Multiply a proper fraction by a whole number where the product is greater than a whole | Maths

Starter quiz

Tick the non-unit fractions.
- $\frac{3}{10}$ ✓
- $\frac{5}{6}$ ✓
- $\frac{1}{9}$
- $\frac{2}{7}$ ✓
$What fraction of this shape is not shaded.$

What fraction of this shape is not shaded.
- $\frac{3}{3}$
- $\frac{1}{3}$
- $\frac{3}{4}$ ✓
- $\frac{1}{4}$
Which expressions are represented by the number line.
- $\frac{2}{7}$ × 6
- $\frac{2}{7}$ × 3 ✓
- $\frac{2}{7}$ + $\frac{2}{7}$ + $\frac{2}{7}$ ✓
- $\frac{3}{7}$ × 2
Which equation represents this image?
- $\frac{2}{9}$ × 4 = $\frac{8}{18}$
- $\frac{2}{9}$ × 4 = $\frac{8}{9}$ ✓
- $\frac{9}{2}$ × 4 = $\frac{36}{2}$
- 4 × $\frac{2}{9}$ = $\frac{8}{9}$ ✓
- $\frac{2}{9}$ = 4 × $\frac{8}{9}$
Match the equation to the correct product.
- $\frac{1}{4}$ × 3 =
  
  ⇔
  
  $\frac{3}{4}$ ✓
- $\frac{1}{6}$ × 2 =
  
  ⇔
  
  $\frac{2}{6}$ ✓
- $\frac{1}{6}$ × 4 =
  
  ⇔
  
  $\frac{4}{6}$ ✓
- $\frac{1}{4}$ × 2 =
  
  ⇔
  
  $\frac{2}{4}$ ✓
Order the expressions from largest to smallest.
- 1
  
  ⇔
  
  $\frac{2}{9}$ × 4
- 2
  
  ⇔
  
  $\frac{2}{9}$ × 2
- 3
  
  ⇔
  
  $\frac{3}{9}$ × 1
- 4
  
  ⇔
  
  $\frac{1}{9}$ × 2
- 5
  
  ⇔
  
  $\frac{5}{9}$ × 0

Exit quiz

$Tick the fraction represented by the image.$

Tick the fraction represented by the image.
- $\frac{6}{8}$ ✓
- $\frac{6}{9}$
- $\frac{7}{8}$
- $\frac{8}{6}$
Which image matches the expression $\frac{2}{3}$ × 3?
Which equation represents this image?
- $\frac{5}{7}$ × 3 = $\frac{15}{21}$
- $\frac{5}{7}$ × 3 = $\frac{15}{7}$ ✓
- $\frac{5}{7}$ × 3 = $\frac{7}{15}$
- 3 × $\frac{5}{7}$ = $\frac{15}{21}$
- 3 × $\frac{5}{7}$ = $\frac{15}{7}$ ✓
Tick the correct products for this equation. 4 × $\frac{2}{10}$ =
- $\frac{8}{10}$ ✓
- $\frac{42}{10}$
- $\frac{6}{10}$
- $\frac{8}{40}$
- $\frac{6}{14}$
Tick the correct products for this equation. 3 × $\frac{3}{5}$ =
- $\frac{33}{5}$
- $\frac{9}{5}$ ✓
- $1\frac{4}{5}$ ✓
- $\frac{6}{5}$
- $1\frac{9}{5}$
Which expression would be equal to this product? $\frac{24}{6}$
- $\frac{6}{6}$ × 4 ✓
- $\frac{3}{6}$ × 12
- $\frac{4}{6}$ × 6 ✓
- $\frac{1}{6}$ × 24 ✓
- $1\frac{8}{3}$ × 6

Worksheet

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Presentation

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Lesson Details

Key learning points

If 3 groups of 4 are equal to 12 then 3 groups of 4 fifths are equal to 12 fifths.
If the product is an improper fraction you can convert it to a mixed number.
The numerator of the fraction is multiplied by the whole number and the denominator remains the same.

Common misconception

Pupils resort to a procedure with little understanding for how we convert between improper fractions and mixed numbers.

Encourage pupils to make connections between improper fractions and mixed numbers using both area models and number lines. Focus on reasoning by manipulating parts to complete wholes and where the wholes and parts are represented on the number line.

Keywords

Represent - To represent something is to show it in a different way.
Unitise - Unitising means treating groups that contain or represent the same number of things as units or ones.
Mixed number - A number which combines both a whole number and a fraction.
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.