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Year 5

Explain the relationship between numerators and denominators across equivalent fractions

I can explain the relationship across numerators and denominators in equivalent fractions.

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New
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Year 5

Explain the relationship between numerators and denominators across equivalent fractions

I can explain the relationship across numerators and denominators in equivalent fractions.

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Share activities with pupils
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Lesson details

Key learning points

  1. In equivalent fractions the numerators will share a common factor and the denominators will share a common factor.
  2. In equivalent fractions, the numerators and denominators have been scaled up or down by the same factor.
  3. If you multiply the numerator and denominator by the same factor, the fractions will be equivalent.

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.

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.

Make sure that the pupils do not just keep doubling the numerators and denominators to create equivalent fractions. By doing this, they miss out fractions with odd numerators and focus on the idea that they are multiplying and perhaps making the fraction bigger rather than maintaining equivalence.
Teacher tip

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).

Lesson video

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Starter quiz

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6 Questions

Q1.
What is the missing numerator in this pair of equivalent fractions?
An image in a quiz
Correct Answer: 6, six
Q2.
What is the missing denominator in this pair of equivalent fractions?
An image in a quiz
Correct Answer: 25, twenty-five
Q3.
What is the missing numerator in this pair of equivalent fractions?
An image in a quiz
Correct Answer: 1, one
Q4.
The same number is the missing denominator in one fraction and the numerator in the other fraction. What is the missing number?
An image in a quiz
Correct Answer: 10, ten
Q5.
Match the pairs of equivalent fractions.
Correct Answer:$${2}\over{4}$$,$${1}\over{2}$$

$${1}\over{2}$$

Correct Answer:$${2}\over{8}$$,$${1}\over{4}$$

$${1}\over{4}$$

Correct Answer:$${2}\over{6}$$,$${1}\over{3}$$

$${1}\over{3}$$

Correct Answer:$${2}\over{10}$$,$${1}\over{5}$$

$${1}\over{5}$$

Q6.
Which of these statements are correct?
$${2}\over{5}$$ < $${3}\over{10}$$
Correct answer: $${1}\over{5}$$ < $${3}\over{10}$$
$${2}\over{5}$$ < $${4}\over{10}$$
Correct answer: $${2}\over{5}$$ > $${2}\over{10}$$

Exit quiz

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6 Questions

Q1.
Which of the statements describe equivalent fractions? Equivalent fractions ...
... have the same numerator and denominator.
Correct answer: ... have the same value and position on a number line.
Correct answer: ... represent the same proportion of a whole.
Correct answer: ... may look different when they are written down.
... and double or half the size of each other.
Q2.
What relationship is shown by the arrows in the image?
An image in a quiz
The denominator is 1 more than the numerator.
Correct answer: The denominator is 2 times the value of the numerator.
Correct answer: 1 out of 2 is the same proportion of the whole as 3 out of 6
Correct answer: The numerator is half the value of the denominator.
Q3.
Which other fractions would be equivalent to the ones in the image?
An image in a quiz
$${1}\over{3}$$
Correct answer: $${2}\over{4}$$
$${2}\over{5}$$
Correct answer: $${4}\over{8}$$
Q4.
What is the relationship shown by the arrows in this image?
An image in a quiz
The fractions are getting bigger.
Correct answer: The numerator and denominator have been scaled by the same factor.
Q5.
What factor is missing from these arrows? ×
An image in a quiz
Correct Answer: 3, three
Q6.
What is the missing numerator in this pair of equivalent fractions? The missing numerator is
An image in a quiz
Correct Answer: 49, forty-nine