D - Operations With Fractions | Attempts: 214

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| By Deborah Eberhardt

Deborah Eberhardt

Community Contributor

Quizzes Created: 5 | Total Attempts: 2,922

Questions: 9 | Attempts: 214 | Updated: Mar 22, 2023

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Basic Operations with fractions. Simplify as much as possible

Questions and Answers

1.

2/7 + 2/5
- A.
  
  4/35
- B.
  
  4/12
- C.
  
  2/35
- D.
  
  4/24
- E.
  
  24/35
Correct Answer
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
Correct Answer
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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1
1
3.

9/14 - 1/4
- A.
  
  8/10
- B.
  
  11/28
- C.
  
  11/56
- D.
  
  7/28
- E.
  
  9/16
Correct Answer
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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1
0
4.

1/12 * 4/7
- A.
  
  4/84
- B.
  
  4/21
- C.
  
  3/24
- D.
  
  9/12
- E.
  
  1/21
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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
Correct Answer
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

D - Operations With Fractions

2/7 + 2/5

8/11 ÷ 1/2

9/14 - 1/4

1/12 * 4/7

5 ÷ 3/4

11 * 7/11

1/6 + 5/9

3 - 2/3

7/9 - 2/3