What is a Percentage?

The word percent comes from the Latin per centum, meaning "for every hundred". Knowing this makes the concept much easier to remember!

Percentage

A percentage is a ratio that compares a part to a whole, where the whole is always represented as 100. The symbol for percentage is %.

Think of it like cutting something into exactly 100 equal pieces. Each piece is 1%.

If 1 piece out of 100 is shaded → 1% or $\frac{1}{100}$
If 55 pieces out of 100 are shaded → 55% or $\frac{55}{100}$

This means a percentage is really just a fraction with a denominator of 100.

Analogy

Imagine a chocolate bar broken into exactly 100 equal squares. Eating 30 squares means you ate 30% of the bar. Eating all 100 squares? That's 100% — the whole bar!

Converting Between Fractions and Percentages

Since percentages are fractions out of 100, converting between fractions and percentages is straightforward.

Fraction → Percentage

Method 1: Make an equivalent fraction with denominator 100, then write the numerator with a % sign.

⚠️ This only works when the denominator divides evenly into 100 (i.e. the denominator is a factor of 100: 1, 2, 4, 5, 10, 20, 25, 50, or 100). For other fractions, use Method 2. Also, simplify the fraction first if possible — then check if the simplified denominator is a factor of 100.

Method 2: Divide the numerator by the denominator, then multiply by 100%. This works for all fractions.

Percentage → Fraction

Write the percentage as a fraction over 100, then simplify as much as possible.

Example

Convert fractions to percentages (Method 1 — denominator is a factor of 100):

$\frac{19}{25} = \frac{19 \times 4}{25 \times 4} = \frac{76}{100} = 76$

$\frac{7}{35}$ — first simplify: $\frac{7}{35} = \frac{1}{5}$ . Now 5 is a factor of 100, so:
$\frac{1}{5} = \frac{1 \times 20}{5 \times 20} = \frac{20}{100} = 20$

$\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 75$

Convert fractions to percentages (Method 2 — divide then multiply by 100):

$\frac{3}{8} = 3 \div 8 = 0.375 0.375 \times 100$

$\frac{1}{3} = 1 \div 3 = 0.3333 \dots \approx 33.3$

Note: Some fractions like $\frac{1}{3}$ give recurring decimals. We usually write these as approximate percentages (e.g. ≈ 33.3%). You can also write $\frac{1}{3}$ exactly as $33 \frac{1}{3}$ , which avoids rounding altogether. Dot notation (e.g. $0. \dot{3}$ ) is another way to show a recurring decimal, but rounding is the most common approach at this level.

Convert percentages to fractions:

$29$

$85$ (dividing top and bottom by 5)

Exam Tip

To multiply a fraction's denominator to reach 100, ask: "What do I multiply the denominator by to get 100?" Then do the same to the numerator. If you can't find a whole-number multiplier, use Method 2 instead. And remember — simplify first!

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