Reason about how to write a fraction in its simplest form | Maths

Starter quiz

Write down a common factor of 4 and 20
- '4' ✓
Tick the highest common factor of 12 and 18
- 2
- 3
- 6 ✓
- 12
To find the simplest form of a fraction, we:
- divide the numerator and denominator by a common factor.
- make the numerator 1
- make the fraction as small as we can.
- divide the numerator and denominator by the highest common factor. ✓
Tick the fraction that is the simplest form of ${8} \over {16}$
- ${2} \over {8}$
- ${1} \over {8}$
- ${1} \over {16}$
- ${1} \over {2}$ ✓
Tick the fraction that is the simplest form of ${6} \over {8}$
- ${1} \over {8}$
- ${3} \over {4}$ ✓
- ${2} \over {4}$
- ${1} \over {6}$
If ${2} \over {3}$ is the simplest form of a fraction, tick the equivalent fractions.
- ${4} \over {6}$ ✓
- ${4} \over {12}$
- ${8} \over {12}$ ✓
- ${8} \over {9}$

Exit quiz

Tick the fraction that is the simplest form of ${15} \over {20}$
- ${1} \over {20}$
- ${5} \over {4}$
- ${3} \over {4}$ ✓
- ${1} \over {4}$
Match the equivalent fraction to its simplest form.
- ${1} \over {3}$
  
  ⇔
  
  ${3} \over {9}$ ✓
- ${1} \over {4}$
  
  ⇔
  
  ${2} \over {8}$ ✓
- ${1} \over {5}$
  
  ⇔
  
  ${3} \over {15}$ ✓
- ${1} \over {6}$
  
  ⇔
  
  ${5} \over {30}$ ✓
Tick the fractions in their simplest form.
- ${1} \over {3}$ ✓
- ${5} \over {5}$
- ${7} \over {8}$ ✓
- ${2} \over {12}$
- ${5} \over {25}$
Tick the correct symbol to compare these fractions. ${4} \over {12}$ ___ ${5} \over {15}$
- <
- >
- = ✓
Tick the correct symbol to compare these fractions. ${6} \over {15}$ ___ ${40} \over {100}$
- <
- >
- = ✓
Order the following fractions from largest to smallest
- 1
  
  ⇔
  
  ${6} \over {18}$
- 2
  
  ⇔
  
  ${8} \over {32}$
- 3
  
  ⇔
  
  ${9} \over {45}$
- 4
  
  ⇔
  
  ${7} \over {42}$

Worksheet

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Presentation

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Lesson Details

Key learning points

A common factor is a number which is a factor of both the numerator and denominator.
A fraction is in its simplest form when there is no common factor of the numerator and the denominator.

Common misconception

Pupils try to make a fraction in a simpler form by finding separate factors for the numerator and denominator to simplify.

Share examples for why this cannot be true with images to highlight the difference in the size of the fractions. Draw attention to the fact that it is both the numerator and denominator that needs to be scaled by a common factor.

Keywords

Common factor - When we compare lists of factors of two or more numbers, common factors are those shared by all the numbers.
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.
Equivalent - If two numbers or expressions have the same value, they are said to be equivalent.