fractions

A fraction is a way of writing a number that stands for part of a whole — like one slice of a pizza cut into eight equal pieces.

What a Fraction Really Means

Imagine a chocolate bar you snap into 4 equal pieces. If you eat 3 of them, you have eaten $\frac{3}{4}$ of the bar.

Every fraction has two numbers:

• The bottom number (the denominator) tells you how many equal pieces the whole is cut into.
• The top number (the numerator) tells you how many of those pieces you have.

So in $\frac{3}{4}$, the whole is cut into 4 pieces, and you have 3 of them.

A Very Old Idea

Fractions are ancient. The Egyptians were writing them over 3,700 years ago. The Rhind Mathematical Papyrus, copied by a scribe named Ahmes around 1550 BCE, is full of them. Curiously, the Egyptians mostly used "unit fractions" — fractions with 1 on top, like $\frac{1}{2}$ or $\frac{1}{5}$ — to share out bread and beer among workers.

The Rhind Mathematical Papyrus (c. 1550 BCE), an Egyptian scroll packed with fraction problems — source

The slanted line we use, called a solidus (as in $1/2$), and the neat top-and-bottom style came much later, spread through Europe by the Italian mathematician Fibonacci in his book Liber Abaci (1202).

Equal Pieces, Different Names

Here is a magic trick of fractions: many different-looking fractions are secretly the same amount.

$$\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$$

Cut a cake into 2 and take 1 piece, or cut it into 6 and take 3 — you get exactly the same amount of cake. These are called equivalent fractions.

Where You Meet Them

Fractions hide everywhere in daily life:

• Recipes: "add $\frac{1}{2}$ cup of sugar."
• Time: a "quarter past" means $\frac{1}{4}$ of an hour has passed.
• Money: an American quarter is $\frac{1}{4}$ of a dollar.

Once you see fractions as sharing things fairly into equal parts, they stop being scary — they are just the maths of splitting a pizza.

Further exploration

• Liber Abaci by Fibonacci (1202) — the medieval book that helped bring fraction notation to Europe.
• The Rhind Mathematical Papyrus — a real Egyptian primary source showing how ancient people used fractions to share food.