Explain how to divide a fraction by a whole number efficiently | Maths

Starter quiz

Tick the equivalent multiplication expression for ${1} \over {8}$ ÷ 2
- 2 × ${1} \over {8}$
- ${1} \over {8}$ × ${1} \over {2}$ ✓
- ${1} \over {2}$ × ${1} \over {8}$ ✓
- 8 × 2
Tick the equivalent multiplication expression for ${4} \over {5}$ ÷ 5
- 5 × ${4} \over {5}$
- ${4} \over {5}$ × ${1} \over {5}$ ✓
- ${1} \over {5}$ × 4
- ${4} \over {5}$ × 5
Tick the missing number.
- ${1} \over {3}$
- 3 ✓
- 4
- 31
What is the result of ${4} \over {6}$ ÷ 2 =
- ${8} \over {6}$
- ${4} \over {12}$ ✓
- ${2} \over {6}$
- ${1} \over {6}$
Write the divisor.
- '3' ✓
Write the divisor.
- '1' ✓

Exit quiz

Tick the calculations that are best solved using multiplication.
- ${1} \over {7}$ ÷ 2 = ✓
- ${2} \over {7}$ ÷ 2 =
- ${3} \over {7}$ ÷ 2 = ✓
- ${4} \over {7}$ ÷ 2 =
- ${6} \over {7}$ ÷ 2 =
Tick the calculations that are best solved using division.
- ${3} \over {5}$ ÷ 2 =
- ${4} \over {5}$ ÷ 2 = ✓
- ${5} \over {5}$ ÷ 2 =
- ${6} \over {5}$ ÷ 2 = ✓
- ${7} \over {5}$ ÷ 2 =
Tick the possible solutions for: ${6} \over {10}$ ÷ 3 = ___
- ${3} \over {10}$
- ${2} \over {10}$ ✓
- ${6} \over {30}$ ✓
- ${3} \over {6}$
Tick the possible solutions for: ${12} \over {15}$ ÷ 3 = ___
- ${4} \over {5}$
- ${4} \over {15}$ ✓
- ${12} \over {5}$
- ${12} \over {45}$ ✓
Tick the equations where the result would be a unit fraction.
- ${12} \over {12}$ ÷ 3 = ✓
- ${4} \over {15}$ ÷ 4 = ✓
- ${5} \over {15}$ ÷ 5 = ✓
- ${10} \over {15}$ ÷ 5 =
Tick the possible missing numbers.
- ${8} \over {24}$
- ${8} \over {12}$ ✓
- ${4} \over {6}$ ✓
- ${1} \over {3}$
- ${2} \over {6}$

Worksheet

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Presentation

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Lesson Details

Key learning points

When you divide a fraction by a whole number, you can calculate this efficiently.
When the numerator is a multiple of the divisor, you can unitise to make the calculation easier to manage.
When the numerator is not a multiple of the whole, you can convert the equation to to multiply by a unit fraction.
When you divide a non-unit fraction by a whole number, you notice the denominator is multiplied by the whole number.

Common misconception

Pupils automatically convert the division equation to multiply by a unit fraction regardless of the calculation.

Many calculations can be managed through developing a sense of fractions. Where pupils have a sense of fractional magnitude, it is often easier to solve these calculations mentally. Continue to encourage representing these equations using model.

Keywords

Divisor - The divisor is the number that we divide by. For example, in this equation, 3 is the divisor.