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Lesson 4 of 5
  • Year 5

Solve problems involving multiplication of mixed numbers by a whole number

I can solve problems by multiplying fractions (proper and improper) and mixed numbers by a whole number.

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View unit
Lesson 4 of 5
New
New
  • Year 5

Solve problems involving multiplication of mixed numbers by a whole number

I can solve problems by multiplying fractions (proper and improper) and mixed numbers by a whole number.

Download all

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Lesson details

Key learning points

  1. Partition the mixed number into a whole number and a fraction.
  2. Multiply the whole number part by the whole number factor.
  3. Multiply the fraction by the whole number using unitising language.
  4. Multiply the fraction by the whole number using unitising language.

Keywords

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

  • Estimate - We can estimate to find a value that is close enough to the right answer, usually with some thought or calculation involved.

  • Mixed number - A whole number and a fraction can be combined to form a mixed number.

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

Common misconception

Pupils may underestimate the product for example where the fractional part, when multiplied by an integer bridges over a whole.

Encourage pupils to look at the size of the fraction each time and ask whether it will bridge a whole or not and add that onto the estimate of the whole number multiplied by the integer.


To help you plan your year 5 maths lesson on: Solve problems involving multiplication of mixed numbers by a whole number, download all teaching resources for free and adapt to suit your pupils' needs...

Whilst leaving the product as an improper fraction may give the correct answer in an assessment situation, encourage pupils to reason about situations where leaving the product as a mixed number or improper fraction is most relevant. In the majority of cases, it is better to leave as a mixed number.
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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).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Tick the expressions.

Correct answer: 3 × $$ \frac{1}{2} $$
Correct answer: 4 × $$ 2\frac{3}{9} $$
Correct answer: $$ \frac{7}{8} $$ + 3
6 × $$ \frac{7}{8} $$ = 1

Q2.
Tick the correct expressions that represent the image.

An image in a quiz
Correct answer: 3 × $$ \frac{3}{4} $$
3 × $$ \frac{4}{3} $$
4 × $$ \frac{3}{4} $$
Correct answer: $$ \frac{3}{4} $$ × 3

Q3.
Tick the most appropriate estimation for 312 + 486

600
700
Correct answer: 800
900

Q4.
Tick expressions where the product would be less than one whole.

$$ \frac{5}{8} $$ × 2
$$ \frac{2}{6} $$ × 3
Correct answer: $$ \frac{1}{6} $$ × 2
Correct answer: $$ \frac{3}{9} $$ × 2
Correct answer: $$ \frac{2}{12} $$ × 4

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 - $$ \frac{2}{5} $$ × 4
2 - $$ \frac{3}{5} $$ × 2
3 - $$ \frac{1}{5} $$ × 5
4 - $$ \frac{4}{5} $$ × 1
5 - $$ \frac{5}{5} $$ × 0

Assessment exit quiz

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6 Questions

Q1.
Tick the expression that matches the problem. Izzy runs $$ 2\frac{1}{4} $$ kilometres on both Saturday and Sunday.

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

Q2.
Tick the most appropriate estimates for $$ 4\frac{1}{6} $$ × 3

11
Correct answer: 12
Correct answer: 13
14

Q3.
Estimate the value of this expression. Give your estimate as a whole number. $$ 2\frac{1}{8} $$ × 3

Correct Answer: 6, six

Q4.
Give the missing numerator.

An image in a quiz
Correct Answer: 58, fifty eight, fifty-eight

Q5.
Tick the product of this equation. $$ 5\frac{1}{3} $$ × 2 = ___

Correct answer: $$ 10\frac{2}{3} $$
Correct answer: $$ \frac{32}{3} $$
$$ \frac{10}{3} $$
$$ 10\frac{1}{3} $$
$$ \frac{12}{3} $$

Q6.
Order the expressions from largest to smallest.

1 - $$ 1\frac{4}{5} $$ × 6
2 - $$ 1\frac{1}{5} $$ × 5
3 - $$ 1\frac{2}{5} $$ × 4
4 - $$ 1\frac{3}{5} $$ × 3
5 - $$ 1\frac{1}{5} $$ × 2