Explain how to compare pairs of non-related fractions by comparing to a half | Maths

Starter quiz

Double 16 is equal to ______

'32' ✓
Tick the largest fraction.

${3} \over {7}$ ✓

${3} \over {8}$

${3} \over {9}$

${3} \over {10}$
Half of 500 is ______

'250' ✓
Tick the fractions that represent one half.

${1} \over {2}$ ✓

${2} \over {4}$ ✓

${4} \over {6}$

${4} \over {8}$ ✓

${10} \over {15}$
Use the correct symbol to compare: ${3} \over {6}$ ___ ${4} \over {12}$

<

> ✓

=
Use the correct symbol to compare: ${2} \over {6}$ ___ ${3} \over {9}$

<

>

= ✓

Exit quiz

What is the relationship between the numerator and the denominator of a fraction that is equivalent to one half?

The numerator is double the size of the denominator.

The denominator is half the size of the numerator.

The denominator is double the size of the numerator. ✓

The denominator is two times the size of the numerator. ✓
Tick the fractions that represent one half.

${4} \over {7}$

${5} \over {10}$ ✓

${10} \over {20}$ ✓

${20} \over {10}$

${1} \over {5}$
Tick the fractions greater than one half.

${3} \over {12}$

${2} \over {4}$

${4} \over {7}$ ✓

${5} \over {9}$ ✓

${2} \over {3}$ ✓
Tick the fractions less than one half.

${1} \over {3}$ ✓

${2} \over {8}$ ✓

${5} \over {6}$

${4} \over {8}$

${4} \over {7}$
Order the fractions from largest to smallest.

1

⇔

${3} \over {10}$

2

⇔

${1} \over {2}$

3

⇔

${4} \over {7}$
$Tick the fractions that would fit in the equation.$

Tick the fractions that would fit in the equation.

${3} \over {6}$ ✓

${1} \over {10}$

${6} \over {12}$ ✓

${15} \over {16}$

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

In fractions equivalent to a half, the numerator is half the value of the denominator.
When the numerator is more than half the value of the denominator, the fraction is greater than a half.
When the numerator is less than half the value of the denominator, the fraction is less than a half.

Common misconception

Pupils struggle to compare fractions to a half as they mainly consider it in its simplest form.

Encourage pupils to visualise their fractions on a number line. Also spend time thinking about the relationship between the numerator and the denominator in fractions equivalent to one-half and use this generalisation to help moving forward.

Keywords

Proper fraction - A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number).
Order - To order things means to put things into their correct place following a set rule.