Use the relationship between the numerator and denominator in equivalent fractions to solve problems | Maths

Starter quiz

Order these fractions from the smallest to the largest
- 1
  
  ⇔
  
  ${1}\over{7}$
- 2
  
  ⇔
  
  ${2}\over{7}$
- 3
  
  ⇔
  
  ${3}\over{7}$
- 4
  
  ⇔
  
  ${4}\over{7}$
- 5
  
  ⇔
  
  ${5}\over{7}$
Order these fractions from the largest to the smallest
- 1
  
  ⇔
  
  ${3}\over{4}$
- 2
  
  ⇔
  
  ${3}\over{5}$
- 3
  
  ⇔
  
  ${3}\over{6}$
- 4
  
  ⇔
  
  ${3}\over{7}$
- 5
  
  ⇔
  
  ${3}\over{8}$
Match the statements to make the sentences correct.
- 1 is the same proportion of 2 as
  
  ⇔
  
  4 is of 8 ✓
- 3 is the same proportion of 9 as
  
  ⇔
  
  1 is of 3 ✓
- 1 is the same proportion of 4 as
  
  ⇔
  
  3 is of 12 ✓
- 2 is the same proportion of 5 as
  
  ⇔
  
  4 is of 10 ✓
Which fractions are equivalent to ${1}\over{7}$ ?
- ${2}\over{14}$ ✓
- ${4}\over{10}$
- ${2}\over{8}$
- ${11}\over{77}$ ✓
Which of these fractions are less than ${1}\over{2}$ ?
- ${2}\over{3}$
- ${2}\over{4}$ ✓
- ${3}\over{4}$
- ${3}\over{6}$ ✓
Which fractions are greater than ${1}\over{3}$ ?
- ${2}\over{8}$
- ${2}\over{4}$ ✓
- ${2}\over{5}$ ✓
- ${2}\over{7}$

Exit quiz

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

What is the missing denominator in this pair of equivalent fractions?
- '30' ✓
$What is the missing numerator in this pair of equivalent fractions?$

What is the missing numerator in this pair of equivalent fractions?
- '5' ✓
$What is the missing numerator in this pair of equivalent fractions?$

What is the missing numerator in this pair of equivalent fractions?
- '1' ✓
$The same number is the missing numerator in one fraction and the denominator in the other fraction. What is the missing number?$

The same number is the missing numerator in one fraction and the denominator in the other fraction. What is the missing number?
- '8' ✓
Match the pairs of equivalent fractions.
- ${1}\over {7}$
  
  ⇔
  
  ${4}\over {28}$ ✓
- ${1}\over {10}$
  
  ⇔
  
  ${4}\over {40}$ ✓
- ${4}\over {8}$
  
  ⇔
  
  ${40}\over {80}$ ✓
- ${2}\over {6}$
  
  ⇔
  
  ${4}\over {12}$ ✓
Which of these statements are correct?
- ${2}\over{12}$ > ${1}\over{6}$
- ${6}\over{24}$ < ${1}\over{2}$ ✓
- ${4}\over{12}$ = ${8}\over{16}$
- ${4}\over{12}$ = ${8}\over{24}$ ✓

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
If a fraction is equivalent to a half, the numerator will be half the value of the denominator
If a fraction is equivalent to fifth, the denominator will be 5 times the value of the numerator

Common misconception

Children need to understand that equivalent fractions must be part of the same whole and that they can be represented as parts of a whole or as a number with a unique position on the number line.

Use the stem sentences to draw attention to how we describe equivalence and use representations to support this. Be clear about when the representation is showing a part of a whole and when it is labelling a 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.
Proportion - The proportion of a number, shape or group of objects is a part of the whole.