Everything Maths Grade 10

1.8 Simplification of fractions EMAQ

We have studied procedures for working with fractions in earlier grades.

1.

a

b



c

d

=

ac

bd

(b̸= 0;d̸= 0)

2.

a

b

+

c

b

=

a+c

b

(b̸= 0)

3.

a

b



c

d

=

a

b



d

c

=

ad

bc

(b̸= 0;c̸= 0;d̸= 0)

Note:dividing by a fraction is the same as multiplying by the reciprocal of the fraction.

In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,

x^2 + 3x

x+ 3

has a quadratic binomial in the numerator and a linear binomial in the denominator. We have to apply the
different factorisation methods in order to factorise the numerator and the denominator before we can simplify
the expression.

x^2 + 3x

x+ 3

=

x(x+ 3)

x+ 3

=x (x̸=3)

Ifx= 3 then the denominator,x+ 3 = 0and the fraction is undefined.

VISIT:

This video shows some examples of simplifying fractions.

See video:2DNVatwww.everythingmaths.co.za

Worked example 18: Simplifying fractions

QUESTION

Simplify:

axb+xab

ax^2 abx

; (x̸= 0;x̸=b)

SOLUTION

Step 1: Use grouping to factorise the numerator and take out the common factoraxin the denominator

(axab) + (xb)

ax^2 abx

=

a(xb) + (xb)

ax(xb)

Step 2: Take out common factor(xb)in the numerator

=

(xb) (a+ 1)

ax(xb)

Chapter 1. Algebraic expressions 31