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Fractional calculation exercises with solutions

In this section you will find solutions to the exercises and old exam problems for fractions. If you have problems with the tasks, you should definitely read our explanatory articles again first.

Tip: Write down the tasks on each piece of paper and only then do the math.

Solution to task 1: work on the word problems

1a) Bring fractions to a denominator, add fractions and reduce the result fraction

1b) Fractions are multiplied by calculating the numerator · numerator and denominator · denominator.

1c) Fractions are divided by multiplying by the reciprocal.

Solutions to exercise 2: add fractions

2a) 1/2 + 3/4 = 2/4 +3/4 = 5/4

2b) 2/3 + 1/3 = 3/3 = 1

2c) 4/5 + 1/2 = 8/10 + 5/10 = 13/10

2d) 8/7 + 1/2 = 16/14 + 7/14 = 23/14

2e) 6/9 +2/3 = 6/9 + 6/9 = 12/9 = 4/3

2f) 5/2 + 2/8 = 20/8 + 2/8 = 22/8 = 11/4

2g) 1/9 + 7/3 = 1/9 + 21/9 = 22/9

2h) 2/10 + 4/10 = 6/10 = 3/5

2i) 4/12 + 5/12 = 9/12 = 3/4

2j) 6/18 + 2/6 = 1/3 + 1/3 = 2/3

Solutions to exercise 3: subtract fractions

3a) 3/4 - 1/2 = 3/4 - 2/4 = 1/4

3b) 7/8 - 1/4 = 7/8 - 2/8 = 5/8

3c) 8/3 - 2/3 = 6/3 = 2

3d) 4/5 - 1/4 = 16/20 - 5/20 = 11/20

3e) 3/3 - 1/2 = 6/6 - 3/6 = 3/6 = 1/2

3f) 17/4 - 14/4 = 3/4

3g) 9/2 - 10/2 = -1/2

3h) 4/4 - 8/2 = 2/2 - 8/2 = -6/2 = -3

3i) 8/1 - 12/2 = 8 - 6 = 2

3j) 18/3 - 20/3 = -2/3

Solutions to exercise 4: multiply fractions

4a) 1/3 · 2/3 = 2/9

4b) 2/4 1/2 = 2/8 = 1/4

4c) 6/1 · 2/3 = 12/3 = 4

4d) 5/6 3/5 = 15/30 = 1/2

4e) 8/2 x 5/3 = 40/6 = 20/3

4f) 6/9 · 2/8 = 12/72 = 1/6

4g) 2/4 6/7 = 12/28 = 6/14 = 3/7

4h) 6/3 · 2/3 = 12/9 = 4/3

4i) 8/2 · 10/12 = 80/24 = 40/12 = 20/6 = 10/3

4j) 12/7 1/2 = 12/14 = 6/7

Solutions to exercise 5: Divide fractions

5a) 6/3: 2/1 = 6/3 1/2 = 6/6 = 1

5b) 1/2: 3/4 = 1/2 * 4/3 = 4/6 = 2/3

5c) 9/2: 1/2 = 9/2 * 2/1 = 18/2 = 9

5d) 4/5: 2/3 = 4/5 3/2 = 12/10 = 6/5

5e) 7/2: 5/6 = 7/2 6/5 = 42/10 = 21/5

5f) 2/9: 2/10 = 2/9 · 10/2 = 20/18 = 10/9

5g) 2/3: 6/3 = 2/3 x 3/6 = 6/18 = 1/3

5h) 10/20: 3/13 = 10/20 · 13/3 = 130/60 = 13/6

5i) 11/12: 10/10 = 11/12 · 1 = 11/12

5j) 8/17: 2/10 = 8/17 x 10/2 = 80/34 = 40/17

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