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Explain how to divide a non-unit fraction by a whole number

I can explain how to divide a non-unit fraction by a whole number.

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Year 6

Explain how to divide a non-unit fraction by a whole number

I can explain how to divide a non-unit fraction by a whole number.

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Lesson details

Key learning points

Dividing a non-unit fraction by a whole number can be re-written as multiplying by a unit fraction.
To divide a non-unit fraction by a whole number, you notice the denominator has been multiplied by the whole number.

Keywords

Represent - To represent something means to show something in a different way.

Common misconception

Pupils think the product is only the fraction of the shaded part and not the fraction of the original whole.

Ensure precision in wording when clarifying what the question is asking of each pupil. It is important they recognise how the shaded parts relates back to the original whole each time.

This lesson extends on dividing a unit fraction by a whole number to dividing a non-unit fraction by a whole number. Identifying where the non-unit fraction is within each model is vital. Ensure time is spent creating and exploring area models that represent this.

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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
Tick the equivalent division equation for $$ {1} \over {4}$$ × $$ {1} \over {3}$$ = $$ {1} \over {12}$$

Correct answer: $$ {1} \over {4}$$ ÷ 3 = $$ {1} \over {12}$$

$$ {1} \over {4}$$ ÷ 4 = $$ {1} \over {12}$$

$$ {1} \over {3}$$ ÷ 3 = $$ {1} \over {12}$$

$$ {1} \over {12}$$ ÷ $$ {1} \over {4}$$ = $$ {1} \over {3}$$

Q2.
Use this equation to find the missing denominator:

Correct Answer: 3

Q3.
Tick the correct answer to the calculation $$ {1} \over {3}$$ ÷ 6 =

Correct answer: $$ {1} \over {18}$$

$$ {1} \over {9}$$

$$ {6} \over {3}$$

Q4.
Write down the missing denominator.

Correct Answer: 32

Q5.
Tick the equivalent multiplication expression for $$ {1} \over {9}$$ ÷ 2

$$ {1} \over {9}$$ × 2

2 × $$ {1} \over {9}$$

Correct answer: $$ {1} \over {9}$$ × $$ {1} \over {2}$$

9 × 2

Q6.
Tick the possible pairs of numbers that would make this equation correct:

2 and 3

3 and 4

Correct answer: 4 and 4

2 and 6

Correct answer: 8 and 2

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
Tick the equivalent multiplication expressions for $$ {1} \over {4}$$ ÷ 2

Correct answer: $$ {1} \over {4}$$ × $$ {1} \over {2}$$

2 × $$ {1} \over {4}$$

Correct answer: $$ {1} \over {2}$$ × $$ {1} \over {4}$$

4 × 2

Q2.
Tick the equivalent multiplication expression for $$ {3} \over {4}$$ ÷ 2

Correct answer: $$ {3} \over {4}$$ × $$ {1} \over {2}$$

2 × $$ {3} \over {4}$$

$$ {3} \over {4}$$ × 2

34 × 2

Q3.
Tick the missing number $$ {4} \over {5}$$ × $$ {1} \over {3}$$ = $$ {4} \over {5}$$ ÷ ___

$$ {1} \over {3}$$

Correct answer: 3

Q4.
What is the result of $$ {2} \over {6}$$ ÷ 3?

$$ {2} \over {3}$$

$$ {2} \over {9}$$

Correct answer: $$ {2} \over {18}$$

$$ {6} \over {6}$$

Q5.
What is the missing divisor?

Correct Answer: 6

Q6.
Tick the possible answers. Jun walks for three-quarters of a mile. He listens to music for one-third of his walk. What fraction of a mile does Jun listen to music for?

$$ {3} \over {9}$$

Correct answer: $$ {3} \over {12}$$

$$ {1} \over {12}$$

Correct answer: $$ {1} \over {4}$$

$$ {3} \over {4}$$

Lesson appears in

UnitMaths / Multiplication and division of fractions

Maths

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Explain how to divide a non-unit fraction by a whole number

Explain how to divide a non-unit fraction by a whole number

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Tick the equivalent division equation for $$ {1} \over {4}$$ × $$ {1} \over {3}$$ = $$ {1} \over {12}$$

Q2.Use this equation to find the missing denominator:

Q3.Tick the correct answer to the calculation $$ {1} \over {3}$$ ÷ 6 =

Q4.Write down the missing denominator.

Q5.Tick the equivalent multiplication expression for $$ {1} \over {9}$$ ÷ 2

Q6.Tick the possible pairs of numbers that would make this equation correct:

Assessment exit quiz

6 Questions

Q1.Tick the equivalent multiplication expressions for $$ {1} \over {4}$$ ÷ 2

Q2.Tick the equivalent multiplication expression for $$ {3} \over {4}$$ ÷ 2

Q3.Tick the missing number $$ {4} \over {5}$$ × $$ {1} \over {3}$$ = $$ {4} \over {5}$$ ÷ ___

Q4.What is the result of $$ {2} \over {6}$$ ÷ 3?

Q5.What is the missing divisor?

Q6.Tick the possible answers. Jun walks for three-quarters of a mile. He listens to music for one-third of his walk. What fraction of a mile does Jun listen to music for?

Lesson appears in

UnitMaths / Multiplication and division of fractions

Maths

Q1.
Tick the equivalent division equation for $$ {1} \over {4}$$ × $$ {1} \over {3}$$ = $$ {1} \over {12}$$

Q2.
Use this equation to find the missing denominator:

Q3.
Tick the correct answer to the calculation $$ {1} \over {3}$$ ÷ 6 =

Q4.
Write down the missing denominator.

Q5.
Tick the equivalent multiplication expression for $$ {1} \over {9}$$ ÷ 2

Q6.
Tick the possible pairs of numbers that would make this equation correct:

Q1.
Tick the equivalent multiplication expressions for $$ {1} \over {4}$$ ÷ 2

Q2.
Tick the equivalent multiplication expression for $$ {3} \over {4}$$ ÷ 2

Q3.
Tick the missing number $$ {4} \over {5}$$ × $$ {1} \over {3}$$ = $$ {4} \over {5}$$ ÷ ___

Q4.
What is the result of $$ {2} \over {6}$$ ÷ 3?

Q5.
What is the missing divisor?

Q6.
Tick the possible answers. Jun walks for three-quarters of a mile. He listens to music for one-third of his walk. What fraction of a mile does Jun listen to music for?