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 whole-number percentage to a fraction over 100, then simplify
Convert a decimal percentage (e.g. 12.5%) to a fraction in simplest form
Recall key percentage–fraction equivalents from memory
Apply percentage-to-fraction conversion in context
Real-World Applications
Shopping: A 25% discount is the same as \(\frac{1}{4}\) off — knowing this lets you calculate the discount mentally.
Probability: A 40% chance of rain is a probability of \(\frac{2}{5}\) — fractions are often more intuitive.
Construction: A 50% mixture is \(\frac{1}{2}\) — fractions are commonly used in recipes and mixing ratios.
The Core Method: Write Over 100, Then Simplify
"Per cent" means out of 100. So any percentage can be written directly as a fraction with denominator 100. Then simplify by dividing both numerator and denominator by their largest common factor.
Example 1 — Convert 40% to a fraction in simplest form
1
\(40\% = \frac{40}{100}\)
2
Largest common factor of 40 and 100 is 20
3
\(\frac{40 \div 20}{100 \div 20} = \frac{2}{5}\)
4
Answer: \(\mathbf{\frac{2}{5}}\)
Example 2 — Convert 35% to a fraction
1
\(\frac{35}{100}\)
2
Largest common factor of 35 and 100 is 5: \(\frac{35 \div 5}{100 \div 5} = \frac{7}{20}\)
3
Answer: \(\mathbf{\frac{7}{20}}\)
Example 3 — Convert 60% to a fraction
1
\(\frac{60}{100}\)
2
Largest common factor of 60 and 100 is 20: \(\frac{60 \div 20}{100 \div 20} = \frac{3}{5}\)
3
Answer: \(\mathbf{\frac{3}{5}}\)
Simplification tip: Both the numerator and denominator will often be divisible by 2 or 5. Try dividing by 5 first (since the denominator is always 100). If both are even, also try dividing by 2.
✓ Quick Check 1 — Integer percentages to fractions
Question 1 of 10
Decimal Percentages (e.g. 12.5%)
When a percentage has a decimal part (like 12.5% or 7.5%), you need an extra step to clear the decimal from the numerator.
\(\frac{12.5}{100}\) — multiply both by 2 to clear the decimal
2
\(\frac{25}{200}\)
3
Largest common factor of 25 and 200 is 25: \(\frac{25 \div 25}{200 \div 25} = \frac{1}{8}\)
4
Answer: \(\mathbf{\frac{1}{8}}\)
Example 5 — Convert 37.5% to a fraction
1
\(\frac{37.5}{100}\) — multiply by 2: \(\frac{75}{200}\)
2
Largest common factor of 75 and 200 is 25: \(\frac{75 \div 25}{200 \div 25} = \frac{3}{8}\)
3
Answer: \(\mathbf{\frac{3}{8}}\)
Key rule: Multiply top and bottom by the same number to clear the decimal — ×10 per decimal place always works (1 d.p. → ×10, 2 d.p. → ×100, 3 d.p. → ×1000). For percentages like 12.5% and 37.5%, ×2 is a quicker shortcut because the decimal part is exactly .5 — it won't clear a decimal like 13.4%, where you'd need ×10.
Key Percentage–Fraction Pairs to Know
These appear constantly in exam questions. Knowing them by heart saves time and prevents errors.
Percentage
Fraction
Percentage
Fraction
50%
\(\frac{1}{2}\)
10%
\(\frac{1}{10}\)
25%
\(\frac{1}{4}\)
20%
\(\frac{1}{5}\)
75%
\(\frac{3}{4}\)
40%
\(\frac{2}{5}\)
33.3%
\(\frac{1}{3}\)
60%
\(\frac{3}{5}\)
66.7%
\(\frac{2}{3}\)
80%
\(\frac{4}{5}\)
12.5%
\(\frac{1}{8}\)
37.5%
\(\frac{3}{8}\)
62.5%
\(\frac{5}{8}\)
87.5%
\(\frac{7}{8}\)
Example 6 — Using known equivalents in context
A shop offers 12.5% off all items. You know \(12.5\% = \frac{1}{8}\). A jacket costs £72. Find the discount.
1
Discount = \(\frac{1}{8}\) of £72
2
\(72 \div 8 = £9\)
3
Sale price = \(£72 - £9 = £63\)
✓ Quick Check 2 — Decimal percentages and key pairs
Question 1 of 10
Percentages Greater Than 100% → Improper Fractions or Mixed Numbers
Percentages above 100% give fractions greater than 1 — either improper fractions or mixed numbers.
Example 7 — Convert 125% to a mixed number fraction
1
\(\frac{125}{100}\)
2
HCF of 125 and 100 is 25: \(\frac{125 \div 25}{100 \div 25} = \frac{5}{4}\)
3
As a mixed number: \(1\frac{1}{4}\)
4
Answer: \(\mathbf{\frac{5}{4}}\) or \(\mathbf{1\frac{1}{4}}\)
Practice: Convert these percentages to fractions (simplest form)
Type your answer as a fraction e.g. 1/2 (or a mixed number e.g. 1 1/4), then click Check.
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Question
Answer
Result
1
Convert 40% to a fraction in simplest form
2
Convert 35% to a fraction
3
Convert 60% to a fraction
4
Convert 12.5% to a fraction
5
Convert 37.5% to a fraction
6
Convert 25% to a fraction
7
Convert 125% to a fraction
8
Convert 150% to a fraction
9
Convert 20% to a fraction
10
Convert 75% to a fraction
⚠ Things to Watch Out For
Forgetting to simplify: Always simplify the fraction to its lowest terms — leaving it as \(\frac{40}{100}\) instead of \(\frac{2}{5}\) is an incomplete answer.
Decimal percentages need an extra step: For percentages like 12.5%, multiply top and bottom by 10 first to clear the decimal before simplifying.
Percentages over 100%: These become improper fractions or mixed numbers, e.g. 125% = \(\frac{5}{4}\) = \(1\frac{1}{4}\) — this is correct, not an error.
Stopping too early: Writing the percentage over 100 (e.g. \(\frac{35}{100}\)) is only the first step — you must simplify to finish the conversion.
Confusing with percentage-to-decimal: Percentage to fraction and percentage to decimal are different conversions with different final answers — check which one the question asks for.