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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Video

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.