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.

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.

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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.

### 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.

### 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.

### 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).

## Starter quiz

### 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.
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
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.
<
=
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

## Exit quiz

### 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
14
Q3.
Estimate the value of this expression. Give your estimate as a whole number. $$2\frac{1}{8}$$ × 3
Q4.
Give the missing numerator.
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