results: 23.4375 + 0.8888888888888888 = 24.32647938144328 ### Answer: 24.32647938144328 (Note: This answer is rounded to 15 decimal places. The exact answer is a repeating decimal.)
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))?
Mixtral 8x7B:
Reasoning: First, perform the division operations inside the parentheses: (25 - 0.5495) Then, subtract: 25 - 0.5495 = 24.4505 ### Answer: 24.4505
Expected answer: 2225/91
Correct? No
Problem: What is the result of ((77 / 30) + (18 / 51))?
Mixtral 8x7B:
Reasoning: First, we need to calculate the two fractions separately: 77 / 30 = 2.56666666667 (rounded to 8 decimal places) 18 / 51 = 0.35294117647 (rounded to 8 decimal places) Then, we add the two results: 2.56666666667 + 0.35294117647 = 2.91960784314 (rounded to 8 decimal places) ### Answer: 2.91960784 (rounded to 8 decimal places)
Expected answer: 1489/510
Correct? No
Problem: What is the result of (36 / 37) + (8 / 4)?
Mixtral 8x7B:
Reasoning: First, we perform the division operations: 36 / 37 ≈ 0.972973 (rounded to 12 decimal places) 8 / 4 = 2 Then, we perform the addition operation: 0.972973 + 2 = 2.972973 ### Answer: 2.972973 (rounded to 12 decimal places)
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.
Mixtral 8x7B:
Reasoning: First, calculate each part of the expression: (57 / 22) = 2.59090909... (72 / 48) = 1.5 Then, subtract: 2.59090909... - 1.5 = 1.09090909... Now, convert the result to a fraction: 1.09090909... = 1 9/10 ### Answer: 1 9/10
Expected answer: 12/11
Correct? No
Problem: What is the sum of 48 divided by 16 and 12 divided by 29?
Mixtral 8x7B:
Reasoning: 48 divided by 16 equals 3. 12 divided by 29 is approximately 0.4138. The sum of these two numbers is 3 + 0.4138 = <<3+0.4138=3.4138>>3.4138. ### Answer: 3.4138
Expected answer: 99/29
Correct? No
Problem: What is the sum of 37/20 and 16/75? Write your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 37/20 and 16/75, we need to get them over a common denominator. The least common multiple of 20 and 75 is 150. So, we convert 37/20 to 111/150 and 16/75 to 32/150. Then, we add the fractions: 111/150 + 32/150 = 143/150. ### Answer: 143/150
Expected answer: 619/300
Correct? No
Problem: Calculate the summation: 83/40 + 6/8.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. The least common multiple of 40 and 8 is 40. So, we convert 6/8 to 15/40. Then, we add the fractions: 83/40 + 15/40 = (83+15)/40 = 98/40. We can simplify this fraction to 24.5/10 or 245/100. ### Answer: 245/100 or 2.45
Expected answer: 113/40
Correct? No
Problem: Find the result of the addition of the fractions 37/69 and 67/61.
Mixtral 8x7B:
To add the fractions 37/69 and 67/61, we first need to find a common denominator for the two fractions. The least common multiple (LCM) of 69 and 61 is 4299. Now, convert each fraction to an equivalent fraction with denominator 4299: 37/69 = (37 \* 61) / (69 \* 61) = 2257/4299 67/61 = (67 \* 69) / (61 \* 69) = 4603/4299 Now, add the two fractions: 2257/4299 + 4603/4299 = (2257 + 4603) / 4299 = 6860/4299 The fraction 6860/4299 is already in simplest form, but it can be expressed as a mixed number: 1 2560/4299. ### Answer: 1 2560/4299 or approximately 1.575
Expected answer: 6880/4209
Correct? No
Problem: What is the sum of 89/84 and 75/34?
Mixtral 8x7B:
Reasoning: To add the fractions 89/84 and 75/34, we need to find a common denominator. The least common multiple (LCM) of 84 and 34 is 252. So, we convert each fraction to have this common denominator: 89/84 = (89 \* 3) / (84 \* 3) = 267 / 252 75/34 = (75 \* 7) / (34 \* 7) = 525 / 238 Now, we can add the fractions: 267 / 252 + 525 / 238 = (267 \* 238 + 525 \* 252) / (252 \* 238) = 130719 / 60144 ### Answer: 130719/60144
Expected answer: 4663/1428
Correct? No
Problem: What is the result when you add 51/78 and 44/83?
Mixtral 8x7B:
Reasoning: To add two fractions, we need to have the same denominator. The least common denominator (LCD) of 78 and 83 is 78 \* 83 = <<78*83=6494>>6494. The first fraction, 51/78, can be written as (51 \* 83) / 6494 = 4203/6494. The second fraction, 44/83, can be written as (44 \* 78) / 6494 = 3432/6494. Now, we can add the two fractions: 4203/6494 + 3432/6494 = (4203 + 3432) / 6494 = 7635/6494. The fraction 7635/6494 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1: 7635/6494 is already in its simplest form. ### Answer: 7635/6494
Expected answer: 2555/2158
Correct? No
Problem: Calculate the sum of the fractions 99/85 and 77/55.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. The least common multiple of 85 and 55 is 425. So, we convert each fraction to have this common denominator: 99/85 = (99 x 5) / 425 = 495 / 425 77/55 = (77 x 8) / 425 = 616 / 425 Now, we can add the fractions: 495 / 425 + 616 / 425 = (495 + 616) / 425 = 1111 / 425 ### Answer: 1111/425 or 2 541/425 (when simplified)
Expected answer: 218/85
Correct? No
Problem: What is the value of 97 / 56 - 31 / 52? Represent your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: First, calculate the value of 97/56: 97 is a prime number, and 56 can be factored as 2^3 * 7. Therefore, 97/56 cannot be simplified further. Next, calculate the value of 31/52: 52 can be factored as 2^2 * 13. Therefore, 31/52 cannot be simplified further. Now, subtract the two values: 97/56 - 31/52 = (97*2)/(56*2) - 31/52 = 194/112 - 31/52 = (194-31)/52 = 163/52. The fraction 163/52 cannot be simplified further, as 163 and 52 are coprime. ### Answer: 163/52
Expected answer: 827/728
Correct? No
Problem: Calculate the result of the following fraction operation: (78 / 74) + (72 / 51).
Mixtral 8x7B:
Reasoning: First, we need to perform the division operations: 78 / 74 ≈ 1.0541 (rounded to five decimal places for the addition) 72 / 51 ≈ 1.4118 (rounded to five decimal places for the addition) Then, we add the results: 1.0541 + 1.4118 = 2.4659 ### Answer: 2.4659
Expected answer: 1551/629
Correct? No
Problem: What is the result of the operation (33 / 23) - (12 / 75)? Express your answer as a fraction.
Mixtral 8x7B:
Reasoning: First, perform the division operations: 33 / 23 ≈ 1.43, and 12 / 75 ≈ 0.16 Then, subtract the results: 1.43 - 0.16 = 1.27 Finally, convert the decimal number to a fraction: 1.27 = 127/100 ### Answer: 127/100
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.
Mixtral 8x7B:
Reasoning: First, perform the division operations: 85/42 ≈ 2.0238 and 98/99 ≈ 0.9899. Then, subtract the results: 2.0238 - 0.9899 = 1.0339. Finally, simplify the result to the nearest hundredth: 1.03. ### Answer: 1.03
Expected answer: 1433/1386
Correct? No
Problem: What is the sum of 19/30 and 75/77? Express your answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 19/30 and 75/77, we need to get them over a common denominator. The least common multiple of 30 and 77 is 2310. So, we convert 19/30 to 19\*77/30\*77 = 1483/2310 and 75/77 to 75\*30/77\*30 = 2250/2310. Now, we can add the fractions: 1483/2310 + 2250/2310 = (1483+2250)/2310 = 3733/2310. To simplify the fraction, we need to find the greatest common divisor (GCD) of 3733 and 2310. The GCD is 1. So, the fraction 3733/2310 cannot be simplified further. ### Answer: 3733/2310
Expected answer: 3713/2310
Correct? No
Problem: What is the sum of 57/66 and 39/64? Please express your answer as a fraction.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. The least common multiple of 66 and 64 is 264. So, we convert 57/66 to 90/264 and 39/64 to 59/264. Then, we add the fractions: 90/264 + 59/264 = 149/264. ### Answer: 149/264
Expected answer: 1037/704
Correct? No
Problem: What is the sum of 80/13 and 2/48?
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have the same denominator. The least common multiple of 13 and 48 is 598. 80/13 = 80/13 * 48/48 = 3696/624 2/48 = 2/48 * 13/13 = 26/624 So, 80/1
Expected answer: 1933/312
Correct? No
Problem: Calculate the result of the operation ((55 / 30) - (1 / 72)).
Mixtral 8x7B:
Reasoning: First, calculate the value of 55/30, which is approximately equal to 1.8333. Next, calculate the value of 1/72, which is approximately equal to 0.0139. Then, subtract 1/72 from 55/30: 1.8333 - 0.0139 = 1.8194. ### Answer: 1.8194
Expected answer: 131/72
Correct? No
Problem: Calculate the sum of the fractions 69/21 and 71/86.
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. The least common multiple of 21 and 86 is 1842. So, we convert the fractions to have this common denominator: 69/21 = (69 \* 86) / (21 \* 86) = 6003/1842 71/86 = (71 \* 21) / (86 \* 21) = 1491/1842 Now, we can add the fractions: 6003/1842 + 1491/1842 = (6003 + 1491) / 1842 = 7494/1842 ### Answer: 7494/1842 or simplified to 3747/921.
Expected answer: 2475/602
Correct? No
Problem: What is the sum of 24/60 and 42/45? Answer as a simplified fraction.
Mixtral 8x7B:
Reasoning: To add the fractions 24/60 and 42/45, we need to get them over a common denominator. The least common multiple of 60 and 45 is 180. So, we convert 24/60 to 12/30 and 42/45 to 36/30. Then, we add the fractions: 12/30 + 36/30 = 48/30. Finally, we simplify the fraction: 48/30 = 16/10 = 8/5. ### Answer: 8/5
Expected answer: 4/3
Correct? No
Problem: What is the sum of 64/76 and 35/33?
Mixtral 8x7B:
Reasoning: To add the fractions 64/76 and 35/33, we need to find a common denominator. The least common multiple (LCM) of 76 and 33 is 264. So, convert 64/76 to have a denominator of 264: 64/76 = (64 \* 3)/264 = 192/264 And convert 35/33 to have a denominator of 264: 35/33 = (35 \* 8)/264 = 280/264 Now, add the two fractions: 192/264 + 280/264 = (192 + 280)/264 = 472/264 Simplify the fraction: 472/264 = 236/132 ### Answer: 236/132 or about 1.7917 (rounded to 4 decimal places)
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.
Mixtral 8x7B:
Reasoning: To find the sum of 47/1
Expected answer: 1003/80
Correct? No
Problem: What is the result of the operation (58 / 2) + (31 / 32)?
Mixtral 8x7B:
Reasoning: First, perform the division operations: 58 / 2 = 29
Expected answer: 959/32
Correct? No
Problem: What is the sum of 26/90 and 50/26 when calculated as a fraction?
Mixtral 8x7B:
Reasoning: To find the sum of two fractions, we need to find a common denominator. In this case, the common denominator of 90 and 26 is 90*26 = 2340. So, (26/90) + (50/26) = (26\*1 + 50\*36)/90*26 = 186 + 1800 / 2340 = 1986 / 2340 = 1\*1620 + 186 / 2\*1170 + 186 = 3480/2340 = 3/2. ### Answer: The sum of 26/90 and 50/26 is 3/2 or 1 1/2.
Expected answer: 1294/585
Correct? No
Problem: Calculate the sum of 80/98 and 92/82.
Mixtral 8x7B:
Reasoning: To add the fractions 80/98 and 92/82, we need to find a common denominator. The least common multiple (LCM) of 98 and 82 is 14898. 80/98 = (80 \* 151) / 14898 = 12120 / 14898 92/82 = (92 \* 180) / 14898 = 16560 / 14898 Now, we can add the fractions: 12120 / 14898 + 16560 / 14898 = (12120 + 16560) / 14898 = 28680 / 14898 The fraction 28680/14898 simplifies to 15/79. ### Answer: 15/79
Expected answer: 3894/2009
Correct? No
Problem: Calculate the sum of 89/44 and 69/5.
Mixtral 8x7B:
Reasoning: To add the fractions 89/44 and 69/5, we need to find a common denominator. The least common multiple of 44 and 5 is 220, so we convert both fractions to have this common denominator: 89/44 = (89 \* 5) / 220 = 445/220 69/5 = (69 \* 44) / 220 = 3016/220 Now we can add the fractions: 445/220 + 3016/220 = (445 + 3016) / 220 = 3461/220 ### Answer: 3461/220
Expected answer: 3481/220
Correct? No
Problem: Calculate the following expression: 79/32 - 52/55.
Mixtral 8x7B:
Reasoning: To subtract the fractions, we need to get a common denominator. The common denominator of 32 and 55 is 16*55 = 880. So, convert each fraction to have this common denominator: 79/32 = (79*27.5)/(32*27.5) = 2177.5/880 52/55 = (52*15.4545)/(55*15.4545) = 801.0909/880 Now, subtract the fractions: 2177.5/880 - 801.0909/880 = (2177.5 - 801.0909)/880 = 1376.4091/880 ### Answer: 1376.4091/880 or approximately 1.564 when rounded to 3 decimal places.
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?
Mixtral 8x7B:
Reasoning: The usual length of a piece of wood is 45/2 feet. The piece they sold is 18/90 = <<18/90=2/15>>2/15 shorter than the usual length, so it is 45/2 - 2/1
Expected answer: 223/10
Correct? No
Problem: What is the sum of 99/92 and 15/74 as a simplified fraction?
Mixtral 8x7B:
Reasoning: To add the fractions, we need to have a common denominator. The least common multiple of 92 and 74 is 6704. So, we convert the fractions to have this common denominator: 99/92 = (99 x 74) / (92 x 74) = 7336 / 6704 15/74 = (15 x 92) / (74 x 92) = 1380 / 6704 Now, we can add the fractions: 7336 / 6704 + 1380 / 6704 = (7336 + 1380) / 6704 = 8716 / 6704 To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 8716 and 6704 is 8. Dividing both the numerator and the denominator by 8, we get: 8716 / 6704 = (8716 / 8) / (6704 / 8) = 1089 / 838 ### Answer: The sum of 99/92 and 15/74 as a simplified fraction is 1089/838.
Expected answer: 4353/3404
Correct? No
Problem: Calculate the result of 54/1 + 62/30. Express your answer in simplest terms.
Mixtral 8x7B:
Reasoning: To add the fractions 54/1 and 62/30, we need to find a common denominator. The least common multiple of 1 and 30 is 30, so we convert both fractions to have this denominator: 54/1 = 54 \* 30/1 \* 30 = 1620/30 62/30 = 62/30 \* 1/1 = 62/30 Now we can add the fractions: 1620/30 + 62/30 = (1620 + 62)/30 = 1682/30 To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 2: 1682/30 = 841/15 ### Answer: 841/15
Expected answer: 841/15
Correct? Yes
Problem: If we subtract 53/41 from the result of 54/1 + 62/30, what is the new result? Express your answer in simplest terms.
Mixtral 8x7B:
Reasoning: We first calculate the result of 54/1 + 62/30: 54/1 + 62/30 = 841/15 Then, we subtract 53/41 from this result: (841/15) - (53/41) To subtract the fractions, we need to find a common denominator. The least common multiple of 15 and 41 is 595. So, we convert both fractions to have this denominator: 841/15 = 841 \* 39/15 \* 39 = 325999/595 53/41 = 53 \* 15/41 \* 15 = 1185/595 Now we can subtract the fractions: (325999/595) - (1185/595) = (325999 - 1185)/595 = 324814/595 To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 2: 324814/595 = 162407/297.5 ### Answer: 162407/297.5
Expected answer: 33686/615
Correct? No
Problem: If we had originally started with 93 instead of 54, and added 62/30 to that, what would be the new result? Express the answer in simplest terms.
Mixtral 8x7B:
Reasoning: To add the fractions 93/1 and 62/30, we need to find a common denominator. The least common multiple of 1 and 30 is 30, so we convert both fractions to have this denominator: 93/1 = 93 \* 30/1 \* 30 = 2790/30 62/30 = 62/30 \* 1/1 = 62/30 Now we can add the fractions: 2790/30 + 62/30 = (2790 + 62)/30 = 2852/30 To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 4: 2852/30 = 713/7.5 ### Answer: 713/7.5
Expected answer: 1426/15
Correct? Yes
Problem: What value do you get by adding 85/29 and 47/7?
Mixtral 8x7B:
Reasoning: To add the fractions 85/29 and 47/7, we need to get them over a common denominator. The least common multiple of 29 and 7 is 203, so we convert the fractions to have this denominator: 85/29 = 85/29 47/7 = (47 \* 4) / (7 \* 4) = 188/28 Now we can add the fractions: 85/29 + 188/28 = (85 + 188) / 29 = 273/29 ### Answer: 273/29
Expected answer: 1958/203
Correct? No