Adding and Subtracting Fractions

In short: You can only add or subtract fractions with the same denominator (bottom number). Change them to the lowest common denominator first, then add or subtract the tops, and never add the bottoms: $\frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$.

Before you start

• Equivalent fractions: $\frac{1}{3}=\frac{4}{12}$ (see Types of Fractions).
• Changing between mixed numbers and improper fractions: $1\frac{3}{8}=\frac{11}{8}$.
• Multiples of a number are its times table. Multiples of 4: 4, 8, 12, 16, ...

Same denominator: just add the tops

$\frac{2}{7}+\frac{3}{7}=\frac{5}{7}$. The pieces are already the same size (sevenths), so count them. The bottom does not change.

Different denominators

Mixed numbers

Add or subtract the whole numbers first, then the fractions.

Subtracting when the second fraction is bigger

Sometimes you cannot take the second fraction from the first. Then subtract the whole numbers, and change what is left into an improper fraction.

Quick summary

• You can only add or subtract fractions with the same denominator.
• Use the lowest common denominator, then add or subtract the numerators.
• Never add the denominators.
• With mixed numbers, do the whole numbers first, then the fractions.
• If the second fraction is bigger, borrow a whole or change to an improper fraction.
• Always simplify the answer.

Quiz