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:

x2 + y5 = (x)(5) + (2)(y)(2)(5)

= 5x+2y10

Example:

x + 43 + x − 34 = (x+4)(4) + (3)(x−3)(3)(4)

= 4x+16 + 3x−912

= 7x+712

Subtracting Fractions

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

subtracting fractions

Example:

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

(x2 − 22) − x2x2 − 2x

−4x2 − 2x

 

Multiplying Fractions

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

Multiplying Fractions Rule

Example:

3xx−2  ×  x3  = (3x)(x)3(x−2)  

3x23(x−2)  

x2x−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:

3y2x+1  ÷  y2  =  3y2x+1  ×  2y  

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

= 6y2(x+1)(y)  

6yx+1

 


Hard: