Use knowledge of adding and subtracting related unit fractions to solve problems | Maths

Starter quiz

Fractions have a common denominator when:
- one has a denominator that is a multiple of the other fraction’s denominator.
- they have the same number for the numerator.
- they have the same number for the denominator. ✓
- they have the same numerator and denominator.
$Type in the number to show how the numerator and denominator has been multiplied to create a related fraction.$

Type in the number to show how the numerator and denominator has been multiplied to create a related fraction.
- '4' ✓
$This image shows <Math> {1} \over {5}</Math> − <Math> {1} \over {10}</Math> = ____ Tick the equation which shows the appropriate related fraction.$

This image shows ${1} \over {5}$ − ${1} \over {10}$ = ____ Tick the equation which shows the appropriate related fraction.
- ${2} \over {10}$ − ${1} \over {10}$ = ____ ✓
- ${3} \over {15}$ − ${1} \over {10}$ = ____
- ${4} \over {20}$ − ${1} \over {10}$ = ____
- ${5} \over {25}$ − ${1} \over {10}$ = ____
Tick the correct equation once it has been adjusted to include the most appropriate related fraction. ${1} \over {3}$ − ${1} \over {15}$ = ___
- ${1} \over {15}$ − ${1} \over {15}$ = ___
- ${2} \over {15}$ − ${1} \over {15}$ = ___
- ${3} \over {15}$ − ${1} \over {15}$ = ___
- ${5} \over {15}$ − ${1} \over {15}$ = ___ ✓
Tick the correct solution: ${1} \over {9}$ − ${1} \over {18}$ = ___
- ${1} \over {9}$
- ${1} \over {2}$
- ${1} \over {18}$ ✓
- ${2} \over {18}$
Tick the correct solution: ${2} \over {3}$ − ${2} \over {15}$ = ___
- ${8} \over {15}$ ✓
- ${8} \over {3}$
- $2 {1} \over {3}$
- ${10} \over {3}$

Exit quiz

Match the fractions with common denominators.
- ${1} \over {4}$
  
  ⇔
  
  ${9} \over {4}$ ✓
- ${1} \over {12}$
  
  ⇔
  
  ${4} \over {12}$ ✓
- ${1} \over {9}$
  
  ⇔
  
  ${5} \over {9}$ ✓
- ${5} \over {3}$
  
  ⇔
  
  ${12} \over {3}$ ✓
Tick the equations where all three fractions are related fractions.
- ${1} \over {3}$ + ${1} \over {6}$ + ${1} \over {2}$ ✓
- ${1} \over {8}$ + ${1} \over {6}$ + ${1} \over {12}$
- ${1} \over {2}$ + ${1} \over {8}$ + ${1} \over {24}$ ✓
- ${2} \over {3}$ + ${1} \over {9}$ + ${1} \over {18}$ ✓
Tick the equations where all three fractions are related fractions.
- ${1} \over {4}$ + ${1} \over {6}$ + ${1} \over {2}$
- ${1} \over {5}$ + ${1} \over {6}$ + ${1} \over {35}$
- ${1} \over {2}$ + ${3} \over {5}$ + ${1} \over {24}$
- ${2} \over {3}$ + ${1} \over {9}$ + ${1} \over {18}$ ✓
Tick the sum for the following equation: ${1} \over {2}$ + ${1} \over {8}$ + ${1} \over {16}$ =
- ${3} \over {16}$
- ${2} \over {8}$
- 1
- ${11} \over {16}$ ✓
- ${16} \over {2}$
Tick the sum for the following equation: ${1} \over {2}$ − ${1} \over {8}$ − ${1} \over {16}$ =
- ${5} \over {16}$ ✓
- ${3} \over {2}$
- ${3} \over {16}$
- ${1} \over {4}$
Compare the expressions using < > or = ${1} \over {5}$ − ${1} \over {10}$ − ${2} \over {20}$ ______ ${2} \over {5}$ − ${2} \over {10}$ − ${4} \over {20}$
- '<' ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

When adding and subtracting fractions with the same denominators you just add or subtract the numerators.
Common multiples help you to convert a fraction to a common denominator.
The language of unitising helps you to add and subtract fractions with the same denominators.
When adding and subtracting fractions with the same denominators you just add the numerators.

Common misconception

Pupils compare expressions by only ever calculating the value of each expression before comparing.

Encourage pupils to consider the magnitude of the fractions they are adding or subtracting. Comparing fractions to one-half is an effective way to help identify their magnitude and whether then expression would be larger or smaller.

Keywords

Related fractions - When the denominator of one fraction is a multiple of the denominator of another fraction, we can say these fractions are related fractions.
Common denominator - When two or more fractions share the same denominator, you can say they have a common denominator.