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Percentages — Fractions to percentages

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Fractions to Percentages (Year 7)

A percentage is a fraction of 100. To change a fraction into a percentage, we make the denominator 100 or multiply by 100.

1. Method 1: Make the Denominator 100

If the bottom number (denominator) can change to 100 easily, change it.

Example: \( \frac{3}{4} \)

\[ \frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 75\% \]

Example: \( \frac{7}{20} \)

\[ \frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100} = 35\% \]

2. Method 2: Multiply by 100%

Any fraction can be changed to a percentage by multiplying by \(100\%\).

Example: \( \frac{2}{5} \)

\[ \frac{2}{5} \times 100\% = 40\% \]

Example: \( \frac{6}{25} \)

\[ \frac{6}{25} \times 100\% = 24\% \]

3. Mixed and Improper Fractions

Change to an improper fraction first, then multiply by \(100\%\).

Example: \( 1\frac{1}{2} \)

\[ 1\frac{1}{2} = \frac{3}{2} \qquad \Rightarrow \qquad \frac{3}{2} \times 100\% = 150\% \]

Example: \( 2\frac{1}{4} \)

\[ 2\frac{1}{4} = \frac{9}{4} \qquad \Rightarrow \qquad \frac{9}{4} \times 100\% = 225\% \]

4. Quick Tips

  • Percent means “out of 100”.
  • If the denominator can easily become 100, use Method 1.
  • Otherwise, multiply by \(100\%\).
  • Mixed fractions must be turned into improper fractions first.

5. Try These

  1. \(\frac{5}{8}\)
  2. \(\frac{3}{25}\)
  3. \(1\frac{3}{5}\)
  4. \(\frac{11}{20}\)
  5. \(\frac{7}{2}\)

Convert each to a percentage.

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