Fractions — all four operations

Before we dive into operations, let's make sure we're confident about what fractions actually are.

Fraction: A fraction represents a part of a whole. It is written as $\frac{a}{b}$, where $a$ is the numerator (how many parts we have) and $b$ is the denominator (how many equal parts the whole is divided into).

Think of a pizza cut into 8 equal slices. If you eat 3 slices, you've eaten $\frac{3}{8}$ of the pizza.

• The numerator (top number) tells you how many parts you're talking about.
• The denominator (bottom number) tells you how many equal parts make up the whole.

Proper Fraction: A fraction where the numerator is smaller than the denominator, e.g. $\frac{3}{5}$. Its value is less than 1.

Improper Fraction: A fraction where the numerator is equal to or greater than the denominator, e.g. $\frac{7}{4}$. Its value is 1 or greater.

Mixed Number: A number made up of a whole number and a proper fraction, e.g. $1\frac{3}{4}$.

Two fractions are equivalent if they represent the same amount, even though they look different.

Equivalent Fractions: Fractions that have the same value but different numerators and denominators. You create them by multiplying or dividing both the numerator and denominator by the same number.

For example:
$\frac{1}{2}=\frac{2}{4}=\frac{3}{6}=\frac{5}{10}$

All of these represent exactly half.

Simplifying (or Reducing) a Fraction: Dividing the numerator and denominator by their highest common factor (HCF) to write the fraction in its simplest form.