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

Starter quiz

Which expressions could represent one-third of one-fifth?

${1} \over {3}$ × ${1} \over {5}$ ✓

${1} \over {3}$ + ${1} \over {5}$

${1} \over {5}$ × ${1} \over {3}$ ✓

${1} \over {5}$ + ${1} \over {3}$
Tick the equations that could represent this image.

${1} \over {3}$ × ${1} \over {5}$ = ${1} \over {5}$

${1} \over {15}$ × ${1} \over {3}$ = ${1} \over {5}$

${1} \over {5}$ × ${1} \over {3}$ = ${1} \over {15}$ ✓

${1} \over {3}$ x ${1} \over {5}$ = ${1} \over {15}$ ✓
To find the product of two unit fractions, you can _________.

multiply the numerators

add the numerators

multiply the denominators ✓

add the denominators

multiply the numerators and the denominators
Tick the product of ${1} \over {8}$ × ${1} \over {2}$

${1} \over {16}$ ✓

${1} \over {10}$

${2} \over {10}$

${2} \over {16}$
What is the missing denominator which would make this equation correct?

'9' ✓
What could the missing digits be?

3 and 4

4 and 4 ✓

2 and 6

2 and 8 ✓

12 and 4

Exit quiz

Tick the equivalent division equation for ${1} \over {5}$ × ${1} \over {2}$ = ${1} \over {10}$

${1} \over {5}$ ÷ 2 = ${1} \over {10}$ ✓

${1} \over {2}$ ÷ 2 = ${1} \over {10}$

${1} \over {10}$ ÷ 2 = ${1} \over {5}$

${1} \over {10}$ ÷ 5 = ${1} \over {2}$
$Use this equation to find the missing denominator: <Math> {1} \over {2}</Math> ÷ 6 = <Math> {1} \over {12}</Math>$

Use this equation to find the missing denominator: ${1} \over {2}$ ÷ 6 = ${1} \over {12}$

'6' ✓
Tick the equivalent multiplication expression for ${1} \over {8}$ ÷ 4 =

${1} \over {8}$ × ${1} \over {4}$ ✓

${1} \over {8}$ × 4

8 × ${1} \over {4}$

8 × 4
Tick the correct answer to the calculation: ${1} \over {2}$ ÷ 7 =

${1} \over {7}$

${1} \over {14}$ ✓

14

${7} \over {2}$
Write down the missing denominator to make this equation correct.

'8' ✓
Tick the possible pairs of numbers that would make this equation correct:

2 and 3

3 and 4 ✓

4 and 2

2 and 6 ✓

8 and 4

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

The partitive structure means you can think of dividing a fraction by a whole number as sharing.
If a unit fraction is divided by a whole number the quotient is smaller than the dividend so the denominator increases.
Dividing a number by 2 is the same as finding half of the number and this can be applied to other fractions.

Common misconception

Pupils change the division symbol to a multiplication symbol and then multiply the fraction by a whole number.

The act of dividing the fraction part is highlighted within the representations provided. Ensure pupils are given time to explore how the area model represents the division and encourage pupils to create their own examples.

Keywords

Represent - To represent something means to show something in a different way.
Dividend - The dividend is what we are dividing.