Converting Fractions to Percentages

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The FDP Triangle

Fractions, Decimals and Percentages are three ways of writing the same value. The triangle below shows how to move between them.

Learning Objectives

Convert a fraction to a percentage by multiplying by 100
Use the decimal as a bridge: fraction → decimal → percentage
Convert fractions whose denominator divides into 100 directly
Recall key fraction–percentage equivalents from memory

Real-World Applications

Test scores: You scored \(\frac{17}{20}\) in a test — converting to 85% makes it easy to compare with other results.
Discounts: A shop offers \(\frac{1}{4}\) off — expressing this as 25% is clearer for customers.
Statistics: \(\frac{3}{8}\) of voters prefer a policy — saying 37.5% communicates this more clearly in a report.

Method 1: Multiply the Fraction by 100

"Per cent" means out of 100. So to convert a fraction to a percentage, multiply it by 100.

\[\text{Percentage} = \frac{a}{b} \times 100\%\]

Example 1 — Convert \(\frac{3}{5}\) to a percentage

\(\frac{3}{5} \times 100\)

\(= \frac{300}{5} = 60\)

Answer: \(\mathbf{60\%}\)

Example 2 — Convert \(\frac{7}{8}\) to a percentage

\(\frac{7}{8} \times 100\)

\(= \frac{700}{8} = 87.5\)

Answer: \(\mathbf{87.5\%}\)

Example 3 — Convert \(\frac{2}{3}\) to a percentage (round to 1 d.p.)

\(\frac{2}{3} \times 100 = \frac{200}{3} = 66.666...\)

Round to 1 d.p.: \(66.7\%\)

Answer: \(\mathbf{66.7\%}\)

Tip: On a calculator, enter the fraction as a division first: for \(\frac{7}{8}\), press 7 ÷ 8 × 100.

✓ Quick Check 1 — Simple fractions to percentages

Question 1 of 10

Method 2: Use the Decimal as a Bridge

You can also convert fraction → decimal first (using division), then decimal → percentage (multiply by 100). This two-step method is useful when the division is straightforward.

\[\frac{a}{b} \xrightarrow{\div} \text{decimal} \xrightarrow{\times 100} \text{percentage}\]

Example 4 — Convert \(\frac{9}{20}\) to a percentage

Step 1 — fraction to decimal: \(9 \div 20 = 0.45\)

Step 2 — decimal to percentage: \(0.45 \times 100 = 45\)

Answer: \(\mathbf{45\%}\)

Example 5 — Convert \(\frac{13}{25}\) to a percentage

\(13 \div 25 = 0.52\)

\(0.52 \times 100 = 52\)

Answer: \(\mathbf{52\%}\)

Method 3: Equivalent Fraction with Denominator 100

If the denominator divides evenly into 100, you can scale the fraction directly to have a denominator of 100 — then the numerator is the percentage.

Example 6 — Convert \(\frac{3}{4}\) using equivalent fractions

\(4 \times 25 = 100\), so multiply numerator and denominator by 25

\(\frac{3 \times 25}{4 \times 25} = \frac{75}{100}\)

Answer: \(\mathbf{75\%}\)

Example 7 — Convert \(\frac{7}{20}\)

\(20 \times 5 = 100\)

\(\frac{7 \times 5}{20 \times 5} = \frac{35}{100}\)

Answer: \(\mathbf{35\%}\)

This method only works when 100 ÷ denominator is a whole number. For \(\frac{1}{3}\) it doesn't work because 100 ÷ 3 = 33.3... Use Method 1 instead.

Key fraction–percentage pairs to memorise:

Fraction	Percentage	Fraction	Percentage
\(\frac{1}{2}\)	50%	\(\frac{1}{5}\)	20%
\(\frac{1}{4}\)	25%	\(\frac{2}{5}\)	40%
\(\frac{3}{4}\)	75%	\(\frac{3}{5}\)	60%
\(\frac{1}{10}\)	10%	\(\frac{1}{3}\)	33.3%
\(\frac{3}{10}\)	30%	\(\frac{2}{3}\)	66.7%

✓ Quick Check 2 — Harder fractions

Question 1 of 10

Fractions Greater Than 1 → Percentages Greater Than 100%

Fractions greater than 1 (improper fractions or mixed numbers) give percentages greater than 100%. This is used in contexts like growth and profit.

Example 8 — Convert \(\frac{7}{4}\) to a percentage

\(\frac{7}{4} \times 100 = \frac{700}{4} = 175\)

Answer: \(\mathbf{175\%}\)

Example 9 — A salary increases from £800 to £900 per month. What is the new salary as a percentage of the old?

Write as a fraction: \(\frac{900}{800} = \frac{9}{8}\)

\(\frac{9}{8} \times 100 = 112.5\)

Answer: \(\mathbf{112.5\%}\) of the original salary

✓ Quick Check 3 — Real-life context

Question 1 of 10

Practice: Convert these fractions to percentages

Type your answer as a number (e.g. 75 or 66.7), then click Check.

#	Question	Answer	Result
1	Convert \(\frac{3}{5}\) to a percentage
2	Convert \(\frac{7}{8}\) to a percentage
3	Convert \(\frac{2}{3}\) to a percentage (round to 1 d.p.)
4	Convert \(\frac{9}{20}\) to a percentage
5	Convert \(\frac{13}{25}\) to a percentage
6	Convert \(\frac{3}{4}\) to a percentage
7	Convert \(\frac{7}{20}\) to a percentage
8	Convert \(\frac{7}{4}\) to a percentage
9	A salary increases from £800 to £900 per month. What is the new salary as a percentage of the old?
10	Convert \(\frac{1}{8}\) to a percentage

Converting Fractions to Percentages

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Learning Objectives

Real-World Applications

Example 1 — Convert \(\frac{3}{5}\) to a percentage

Example 2 — Convert \(\frac{7}{8}\) to a percentage

Example 3 — Convert \(\frac{2}{3}\) to a percentage (round to 1 d.p.)

Example 4 — Convert \(\frac{9}{20}\) to a percentage

Example 5 — Convert \(\frac{13}{25}\) to a percentage

Example 6 — Convert \(\frac{3}{4}\) using equivalent fractions

Example 7 — Convert \(\frac{7}{20}\)

Example 8 — Convert \(\frac{7}{4}\) to a percentage

Example 9 — A salary increases from £800 to £900 per month. What is the new salary as a percentage of the old?

Practice: Convert these fractions to percentages

⚠ Things to Watch Out For