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Fractions, decimals & percentages

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Fractions, decimals & percentages

Fractions, decimals & percentages

One amount, three ways of writing it. Learn a handful of equivalents and you can switch between them without thinking.

1/2 = 0.5 = 50%3/4 = 0.75 = 75%

Per cent means out of 100

A PERCENTAGE is a fraction with a denominator of 100. 50% = 50/100 25% = 25/100 10% = 10/100 So the percentage tells you how many parts out of a hundred are shaded, scored or used.

Turning a percentage into a decimal

Divide by 100. 50% = 0.5 25% = 0.25 10% = 0.1 1% = 0.01 And back the other way: multiply a decimal by 100 to get the percentage.

Turning a fraction into a percentage

Write the fraction with a denominator of 100. 1/2 = 50/100 = 50% 1/4 = 25/100 = 25% 1/5 = 20/100 = 20% 3/4 = 75/100 = 75% If the denominator already divides into 100, this is easy. For 1/5, multiply top and bottom by 20.

The set worth knowing by heart

1/2 = 0.5 = 50% 1/4 = 0.25 = 25% 3/4 = 0.75 = 75% 1/5 = 0.2 = 20% 1/10 = 0.1 = 10% 3/10 = 0.3 = 30% Knowing these means most questions become instant recall rather than calculation.

Worked examples

6 triangles out of 10 coloured

  1. The fraction is 6/10.
  2. Multiply top and bottom by 10 to get hundredths: 60/100.
  3. 60 out of 100 is 60%.

Answer: 6/10 = 60%

Writing 1/5 as a percentage

  1. 5 goes into 100 exactly 20 times.
  2. Multiply top and bottom by 20: 20/100.

Answer: 1/5 = 20%

Writing 40% as a fraction

  1. 40% means 40/100.
  2. Divide top and bottom by 20.

Answer: 40% = 2/5

Finding the missing number: ▢/100 = 50%

  1. Per cent means out of 100.
  2. So 50% is 50 out of 100.

Answer: The missing number is 50

Matching equivalent cards

  1. 0.4 as a percentage is 40%.
  2. 40% as a fraction is 40/100 = 2/5.
  3. So 0.4, 40% and 2/5 all match.

Answer: 0.4 = 40% = 2/5

Where you see this in real life

  • A test score of 18 out of 20 is 90% — the same mark written two ways.
  • A '25% off' sign means the same as 'a quarter off'.
  • Phone battery shown as 50%, 0.5 of full, or half charged.

Key words

Percentage
A fraction with a denominator of 100.
Per cent
Out of 100.
Decimal
A number written with a decimal point.
Equivalent
Of equal value, written differently.
Numerator
The top number of a fraction.
Denominator
The bottom number of a fraction.
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