Explain the relationship within families of equivalent fractions | Maths

Starter quiz

$Which two equivalent fractions could label point a on the number line?$

Which two equivalent fractions could label point a on the number line?

${1}\over{6}$ and ${3}\over{11}$

${1}\over{5}$ and ${2}\over{10}$ ✓

${2}\over{5}$ and ${3}\over{10}$
Which fractions in the list are equivalent to ${1}\over{2}$ ?

${2}\over{3}$

${2}\over{4}$ ✓

${2}\over{5}$

${3}\over{5}$

${3}\over{6}$ ✓
Match the pairs of equivalent fractions.

${1}\over{3}$

⇔

${3}\over{9}$ ✓

${2}\over{3}$

⇔

${4}\over{6}$ ✓

${2}\over{5}$

⇔

${4}\over{10}$ ✓

${2}\over{4}$

⇔

${3}\over{6}$ ✓
$What is the missing scale factor used to create this pair of equivalent fractions?$

What is the missing scale factor used to create this pair of equivalent fractions?

'7' ✓
$What is the missing denominator in this pair of equivalent fractions?$

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

'12' ✓
$What is the missing numerator in this pair of equivalent fractions?$

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

'18' ✓

Exit quiz

$Which fractions can describe the shaded area of this shape?$

Which fractions can describe the shaded area of this shape?

${4}\over{5}$

${6}\over{7}$

${6}\over{8}$ ✓

${9}\over{12}$ ✓

${2}\over{4}$
$Which fractions can be used to label point a on the number line?$

Which fractions can be used to label point a on the number line?

${4}\over{10}$ ✓

${5}\over{11}$

${2}\over{5}$ ✓

${3}\over{6}$
$Which other fractions could be used to label point a on the number line.$

Which other fractions could be used to label point a on the number line.

${6}\over{15}$ ✓

${3}\over{6}$

${4}\over{10}$ ✓

${5}\over{11}$

${10}\over{25}$ ✓
Which fraction is equivalent to ${4}\over{5}$ ?

${5}\over{6}$

${8}\over{9}$

${8}\over{10}$ ✓

${2}\over{3}$
Which fractions are less than ${4}\over{5}$ ?

${6}\over{10}$ ✓

${7}\over{10}$ ✓

${8}\over{10}$

${9}\over{10}$
Which fractions are greater than ${3}\over{5}$ ?

${5}\over{10}$

${6}\over{10}$

${7}\over{10}$ ✓

${8}\over{10}$ ✓

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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

That equivalent fractions do not have the same value. Pupils can create them but do not always understand that they are equal in value.

Explore representations which show the same whole divided in different ways to show the same proportion of the whole. Represent equivalent fractions at the same point on a number line.

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 up and down - Scaling is when a quantity is made a number of times the size. To scale up is to multiply by a factor. To scale down is to multiply by a fraction or to divide.