# D - Operations With Fractions

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| By Deborah Eberhardt
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Deborah Eberhardt
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Basic Operations with fractions. Simplify as much as possible

• 1.

### 2/7 + 2/5

• A.

4/35

• B.

4/12

• C.

2/35

• D.

4/24

• E.

24/35

E. 24/35
Explanation
The given expression is a sum of two fractions: 2/7 and 2/5. To add fractions, we need to find a common denominator. In this case, the common denominator is 35. We can convert both fractions to have a denominator of 35 by multiplying the numerator and denominator of the first fraction by 5, and the numerator and denominator of the second fraction by 7. This gives us (10/35) + (14/35), which simplifies to 24/35. Therefore, the correct answer is 24/35.

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• 2.

### 8/11 ÷ 1/2

• A.

16/11

• B.

4/11

• C.

10/11

• D.

11/4

• E.

5/12

A. 16/11
Explanation
When dividing fractions, we invert the second fraction and multiply it with the first fraction. In this case, we have 8/11 divided by 1/2. Inverting 1/2 gives us 2/1. Multiplying 8/11 with 2/1, we get (8/11) * (2/1) = 16/11. Therefore, the correct answer is 16/11.

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• 3.

### 9/14 - 1/4

• A.

8/10

• B.

11/28

• C.

11/56

• D.

7/28

• E.

9/16

B. 11/28
Explanation
The given expression is a subtraction of two fractions. To subtract fractions, we need to have a common denominator. The common denominator for 14 and 4 is 28. So, we convert the fractions 9/14 and 1/4 into fractions with a denominator of 28. 9/14 becomes 18/28 and 1/4 becomes 7/28. Now, we can subtract the fractions by subtracting their numerators while keeping the denominator the same. 18/28 - 7/28 equals 11/28. Therefore, the correct answer is 11/28.

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• 4.

### 1/12 * 4/7

• A.

4/84

• B.

4/21

• C.

3/24

• D.

9/12

• E.

1/21

E. 1/21
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, 1 times 4 is 4, and 12 times 7 is 84. Therefore, the result of the multiplication is 4/84.

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• 5.

### 5 ÷ 3/4

• A.

6 2/3

• B.

15/4

• C.

2 2/3

• D.

5 3/7

• E.

8/20

A. 6 2/3
Explanation
To divide a whole number by a fraction, we can multiply the whole number by the reciprocal of the fraction. In this case, we have 5 divided by 3/4. The reciprocal of 3/4 is 4/3. Multiplying 5 by 4/3 gives us 20/3, which is equivalent to 6 2/3. Therefore, the correct answer is 6 2/3.

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• 6.

### 11 * 7/11

• A.

11

• B.

77/11

• C.

7

• D.

11/29

• E.

5/22

C. 7
Explanation
The given expression is 11 multiplied by 7/11. When we multiply a number by a fraction, we can simplify the expression by canceling out any common factors between the numerator and denominator. In this case, the number 11 can be canceled out, leaving us with 7 as the result. Therefore, the correct answer is 7.

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• 7.

### 1/6 + 5/9

• A.

6/15

• B.

13/18

• C.

7/18

• D.

3/18

• E.

1/18

B. 13/18
Explanation
To find the sum of fractions, we need to have a common denominator. In this case, the common denominator is 18. Converting 1/6 to have a denominator of 18 gives us 3/18. Converting 5/9 gives us 10/18. Adding these fractions together gives us 13/18.

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• 8.

### 3 - 2/3

• A.

1/3

• B.

5 2/3

• C.

2/3

• D.

2 1/3

• E.

3 1/3

D. 2 1/3
Explanation
The given expression is 3 - 2/3. To subtract a fraction from a whole number, we need to convert the whole number into a fraction with the same denominator as the fraction. In this case, the denominator is 3. So, we convert 3 into a fraction by multiplying it by 3/3, which gives us 9/3. Now, we can subtract the fractions: 9/3 - 2/3 = 7/3. To express this as a mixed number, we divide the numerator (7) by the denominator (3), which gives us 2 with a remainder of 1. Hence, the answer is 2 1/3.

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• 9.

### 7/9 - 2/3

• A.

5/27

• B.

1/9

• C.

2/9

• D.

9 1/9

• E.

6/11

B. 1/9
Explanation
To subtract fractions, we need to have a common denominator. In this case, the common denominator is 9. So, we rewrite 7/9 as 7/9 * 3/3 and 2/3 as 2/3 * 3/3. This gives us (7 * 3 - 2 * 3) / 9 = 21/27 - 6/27 = 15/27. Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3, we get 5/9. Therefore, the correct answer is 5/27.

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• Current Version
• Mar 22, 2023
Quiz Edited by
ProProfs Editorial Team
• Sep 27, 2017
Quiz Created by
Deborah Eberhardt

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