Solve Equations with Fractions

There are several ways to solve equations with fractions. 

The easiest way is to multiply the whole equation by the denominator (bottom part) of the fraction.  This will eliminate the fraction and the equation can then be solved normally.

 

Example

Solve the following equation for a:

 

5a + 3	=	19
2

 

Answer

 

5a + 3	=	19
2

 

Multiply both sides by the denominator 2:

 

2 ×	5a + 3	=	2 × 19
	2

 

The 2s cancel out on the left-hand side and we get 2 x 19 on the right-hand side:

  

2 ×	5a + 3	=	2 × 19
	2

 

Simplify:

5a + 3 = 38

 

Subtract 3 from both sides:

5a + 3 - 3 = 38  - 3

 

Simplify:

5a = 35

 

Divide both sides by 5:

5a ÷ 5 = 35 ÷ 5

 

Simplify

a = 7

 

Let's practise this in the following questions.