Algebra: Equations with Fractions (2)

There are several ways to solve equations with fractions. 

The easiest way is to multiply the whole equation by the lowest common multiple of the denominators (bottom parts) of the fractions.  This will eliminate the fractions and the equation can then be solved normally.

 

Example

Solve the following equation for a:

 

a	+	a	=	14
2		5

 

Answer

 

a	+	a	=	14
2		5

 

Multiply both sides by 10, which is the l.c.m. of 2 and 5. 

Each part must be multiplied.

 

10 x a	+	10 x a	=	10 x 14
2		5

 

Reduce each part of the left hand side and we get 10 x 14 on the right hand side.

  

5 10 x a	+	2 10 x a	=	10 x 14
2		5

  

Simplify

5a + 2a = 140

 

Simplify again

7a = 140

Divide both sides by 7

7a ÷ 7 = 140 ÷ 7

 

Simplify

a = 20