Expressing one number as a percentage of another | Maths

Starter quiz

Two fractions are ____________ if they have the same value.
- equivalent ✓
- improper
- ordinary
- proper
What is 20% as a simplified fraction?
- $\frac{1}{20}$
- $\frac{1}{4}$
- $\frac{20}{100}$
- $\frac{10}{50}$
- $\frac{1}{5}$ ✓
What is 30% as a simplified fraction?
- $\frac{1}{30}$
- $\frac{1}{3}$
- $\frac{3}{10}$ ✓
- $\frac{15}{50}$
- $\frac{1}{20}$
What is 42% as a simplified fraction?
- $\frac{42}{100}$
- $\frac{42}{20}$
- $\frac{1}{42}$
- $\frac{21}{50}$ ✓
- $\frac{42}{50}$
Using short division or otherwise, work out the decimal answer to 25 ÷ 4.
- '6.25' ✓
Using short division or otherwise, work out the decimal answer to 1 ÷ 6.
- $0.1 \dot 6$ ✓
- $0.1 \dot 3$
- $\frac{1}{6}$
- $0.3$
- $0.167$

Exit quiz

$\frac{7}{20}$ as a percentage is ______%.
- '35' ✓
Which decimal is equivalent to 1%?
- 0.001
- 0.01 ✓
- 0.1
- 1.0
- 10.0
$\frac{6}{25}$ as a percentage is ______%.
- '24' ✓
Match each percentage to its decimal equivalent.
- 23%
  
  ⇔
  
  0.23 ✓
- 45%
  
  ⇔
  
  0.45 ✓
- 49%
  
  ⇔
  
  0.49 ✓
- 3%
  
  ⇔
  
  0.03 ✓
- 30%
  
  ⇔
  
  0.3 ✓
- 0.3%
  
  ⇔
  
  0.003 ✓
$\frac{3}{8}$ as a decimal is ______.
- '0.375' ✓
Using short division or otherwise, write $\frac{7}{9}$ as a percentage.
- $77.\dot 7$ % ✓
- $0. \dot 7$ %
- $77. \dot 6$ %
- 77%
- 78%

Worksheet

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Lesson Details

Key learning points

Percentages can be written as a fraction out of 100
One number can be written as a fraction of another.
Using equivalent fractions this can be written as a fraction out of 100
One number can be written as a percentage of another.
Decimals can also be used to write one number as a percentage of another.

Common misconception

A single digit percentage is incorrectly worked out by dividing by 10 and not 100 e.g 3% = 0.3

Two responses can be used to remind students that to covert a percentage into a decimal; we divide by 100; using 3%, ask what 30% is as a decimal and 3% as a decimal. Pupils realise they cannot be the same. A place value chart also helps.

Keywords

Equivalent fractions - Two fractions are equivalent if they have the same value.