Fractions in Algebra

You can add, subtract, multiply and divide fractions in algebra in the same way that you do in simple arithmetic.

Adding Fractions

To add fractions there is a simple rule:

adding fractions rule

(You can see why this works on the Common Denominator page).

Example:

x  +  y  =  (x)(5) + (2)(y)  =  5x+2y
2 5 (2)(5) 10

Example:

x + 4  +  x - 3  =  (x+4)(4) + (3)(x-3)  =  4x+16 + 3x-9  =  7x+7
3 4 (3)(4) 12 12

 

Subtracting Fractions

Subtracting fractions is very similar to adding, except that the + is now -

subtracting fractions

Example:

x + 2  -  x  =  (x+2)(x-2) - (x)(x)  =  x2-22 - x2  =  -4
x x - 2 x(x-2) x2 - 2x x2 - 2x

 

Multiplying Fractions

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

Multiplying Fractions Rule

Example:

3x  ×  x  =  (3x)(x)  =  3x2  =  x2
x-2 3 3(x-2) 3(x-2) x-2

Dividing Fractions

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

divide fractions

Example:

3y2  ÷  y  =  3y2  ×  2  =  (3y2)(2)  =  6y2  =  6y
x+1 2 x+1 y (x+1)(y) (x+1)(y) x+1

 


Hard: