Converting percentages to fractions

To convert a percentage to a fraction, follow these steps:

• Convert the percentage to a decimal by dividing by 100\%.
• Convert the decimal to a fraction over a power of 10.
• Simplify the fraction if possible.

Useful links

• Converting percentages to decimals
• Converting decimals to fractions
• Simplifying fractions
• Highest common factor (HCF)

Example conversions

Convert 75% to a fraction

• Convert to a decimal:
  • 75\% \div 100\% = 0.75
• Convert to a fraction:
  • 0.75 = \frac{75}{100}
• Simplify the fraction:
  • HCF of 75 and 100 is 25.
  • \frac{75 \div 25}{100 \div 25} = \frac{3}{4}
• Answer: 75\% = \frac{3}{4}

Convert 40% to a fraction

• Convert to a decimal:
  • 40\% \div 100\% = 0.40
• Convert to a fraction:
  • 0.40 = \frac{40}{100}
• Simplify the fraction:
  • HCF of 40 and 100 is 20.
  • \frac{40 \div 20}{100 \div 20} = \frac{2}{5}
• Answer: 40\% = \frac{2}{5}

Convert 12.5% to a fraction

• Convert to a decimal:
  • 12.5\% \div 100\% = 0.125
• Convert to a fraction:
  • 0.125 = \frac{125}{1000}
• Simplify the fraction:
  • HCF of 125 and 1000 is 125.
  • \frac{125 \div 125}{1000 \div 125} = \frac{1}{8}
• Answer: 12.5\% = \frac{1}{8}

Convert 273% to a fraction

• Convert to a decimal:
  • 273\% \div 100\% = 2.73
• Convert to a fraction:
  • 2.73 = \frac{273}{100}
• Simplify the fraction:
  • HCF of 273 and 100 is 1.
  • \frac{273 \div 1}{100 \div 1} = \frac{273}{100}
• Answer: 12.5\%=\frac{273}{100}

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