Explain the relationship between numerators and denominators across equivalent fractions | Maths

Starter quiz

$What is the missing numerator in this pair of equivalent fractions?$

What is the missing numerator in this pair of equivalent fractions?

'6' ✓
$What is the missing denominator in this pair of equivalent fractions?$

What is the missing denominator in this pair of equivalent fractions?

'25' ✓
$What is the missing numerator in this pair of equivalent fractions?$

What is the missing numerator in this pair of equivalent fractions?

'1' ✓
$The same number is the missing denominator in one fraction and the numerator in the other fraction. What is the missing number?$

The same number is the missing denominator in one fraction and the numerator in the other fraction. What is the missing number?

'10' ✓
Match the pairs of equivalent fractions.

${2}\over{4}$

⇔

${1}\over{2}$ ✓

${2}\over{8}$

⇔

${1}\over{4}$ ✓

${2}\over{6}$

⇔

${1}\over{3}$ ✓

${2}\over{10}$

⇔

${1}\over{5}$ ✓
Which of these statements are correct?

${2}\over{5}$ < ${3}\over{10}$

${1}\over{5}$ < ${3}\over{10}$ ✓

${2}\over{5}$ < ${4}\over{10}$

${2}\over{5}$ > ${2}\over{10}$ ✓

Exit quiz

Which of the statements describe equivalent fractions? Equivalent fractions ...

... have the same numerator and denominator.

... have the same value and position on a number line. ✓

... represent the same proportion of a whole. ✓

... may look different when they are written down. ✓

... and double or half the size of each other.
What relationship is shown by the arrows in the image?

The denominator is 1 more than the numerator.

The denominator is 2 times the value of the numerator. ✓

1 out of 2 is the same proportion of the whole as 3 out of 6 ✓

The numerator is half the value of the denominator. ✓
$Which other fractions would be equivalent to the ones in the image?$

Which other fractions would be equivalent to the ones in the image?

${1}\over{3}$

${2}\over{4}$ ✓

${2}\over{5}$

${4}\over{8}$ ✓
What is the relationship shown by the arrows in this image?

The fractions are getting bigger.

The numerator and denominator have been scaled by the same factor. ✓
What factor is missing from these arrows? × ______

'3' ✓
$What is the missing numerator in this pair of equivalent fractions? The missing numerator is <span class="blank">______</span>$

What is the missing numerator in this pair of equivalent fractions? The missing numerator is ______

'49' ✓

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Lesson Details

Key learning points

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.
If you multiply the numerator and denominator by the same factor, the fractions will be equivalent.

Common misconception

Pupils may not see the relationship between the numerator and denominator in a fraction as an indication of equivalence. They may only see that they can keep doubling the numerator and denominator.

When working with unit fractions, ensure that pupils explain that the denominator is always e.g. 3 times the value of the numerator when fractions are equivalent to e.g. one third. This will focus them on the equivalence and that key relationship.

Keywords

Numerator - The numerator is the top number in a fraction and shows how many parts we have.
Denominator - The denominator is the bottom number in a fraction and shows how many equal parts the whole has been divided into.
Equivalent fraction - Equivalent fractions are fractions which have the same value, even though they may look different.
Scale/scaling - Scaling is when a quantity is made ___ times the size.