Pre-test -- Operations With Fractions

Explanation
The given expression is a sum of two fractions: 2/5 and 3/5. When we add these fractions together, we get a numerator of 2+3=5 and a denominator of 5. Therefore, the result is 5/5, which simplifies to 1.

Explanation
The given question is asking to add the mixed numbers 6 2/7 and 3 2/5. To add these numbers, we first need to convert the fractions to have a common denominator. The least common multiple of 7 and 5 is 35. So, we convert 2/7 to 10/35 and 2/5 to 14/35. Now, we can add the whole numbers, which gives us 9. Then, we add the fractions, which gives us 24/35. Therefore, the final answer is 9 24/35.

Explanation
When dividing a fraction by a whole number, we can convert the whole number into a fraction by placing it over 1. So, 2 can be written as 2/1. To divide 8/11 by 2/1, we multiply the numerator of the first fraction (8) by the denominator of the second fraction (1), and multiply the denominator of the first fraction (11) by the numerator of the second fraction (2). This gives us (8*1)/(11*2) = 8/22, which simplifies to 4/11. Therefore, the correct answer is 4/11.

Explanation
The given expression is subtracting 1/4 from 9/14. To subtract fractions, we need to have a common denominator. In this case, the common denominator is 28. We can convert 9/14 to 18/28 and 1/4 to 7/28. Subtracting 7/28 from 18/28 gives us 11/28. Therefore, the correct answer is 11/28.

Explanation
The given expression is a multiplication of two fractions. To multiply fractions, we multiply the numerators together and the denominators together. In this case, multiplying 1/12 by 4/7 gives us (1*4)/(12*7) = 4/84. Simplifying this fraction gives us 1/21.

Explanation
The given expression is a division problem. To divide a number by a fraction, we need to multiply by the reciprocal of the fraction. In this case, we divide 5 by 3/4, which is the same as multiplying 5 by 4/3. Multiplying 5 by 4 gives us 20, and dividing 20 by 3 gives us 6 2/3. Therefore, the correct answer is 6 2/3.

Explanation
When you multiply 11 by 7/11, you are essentially multiplying 11 by the fraction 7/11. To multiply fractions, you multiply the numerators (top numbers) and the denominators (bottom numbers). In this case, 11 multiplied by 7 equals 77, and 11 multiplied by 11 equals 121. Therefore, the result is 77/121, which can be simplified to 7/11.

Explanation
To add mixed numbers, we first add the whole numbers together, which gives us 6 + 4 = 10. Then, we add the fractions together. The fractions 7/10 and 9/10 have the same denominator, so we can simply add the numerators: 7 + 9 = 16. Therefore, the sum of the fractions is 16/10. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2. This gives us 16/10 = 8/5. Putting it all together, the sum of the mixed numbers is 10 8/5. Simplifying the whole number and fraction part, we get 10 1 3/5, which is equivalent to 11 3/5.

Explanation
The given expression is a subtraction problem involving mixed numbers. To solve it, we need to find a common denominator, which in this case is 42. We then subtract the fractions by subtracting the numerators and keeping the denominator the same. The whole numbers are added separately. After performing the calculations, we get the result of 1 11/42.

Explanation
The given expression involves adding a fraction and a mixed number. To add fractions, we need to have a common denominator. In this case, the common denominator is 18. Converting 1/6 to a fraction with a denominator of 18 gives us 3/18. Now we can add the fractions: 3/18 + 6/18 = 9/18. Simplifying this fraction gives us 1/2. Adding the whole numbers, 1/2 + 6 gives us 6 1/2. Therefore, the correct answer is 6 13/18.

Explanation
The given expression is a multiplication of two fractions. To multiply fractions, we multiply the numerators together and the denominators together. So, (4/11) * (2/3) = (4 * 2) / (11 * 3) = 8/33. Therefore, the correct answer is 8/33.

Explanation
When dividing a number by a fraction, we can convert the division into multiplication by taking the reciprocal of the fraction. In this case, we have 20 divided by 3/4. To find the reciprocal of 3/4, we flip the fraction to get 4/3. Then, we multiply 20 by 4/3, which gives us 80/3. We can simplify this fraction to 26 2/3, which is the final answer.

Explanation
The given expression is 2 - 5/13. To subtract fractions, we need to have the same denominator. Here, the denominator is already the same. So, we can subtract the numerators. 2 - 5 = -3. Therefore, the answer is -3/13. However, the given options do not include a negative fraction. So, to convert the negative fraction to a mixed number, we divide the numerator by the denominator. -3 divided by 13 is -1 remainder 10. Thus, the answer is 1 10/13.

Explanation
The given expression is 3 - 2/3. To subtract fractions, we need to have a common denominator. In this case, the common denominator is 3. So, we rewrite 3 as 9/3. Now, we can subtract the fractions: 9/3 - 2/3 = 7/3. The result is an improper fraction. To convert it to a mixed number, we divide the numerator (7) by the denominator (3). The quotient is 2 with a remainder of 1. Therefore, the answer is 2 1/3.

Explanation
The expression 9 multiplied by 1/2 can be simplified by multiplying the numerator (9) with the numerator (1) and the denominator (2) with the denominator (1), which gives us 9/2. This fraction can be converted into a mixed number by dividing the numerator (9) by the denominator (2), resulting in a quotient of 4 and a remainder of 1. Therefore, the answer is 4 1/2.

Explanation
To divide a mixed number by a whole number, we convert the mixed number into an improper fraction. In this case, 10 6/13 can be converted to (10 * 13 + 6) / 13, which equals 136/13. Then, we divide 136/13 by 12, which can be written as 12/1. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, (136/13) * (1/12) = (136/13) * (1/12) = 136/156 = 34/39. So, the correct answer is 34/39.

Explanation
To find the answer, we need to follow the order of operations (PEMDAS/BODMAS). First, we perform the division: 10 divided by 13 equals 0.7692. Then, we add this result to 13, which gives us 13.7692. Therefore, the answer is 23 10/13.

Explanation
The given expression is a subtraction of mixed fractions. To subtract mixed fractions, we need to convert them into improper fractions. In this case, 1 6/7 can be written as 13/7 and 3/5 remains the same. Now, we can subtract the fractions by finding a common denominator, which is 35. The subtraction gives us 13/7 - 21/35, which simplifies to (13*5 - 21)/35 = 52/35. Further simplifying this fraction gives us 1 17/35. Therefore, the correct answer is 1 17/35.

Explanation
To subtract fractions, we need to have a common denominator. In this case, the common denominator is 9. So, we convert 7/9 to have a denominator of 9 by multiplying both the numerator and denominator by 1. Similarly, we convert 2/3 to have a denominator of 9 by multiplying both the numerator and denominator by 3. This gives us (7/9)*(1/1) - (2/3)*(3/3) = 7/9 - 6/9 = 1/9. Therefore, the correct answer is 1/9.

Explanation
The given question is asking for the sum of the mixed numbers 2 3/10 and 4 1/5. To add these two numbers, we need to first convert the mixed numbers into improper fractions. 2 3/10 is equal to 23/10 and 4 1/5 is equal to 21/5. Adding these fractions gives us 23/10 + 21/5 = 115/50. Simplifying this fraction gives us 6 1/2, which is the correct answer.