# ALGERAIC FRACTIONS

## ALGERAIC FRACTIONS

To add or subtract fractions with different denominators, first change them to equivalent fractions. This is done by finding the L C M of the denominators

Example1: Simplify 2a/5 + 4a/3

Solution:

The L C M is 15

6a + 20a/ 15 = 26a/15

Example 2: Simplify 3/5x + 1/2x â€“ 1/4x

Solution:

Find the L C M of the expression = 20X

12 + 10 â€“ 5 = 17/20X

## SIMPLIFYING FRACTION

Example 1: Reduce 25X4Y3/35X3y3

solution

Divide through by 5X3Y3(the common factor )

= 5x/7

Example 2: Reduce 8X3Y2/6X3Z

Solution:

Divide through by 2X 3(the common factor)

4Y2/3Z

## MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTION

Example 1: Simplfy (X-2)/7 * 4/(X-2)

Solution : X â€“ 2/7 * 4/ X -2 (X-2) divides themselves

= 4/7

Example 2: Simplify 6X2/11y Ã· 18X/33Y2

Solution

6X2/11y * 33Y2/18X (division sign change to multiplication)

= XY

## FRACTIONS WITH BRACKETS

Example1: simplify the following (a) 2x + 5/4 + 2X â€“ 3 /4 (b) 7X â€“ 2 /4 + X â€“ 4 /6

Solution:

(a).Â  The L C M is 4

(2X + 5) + ( 2X â€“ 3)/4

4x + 2/4 = 2(2X + 1)/4

= 2X + 1/2

(b).Â  7X â€“ 2 /4 + X â€“ 4 /6

Solution:

The L C M = 12

21x â€“ 6 + 2X â€“ 6 â€“ 8 / 12

= 23X â€“ 14/ 12