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Multiplying and dividing fractions

Fraction × whole number, fraction × fraction, and fraction ÷ whole number.

Video coming soon The written summary and downloads below are complete and ready to use.

Multiplying and dividing fractions is quicker than adding them: you never need a common denominator. In this lesson you will learn how to:

  • multiply a fraction by a whole number
  • multiply a fraction by a fraction, and see why “of” means ×
  • divide a fraction by a whole number
  • finish off each answer: simplify, and change improper fractions to mixed numbers

1. A fraction times a whole number

Key idea 3 × 25 means 25 + 25 + 25. Multiply the top number by the whole number. The bottom number stays the same.

Example: 3 × 25

012
3×25=65=115

Three jumps of 2 fifths make 6 fifths. 3 × 2 = 6, and the bottom stays 5. 65 is more than 1 whole, so finish off: 1 15.

Watch out Do not multiply the bottom number as well. 3 × 25 is not 615: that is the same as 25, so nothing has been multiplied.

2. A fraction times a fraction

Key idea Multiply the tops, and multiply the bottoms. “Of” means ×: 12 of 13 is 12 × 13 = 16.

Example: 23 × 34

23 of the columns   34 of the rows   both

23×34=612=12

2 × 3 = 6 pieces are in both, out of 3 × 4 = 12 pieces altogether. Finish off: 612 = 12.

Notice Multiplying by a fraction less than 1 gives a smaller answer: you are taking only part of it.

3. A fraction divided by a whole number

Key idea Dividing shares the fraction into equal parts. Multiply the bottom number by the whole number. The top number stays the same.

Example: 34 ÷ 2

34÷2=38

Cut every quarter into 2: now there are 4 × 2 = 8 pieces. One share is 3 of them: 38. Dividing by 2 is the same as finding 12 of it.

Shortcut If the top number divides exactly, you can divide the top instead: 45 ÷ 2 = 25 (and 410 simplifies to 25 too).

The mistakes that cost marks

  1. Multiplying the bottom by the whole number. Writing 3 × 25 = 615. only the top is multiplied: 3 × 25 = 65 = 1 15.
  2. Adding instead of multiplying. Writing 23 × 34 = 57. multiply the tops (2 × 3) and multiply the bottoms (3 × 4): 612 = 12.
  3. Keeping a common denominator. Changing to twelfths and writing 812 × 912 = 7212. you only need the same bottom numbers to add or take away. To multiply, multiply the tops and the bottoms: 612 = 12.
  4. Dividing by multiplying the top. Writing 34 ÷ 2 = 64. sharing makes it smaller: multiply the bottom, 38.
  5. Expecting a bigger answer. Thinking 12 × 13 must be more than 13. half of something is smaller than it: 16.
  6. Not finishing off. Leaving 612 or 65. simplify (12) and change improper fractions to mixed numbers (1 15).

Quick checklist

Tick each one when you can do it without help.

Download

Print these and work through them away from the screen.

Year 4 practice paper PDF · 11+ style, with answer sheet and answers Year 5 practice paper PDF · 11+ style, with answer sheet and answers Year 6 practice paper PDF · 11+ style, with answer sheet and answers

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