To convert a fraction to a percentage, divide the numerator by the denominator to get a decimal, then multiply by 100. Fractions, decimals and percentages are three ways of writing the same value, and the FDP triangle below shows how to move between all three.
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
1
\(\frac{3}{5} \times 100\)
2
\(= \frac{300}{5} = 60\)
3
Answer: \(\mathbf{60\%}\)
Example 2 — Convert \(\frac{7}{8}\) to a percentage
1
\(\frac{7}{8} \times 100\)
2
\(= \frac{700}{8} = 87.5\)
3
Answer: \(\mathbf{87.5\%}\)
Example 3 — Convert \(\frac{2}{3}\) to a percentage (round to 1 d.p.)
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.
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
1
\(\frac{7}{4} \times 100 = \frac{700}{4} = 175\)
2
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?
1
Write as a fraction: \(\frac{900}{800} = \frac{9}{8}\)
2
\(\frac{9}{8} \times 100 = 112.5\)
3
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
⚠ Things to Watch Out For
Forgetting the final × 100 step: Converting a fraction to a decimal is only halfway — you must multiply by 100 to get the percentage.
Recurring decimals: Fractions like \(\frac{1}{3}\) give a recurring decimal — round sensibly (e.g. to 1 decimal place) unless told otherwise.
Stopping at the decimal: Writing 0.6 instead of 60% is an incomplete answer — always finish by multiplying by 100 and adding the % sign.
Denominators that don't divide evenly into 100: For fractions like sevenths, convert to a decimal first (divide numerator by denominator), then multiply by 100 — don't try to force an equivalent fraction over 100.
Forgetting the % symbol: The final answer must include the % sign to be a complete percentage.