Form 1 · Chapter 4

Relationship between Ratios, Rates and Proportions with Percentages, Fractions and Decimals

Convert between ratios, fractions, decimals and percentages, and use them to solve proportion problems.

Different names, same idea

A part of a whole can be shown as a ratio, a fraction, a decimal or a percentage. They are just different ways of writing the same relationship. If 1 out of 4 pupils walks to school, the fraction is 1/4, the decimal is 0.25, the percentage is 25%, and the ratio of walkers to the rest is 1 : 3.

Key idea / Key idea

Fraction → decimal: divide. Decimal → percentage: × 100. Percentage → fraction: write over 100 and simplify. Ratio a : b → fraction of the whole: a/(a+b).

Converting and comparing

FractionDecimalPercentage
1/20.550%
3/40.7575%
2/50.440%

Worked example / Worked example

In a class the ratio of pass to fail is 3 : 1. What percentage passed?
Total parts = 3 + 1 = 4. Passers = 3/4 of the class.
3/4 = 3 ÷ 4 = 0.75 = 0.75 × 100 = 75%.
So 75% of the class passed.

Percentages make comparing easy because they all share a base of 100. To take a percentage of an amount, change it to a fraction or decimal first: 20% of RM50 = 0.2 × RM50 = RM10.

Remember / Remember

  • Ratio, fraction, decimal and percentage can describe the same part.
  • Percentage means "out of 100".
  • × 100 to get a percentage; ÷ 100 to remove it.
  • For a : b, the first part is a/(a+b) of the whole.

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