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Year 5

Solve problems involving multiplying proper fractions by whole numbers

I can solve problems involving multiplying proper fractions by whole numbers.

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New
New
Year 5

Solve problems involving multiplying proper fractions by whole numbers

I can solve problems involving multiplying proper fractions by whole numbers.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Use the language of unitising '__ groups of __ is equal to __'
  2. The numerator of the fraction is multiplied by the whole number and the denominator remains the same.
  3. If the product is an improper fraction you can convert it to a mixed number.

Common misconception

Multiplying a fraction by a larger whole number means the product will be larger.

In these examples, encourage children to see the whole number as a multiplier. Relate this back to representations where the fraction is shown to represent an area or a quantity. This should help to identify the fraction's magnitude when reasoning.

Keywords

  • Numerator - A numerator is the top number in a fraction. It shows how many parts we have.

  • Denominator - A denominator is the bottom number in a fraction. It shows how many parts a whole has been divided into.

  • Proper fraction - A proper fraction is a fraction where the numerator is less than the denominator.

  • Improper fraction - An improper fraction is a fraction where the numerator is greater than the denominator.

Encourage children to reason about the size of expressions through comparing what the size of the numerator is in comparison to the denominator. Pupils should be able to compare expressions without having to convert to a mixed number in cases where fractions are greater or smaller than a whole.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Tick the fraction that is shaded in the image.
An image in a quiz
$$ \frac{2}{5} $$
Correct answer: $$ \frac{3}{5} $$
$$ \frac{5}{3} $$
$$ \frac{5}{2} $$
Q2.
Tick the correct symbol to compare these two expressions.
An image in a quiz
<
Correct answer: >
=
Q3.
Tick the correct symbol to compare these two expressions.
An image in a quiz
<
>
Correct answer: =
Q4.
Tick the correct products for this equation. 2 × $$ \frac{6}{8} $$ =
$$ \frac{26}{16} $$
$$ \frac{26}{8} $$
Correct answer: $$ \frac{12}{8} $$
$$ 1\frac{2}{8} $$
Correct answer: $$ 1\frac{4}{8} $$
Q5.
Tick the correct products for this equation. $$ \frac{3}{5} $$ × 4 =
Correct answer: $$ \frac{12}{5} $$
$$ \frac{43}{5} $$
$$ \frac{12}{20} $$
Correct answer: $$ 2\frac{2}{5} $$
$$ 1\frac{2}{5} $$
Q6.
Tick the correct set of symbols to compare the expressions.
An image in a quiz
< <
Correct answer: > >
< >
> <
= =

Exit quiz

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6 Questions

Q1.
Write the answer to the following equation. 2 × $$ \frac{3}{6} $$ =
Correct Answer: 1, one, one whole
Q2.
Tick expressions where the product would be greater than one whole.
$$ \frac{2}{7} $$ × 3
Correct answer: $$ \frac{4}{6} $$ × 2
Correct answer: $$ \frac{5}{9} $$ × 3
$$ \frac{1}{8} $$ × 8
Correct answer: $$ \frac{3}{5} $$ × 2
Q3.
Tick expressions where the product would be less than one whole.
Correct answer: $$ \frac{1}{8} $$ × 3
Correct answer: $$ \frac{4}{9} $$ × 2
$$ \frac{2}{9} $$ × 5
$$ \frac{3}{6} $$ × 2
$$ \frac{2}{10} $$ × 5
Q4.
Tick the correct symbol to compare these two expressions.
An image in a quiz
Correct answer: <
>
=
Q5.
Tick the correct symbol to compare these two expressions.
An image in a quiz
Correct answer: <
>
=
Q6.
Order the expressions from largest to smallest.
1 - $$ \frac{3}{7} $$ × 4
2 - $$ \frac{2}{7} $$ × 4
3 - $$ \frac{3}{7} $$ × 2
4 - $$ \frac{1}{7} $$ × 1
5 - $$ \frac{6}{7} $$ × 0