Algebraic fractions

Adding, subtracting, multiplying and dividing simple algebraic fractions using common denominators and cancelling.

Adding and subtracting

Algebraic fractions follow the same rules as number fractions: find a common denominator first.

Example 1●●

Simplify $\dfrac{x}{3} + \dfrac{x}{4}$.

$\dfrac{4x}{12} + \dfrac{3x}{12}$

$= \dfrac{7x}{12}$

Example 2●●

Simplify $\dfrac{2a}{5} - \dfrac{a}{2}$.

$\dfrac{4a}{10} - \dfrac{5a}{10} = -\dfrac{a}{10}$

Example 3●●

Simplify $\dfrac{3x}{4} \div \dfrac{9x}{8}$.

$\dfrac{3x}{4} \times \dfrac{8}{9x}$

$= \dfrac{2}{3}$

Cancel 3 with 9, 4 with 8, and x with x.

Flashcards

$dfrac{x}{2} + dfrac{x}{3}$

$\dfrac{5x}{6}$

$dfrac{a}{b} imes dfrac{b}{c}$

$\dfrac{a}{c}$

Cancel only...

common factors, never terms.

Practice