Fractions in Algebra

We can add, subtract, multiply and divide fractions in algebra in the same way we do in simple arithmetic.

Adding Fractions

To add fractions there is a simple rule:

adding fractions rule

(See why this works on the Common Denominator page).

Example:

x 2 + y 5 = (x)(5) + (2)(y) (2)(5)

= 5x+2y 10

Example:

x + 4 3 + x − 3 4 = (x+4)(4) + (3)(x−3) (3)(4)

= 4x+16 + 3x−9 12

= 7x+7 12

Subtracting Fractions

Subtracting fractions is very similar, except that the + is now −

subtracting fractions

Example:

x + 2 x x x − 2 = (x+2)(x−2) − (x)(x) x(x−2)

= (x2 − 22) − x2 x2 − 2x

= −4 x2 − 2x

Multiplying Fractions

Multiplying fractions is the easiest one of all: multiply the tops together, and the bottoms together:

Multiplying Fractions Rule

Example:

3x x−2 × x 3 = (3x)(x) 3(x−2)

= 3x2 3(x−2)

= x2 x−2

Dividing Fractions

To divide fractions first "flip" the fraction we want to divide by, then use the same method as for multiplying:

divide fractions

Example:

3y2 x+1 ÷ y 2 = 3y2 x+1 × 2 y

= (3y2)(2) (x+1)(y)

= 6y2 (x+1)(y)

= 6y x+1

3881, 3879, 3880, 3882, 337, 336, 2268, 2269

Hard Questions:

190, 240, 241, 242, 257