Adding and Subtracting Fractions

In a Nutshell

Make the denominators the same, then add or subtract the numerators. Simplify if you can.

You can only add or subtract fractions when the pieces are the same size. That means the denominators must match. If they do not, convert both fractions to equivalent fractions with a common denominator (the LCM works best).

Once the denominators match, add (or subtract) the numerators and keep the denominator the same. Then simplify the result if possible.

ad+bd=a+bdad−bd=a−bd\frac{a}{d} + \frac{b}{d} = \frac{a + b}{d} \qquad \frac{a}{d} - \frac{b}{d} = \frac{a - b}{d}

For mixed numbers, you can either convert to improper fractions first or deal with the whole-number parts separately.

Fraction bar model for addition and subtraction Two fraction bars shown side by side, then combined into a single result bar to visualise adding or subtracting fractions. 1/3 + 1/4 A B = 7/12

Choose an addition or subtraction. The two bars are redrawn using the common denominator, then combined into the result bar below.

Watch it work

Question: Calculate 25+13\frac{2}{5} + \frac{1}{3}.

Have a go

Q1. Calculate 14+16\frac{1}{4} + \frac{1}{6}.

Q2. Calculate 34−13\frac{3}{4} - \frac{1}{3}.

Q3. Calculate 56−14\frac{5}{6} - \frac{1}{4}.

Q4. Calculate 112+2231\frac{1}{2} + 2\frac{2}{3}.

Q5. A recipe needs 34\frac{3}{4} cup of sugar and 23\frac{2}{3} cup of flour. How much is that in total?