Use the relationship between the numerator and denominator to simplify fractions | Maths

Starter quiz

Which of the numbers are factors of 8?

1 ✓

2 ✓

4 ✓

6

8 ✓
1, 2, 3, 4, 6 and 12 are all factors of which number in this list?

6

10

12 ✓

16
Which number would be a factor of both 9 and 12?

2

3 ✓

4

6
What number do you get if 6 is scaled up by a factor of 3? ______

'18' ✓
What number do you get if 18 is scaled down by a factor of 2? ______

'9' ✓
Which of these expressions have the same value?

12 ÷ 3 ✓

20 ÷ 4

12 ÷ 4

20 ÷ 5 ✓

100 ÷ 25 ✓

Exit quiz

What is the highest factor which is common to the numerator and denominator in the fraction ${6}\over{12}$

'6' ✓
Is the fraction ${3}\over{6}$ written in its simplest form?

Yes because the numerator and denominator are both one digit numbers

No because the numerator and denominator both share a factor greater than 1 ✓
What is ${3}\over{6}$ written in its simplest form?

${1}\over{6}$

${1}\over{3}$

${1}\over{2}$ ✓

${6}\over{12}$
Is Jun's statement always, sometimes or never true?

Always

Sometimes ✓

Never
Which of these fractions are in their simplest form?

${6}\over{9}$

${6}\over{13}$ ✓

${1}\over{6}$ ✓

${6}\over{14}$

${7}\over{12}$ ✓
Match the fractions to the equivalent in its simplest form.

${6}\over{9}$

⇔

${2}\over{3}$ ✓

${6}\over{14}$

⇔

${3}\over{7}$ ✓

${7}\over{14}$

⇔

${1}\over{2}$ ✓

${9}\over{12}$

⇔

${3}\over{4}$ ✓

${12}\over{15}$

⇔

${4}\over{5}$ ✓

Worksheet

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Presentation

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Video

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 has been simplified, the numerator and denominator are as small as they can be to keep the relationship.
Create an equivalent fraction in a simpler form with lower values of the numerator and denominator.
Use common factors of the numerator and denominator to simplify fractions.

Common misconception

Pupils may not see that the fraction and its simplified version are equivalent. Pupils may not have a deep understanding of how factors relate to fractions.

Stress the equivalence of fractions when simplifying and make use of representations to show that fractions are equivalent using parts of a whole and position on a number line. Discuss the language of factors, common factors and prime numbers.

Keywords

Common factor - When you are comparing the factors of two numbers, a common factor is one shared by both numbers.
Simplest form - When a fraction is in its simplest form, the numerator and denominator only share a common factor of one.
Simplify - To simplify a fraction is to identify the highest common factor shared by the numerator and denominator and to scale down both by that factor.
Scale up/down - To scale up or down is to multiply or divide by a given number or factor.