Adding and subtracting fractions

Adding and subtracting fractions with the same and different denominators, and with mixed numerals.

Same denominator

Add or subtract the numerators and keep the denominator: $\dfrac{2}{7} + \dfrac{3}{7} = \dfrac{5}{7}$.

Example 1●

Find $\dfrac{2}{3} + \dfrac{1}{4}$.

$\dfrac{8}{12} + \dfrac{3}{12}$

LCM of 3 and 4 is 12.

$= \dfrac{11}{12}$

Example 2: mixed numerals●●

Find $3\tfrac{1}{2} - 1\tfrac{5}{6}$.

Improper fractions: $\dfrac{7}{2} - \dfrac{11}{6}$.

$= \dfrac{21}{6} - \dfrac{11}{6} = \dfrac{10}{6}$

$= \dfrac{5}{3} = 1\tfrac{2}{3}$

Flashcards

Adding fractions

Common denominator, then add numerators.

$dfrac{1}{2} + dfrac{1}{3}$

$\dfrac{5}{6}$

Lowest common denominator

The LCM of the denominators.

Practice

Find $\dfrac{2}{3} + \dfrac{1}{4}$.
Find $3\tfrac{1}{2} - 1\tfrac{5}{6}$ as an improper fraction.
Find $\dfrac{2}{7} + \dfrac{3}{7}$.
Find $\dfrac{1}{2} + \dfrac{1}{3}$.
Find $\dfrac{3}{5} - \dfrac{1}{2}$.
Find $2\tfrac{1}{3} + 1\tfrac{1}{2}$ as an improper fraction.
Find $\dfrac{5}{8} - \dfrac{1}{3}$.
Ana eats $\tfrac{1}{2}$ of a pizza and Ben eats $\tfrac{1}{4}$. What fraction is left?