Use understanding of equivalent fractions to solve problems | Maths

Starter quiz

What are the common factors of 12 and 20?

1 ✓

2 ✓

3

4 ✓

6
$Which number is the missing denominator in this pair of equivalent fractions?$

Which number is the missing denominator in this pair of equivalent fractions?

9

10

11

12 ✓

18
$Which number is the missing numerator in this pair of equivalent fractions?$

Which number is the missing numerator in this pair of equivalent fractions?

10

12

20

24 ✓

25
What is the highest factor which is common to the numerator and denominator in the fraction ${9}\over{15}$

'3' ✓
Is the fraction ${6}\over{9}$ written in its simplest form?

Yes because the denominator is an odd number and the numerator is even.

No because the numerator and denominator both share a factor greater than 1 ✓
What is ${6}\over{9}$ written in its simplest form?

${1}\over{6}$

${1}\over{3}$

${3}\over{6}$

${2}\over{3}$ ✓

Exit quiz

$What fraction of the shape is shaded?$

What fraction of the shape is shaded?

${4}\over{8}$

${8}\over{12}$ ✓

${8}\over{4}$

${2}\over{3}$ ✓
Which fraction is in its simplest form?

${7}\over{14}$

${7}\over{9}$ ✓

${7}\over{21}$

${7}\over{10}$ ✓
Match the fractions to their simplest form.

${7}\over{14}$

⇔

${1}\over{2}$ ✓

${6}\over{9}$

⇔

${2}\over{3}$ ✓

${9}\over{12}$

⇔

${3}\over{4}$ ✓

${12}\over{30}$

⇔

${2}\over{5}$ ✓
$Which numbers complete these equivalent fractions? Match the letter to the missing number.$

Which numbers complete these equivalent fractions? Match the letter to the missing number.

a

⇔

5 ✓

b

⇔

2 ✓

c

⇔

4 ✓
Order the fractions from the smallest to the largest

1

⇔

${3}\over{12}$

2

⇔

${1}\over{3}$

3

⇔

${3}\over{5}$

4

⇔

${3}\over{4}$
$Which number can be used to complete both fractions so that they are equivalent proper fractions?$

Which number can be used to complete both fractions so that they are equivalent proper fractions?

'8' ✓

Worksheet

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Lesson Details

Key learning points

If the multiplicative relationship between the numerator and denominator is the same, the fractions will be equivalent.
In equivalent fractions the numerators will share a common factor and the denominators will share a common factor.
In equivalent fractions, the numerators and denominators have been scaled up or down by the same factor.

Common misconception

Some pupils may still think that, because equivalent fractions look different, they do not have the same value.

Use representations such as bar models and shapes as well as number lines to ensure that this understanding is secured both in interpreting fractions as parts of a whole and as numbers with a fixed position on a number line.

Keywords

Equivalent fraction - Equivalent fractions are fractions which have the same value, even though they may look different. They describe the same part or proportion of the whole
Simplify - To simplify a fraction is to identify the highest common factor shared by the numerator and denominator and to scale down both by that factor.
Scale up/down - To scale up or down is to multiply or divide by a given number or factor.