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).

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

= 5x+2y 10

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

= 4x+16 + 3x−9 12

= 7x+7 12

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

$subtracting fractions$

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

Multiplying Fractions Rule

3x x−2 × x 3 = (3x)(x) 3(x−2)

= 3x² 3(x−2)

= x² x−2

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

$divide fractions$

3y² x+1 ÷ y 2 = 3y² x+1 × 2 y

= (3y²)(2) (x+1)(y)

= 6y² (x+1)(y)

= 6y x+1

Hard: