Solve problems involving multiplying proper fractions by whole numbers | Maths

Starter quiz

$Tick the fraction that is shaded in the image.$

Tick the fraction that is shaded in the image.
- $\frac{2}{5}$
- $\frac{3}{5}$ ✓
- $\frac{5}{3}$
- $\frac{5}{2}$
Tick the correct symbol to compare these two expressions.
- <
- > ✓
- =
Tick the correct symbol to compare these two expressions.
- <
- >
- = ✓
Tick the correct products for this equation. 2 × $\frac{6}{8}$ =
- $\frac{26}{16}$
- $\frac{26}{8}$
- $\frac{12}{8}$ ✓
- $1\frac{2}{8}$
- $1\frac{4}{8}$ ✓
Tick the correct products for this equation. $\frac{3}{5}$ × 4 =
- $\frac{12}{5}$ ✓
- $\frac{43}{5}$
- $\frac{12}{20}$
- $2\frac{2}{5}$ ✓
- $1\frac{2}{5}$
Tick the correct set of symbols to compare the expressions.
- < <
- > > ✓
- < >
- > <
- = =

Exit quiz

Write the answer to the following equation. 2 × $\frac{3}{6}$ = ______
- '1' ✓
Tick expressions where the product would be greater than one whole.
- $\frac{2}{7}$ × 3
- $\frac{4}{6}$ × 2 ✓
- $\frac{5}{9}$ × 3 ✓
- $\frac{1}{8}$ × 8
- $\frac{3}{5}$ × 2 ✓
Tick expressions where the product would be less than one whole.
- $\frac{1}{8}$ × 3 ✓
- $\frac{4}{9}$ × 2 ✓
- $\frac{2}{9}$ × 5
- $\frac{3}{6}$ × 2
- $\frac{2}{10}$ × 5
Tick the correct symbol to compare these two expressions.
- < ✓
- >
- =
Tick the correct symbol to compare these two expressions.
- < ✓
- >
- =
Order the expressions from largest to smallest.
- 1
  
  ⇔
  
  $\frac{3}{7}$ × 4
- 2
  
  ⇔
  
  $\frac{2}{7}$ × 4
- 3
  
  ⇔
  
  $\frac{3}{7}$ × 2
- 4
  
  ⇔
  
  $\frac{1}{7}$ × 1
- 5
  
  ⇔
  
  $\frac{6}{7}$ × 0

Worksheet

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Presentation

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Lesson Details

Key learning points

Use the language of unitising '__ groups of __ is equal to __'
The numerator of the fraction is multiplied by the whole number and the denominator remains the same.
If the product is an improper fraction you can convert it to a mixed number.

Common misconception

Multiplying a fraction by a larger whole number means the product will be larger.

In these examples, encourage children to see the whole number as a multiplier. Relate this back to representations where the fraction is shown to represent an area or a quantity. This should help to identify the fraction's magnitude when reasoning.

Keywords

Numerator - A numerator is the top number in a fraction. It shows how many parts we have.
Denominator - A denominator is the bottom number in a fraction. It shows how many parts a whole has been divided into.
Proper fraction - A proper fraction is a fraction where the numerator is less than the denominator.
Improper fraction - An improper fraction is a fraction where the numerator is greater than the denominator.