Explain how dividing by a whole number relates to multiplying by a unit fraction | Maths

Starter quiz

When you multiply a unit fraction by a whole number, the product will always be __________ than the whole number.
- larger
- smaller ✓
- equal to
Tick the operation that can replace ‘of’ in a calculation.
- −
- × ✓
- +
- ÷
20 = 4 × ______
- '5' ✓
Tick the representation that matches the equation: $\frac{1}{3}$ × b = g
Tick the equations that match this bar model.
- 3 × 5 = 15 ✓
- 5 ÷ 15 = 3
- 5 × 3 = 15 ✓
- 15 ÷ 3 = 5 ✓
- 3 ÷ 5 = 15
Write in the correct symbol to compare these two expressions (< > =).
- '<' ✓

Exit quiz

What is the value of each part?
- '4' ✓
The result of both of these equations will give us a __________ number than what we started with.
- smaller ✓
- larger
Tick the expressions that represent the bar model.
- 30 ÷ 5 ✓
- 5 ÷ 30
- 30 × $\frac{1}{5}$ ✓
- $\frac{1}{5}$ × 30 ✓
True or false? $\frac{1}{4}$ × 20 = 20 ÷ 4
- True ✓
- False
Fill in the missing number. $\frac{1}{6}$ × 18 = 18 ÷ ______
- '6' ✓
Solve the equation: 100 × $\frac{1}{5}$ = ______
- '20' ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

Multiplying a number by a unit fraction is equivalent to dividing the number by the denominator of the fraction.
The whole has been divided into 4 equal parts describes dividing into 4 quarters.
The whole has been divided into 4 equal parts describes dividing by 4 (sharing).

Common misconception

Pupils struggle to identify how each of the expressions relate to each other.

Ensure connections are made between the bar models, your language and the expressions. Give particular attention to how the fraction links to how the bar model can be drawn, particularly when dividing the bar model into ___ parts.

Keywords

Expression - An expression contains one or more values, where each value is separated by an operator.
Equation - An equation is used to show that one number, calculation or expression is equal to another.
Denominator - The denominator is the bottom number in a fraction.