New
New
Year 5

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

I can use the relationship between the numerator and denominator in equivalent fractions to solve problems

New
New
Year 5

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

I can use the relationship between the numerator and denominator in equivalent fractions to solve problems

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## Lesson details

### Key learning points

1. If the multiplicative relationship between the numerator and denominator is the same, the fractions will be equivalent
2. If a fraction is equivalent to a half, the numerator will be half the value of the denominator
3. 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.

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
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 - $${5}\over{7}$$
Q2.
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 - $${3}\over{8}$$
Q3.
Match the statements to make the sentences correct.
Correct Answer:1 is the same proportion of 2 as,4 is of 8

4 is of 8

Correct Answer:3 is the same proportion of 9 as,1 is of 3

1 is of 3

Correct Answer:1 is the same proportion of 4 as,3 is of 12

3 is of 12

Correct Answer:2 is the same proportion of 5 as,4 is of 10

4 is of 10

Q4.
Which fractions are equivalent to $${1}\over{7}$$?
Correct answer: $${2}\over{14}$$
$${4}\over{10}$$
$${2}\over{8}$$
Correct answer: $${11}\over{77}$$
Q5.
Which of these fractions are less than $${1}\over{2}$$?
$${2}\over{3}$$
Correct answer: $${2}\over{4}$$
$${3}\over{4}$$
Correct answer: $${3}\over{6}$$
Q6.
Which fractions are greater than $${1}\over{3}$$?
$${2}\over{8}$$
Correct answer: $${2}\over{4}$$
Correct answer: $${2}\over{5}$$
$${2}\over{7}$$

## Exit quiz

### 6 Questions

Q1.
What is the missing denominator in this pair of equivalent fractions?
Q2.
What is the missing numerator in this pair of equivalent fractions?
Q3.
What is the missing numerator in this pair of equivalent fractions?
Q4.
The same number is the missing numerator in one fraction and the denominator in the other fraction. What is the missing number?
Q5.
Match the pairs of equivalent fractions.
Correct Answer:$${1}\over {7}$$,$${4}\over {28}$$

$${4}\over {28}$$

Correct Answer:$${1}\over {10}$$,$${4}\over {40}$$

$${4}\over {40}$$

Correct Answer:$${4}\over {8}$$,$${40}\over {80}$$

$${40}\over {80}$$

Correct Answer:$${2}\over {6}$$,$${4}\over {12}$$

$${4}\over {12}$$

Q6.
Which of these statements are correct?
$${2}\over{12}$$ > $${1}\over{6}$$
Correct answer: $${6}\over{24}$$ < $${1}\over{2}$$
$${4}\over{12}$$ = $${8}\over{16}$$
Correct answer: $${4}\over{12}$$ = $${8}\over{24}$$