Solve problems involving multiplication of mixed numbers by a whole number | Maths

Starter quiz

Tick the expressions.

3 × $\frac{1}{2}$ ✓

4 × $2\frac{3}{9}$ ✓

$\frac{7}{8}$ + 3 ✓

6 × $\frac{7}{8}$ = 1
Tick the correct expressions that represent the image.

3 × $\frac{3}{4}$ ✓

3 × $\frac{4}{3}$

4 × $\frac{3}{4}$

$\frac{3}{4}$ × 3 ✓
Tick the most appropriate estimation for 312 + 486

600

700

800 ✓

900
Tick expressions where the product would be less than one whole.

$\frac{5}{8}$ × 2

$\frac{2}{6}$ × 3

$\frac{1}{6}$ × 2 ✓

$\frac{3}{9}$ × 2 ✓

$\frac{2}{12}$ × 4 ✓
Tick the correct symbol to compare these two expressions.

<

> ✓

=
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

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

$2\frac{1}{4}$ × 1

$2\frac{1}{4}$ × 2 ✓

$2\frac{1}{4}$ × 3

$2\frac{1}{2}$ × 4
Tick the most appropriate estimates for $4\frac{1}{6}$ × 3

11

12 ✓

13 ✓

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

'6' ✓
Give the missing numerator.

'58' ✓
Tick the product of this equation. $5\frac{1}{3}$ × 2 = ___

$10\frac{2}{3}$ ✓

$\frac{32}{3}$ ✓

$\frac{10}{3}$

$10\frac{1}{3}$

$\frac{12}{3}$
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

Worksheet

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Presentation

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Lesson Details

Key learning points

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