What Is a Fraction? Numerators, Denominators and Mixed Numbers

Fractions as equal parts, as points on the number line and as division, plus how improper fractions and mixed numbers are two ways of writing the same amount.

4 min read Supports 3 lessons

Cut a pizza into $8$ equal slices and take $3$ of them. You have three eighths of the pizza, written $\frac{3}{8}$ .

$\frac{3}{8}$ : three of eight equal slices.

The denominator (bottom) says how many equal parts the whole is cut into. It names the size of each piece: eighths, thirds, tenths. The numerator (top) counts how many of those pieces you have.

Key idea

The parts must be equal. Cutting a pizza into one huge slice and seven slivers does not make eighths.

Fractions are numbers

It is easy to think of a fraction as two numbers stacked up. It is really a single number, with its own place on the number line. To find $\frac{3}{4}$ , split the gap from $0$ to $1$ into four equal steps and count three of them.

Three jumps of a quarter land on $\frac{3}{4}$ .

A fraction is a division

$\frac{3}{4}$ also means $3 \div 4$ . Share $3$ pizzas equally between $4$ people and each person gets three quarters of a pizza. That is why the fraction bar and the division sign $\div$ look alike.

\frac{3}{4} = 3 \div 4 = 0.75

Dividing the top by the bottom turns any fraction into a decimal.

Improper fractions and mixed numbers

When the numerator is at least as big as the denominator, the fraction is worth one or more wholes. $\frac{7}{3}$ is called an improper fraction. The same amount written as wholes plus a part, $2\frac{1}{3}$ , is a mixed number.

\tfrac{7}{3}

$\frac{7}{3}$ fills two whole bars and one third of another: $2\frac{1}{3}$ .

$\frac{17}{5}$
Improper fraction to mixed number: divide the top by the bottom.

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Tip

Mixed numbers are easier to picture; improper fractions are easier to calculate with. Convert to improper fractions before you multiply or divide.

Comparing fractions

With the same denominator, the bigger numerator wins: $\frac{5}{8} > \frac{3}{8}$ . With the same numerator, the smaller denominator wins, because the pieces are bigger: $\frac{1}{3} > \frac{1}{5}$ . For anything else, rewrite both with a common denominator.

\tfrac{1}{3}

\tfrac{1}{5}

A third is bigger than a fifth: fewer pieces means bigger pieces.

Watch out

A bigger denominator does not mean a bigger fraction. $\frac{1}{10}$ is much smaller than $\frac{1}{2}$ .

Common questions

Which number is the numerator?: The numerator is the top number. It counts how many parts you have. The denominator, underneath, says how many equal parts make a whole.
Can a fraction be bigger than 1?: Yes. When the numerator is larger than the denominator, as in $\frac{7}{3}$ , the fraction is worth more than one whole. It can also be written as a mixed number, $2\frac{1}{3}$ .

Practise fractions

The What Is a Fraction? lesson has worked examples and unlimited practice that adapts to you.

Open the lesson

Common questions

Which number is the numerator?

The numerator is the top number. It counts how many parts you have. The denominator, underneath, says how many equal parts make a whole.

Can a fraction be bigger than 1?

Yes. When the numerator is larger than the denominator, as in $\frac{7}{3}$ , the fraction is worth more than one whole. It can also be written as a mixed number, $2\frac{1}{3}$ .