Cambridge International Mathematics

Algebraic fractions (Chapter 16) 345

DIVISION

For example,

m

2

¥

n

6

=

m

2

£

6

n

fStep 1g

=

m£ 6

2 £n

fStep 2g

=

m£ 6

2 £n

fStep 3g

=

3 m

n

fStep 4g

Step 1: To divide by a fraction, multiply by

its reciprocal.

Step 2: Multiply numerators and multiply

denominators.

Step 3: Cancel any common factors.

Step 4: Write in simplest form.

Example 8 Self Tutor

Simplify: a

6

x

¥

2

x^2

b

8

p

¥ 2

a

6

x

¥

2

x^2

=

6

x

£

x^2

2

=

3 £ 2 £x£x

x£ 2

=3x

b

8

p

¥2=

8

p

£

1

2

=

8 £ 1

p£ 2

=

4

p

EXERCISE 16B

1 Simplify:

a

a

2

£

b

3

b

x

4

£

2

x

c

c

4

£

2

c

d

a

2

£

a

3

e

a

b

£

x

y

f

x

y

£

y

x

g

x

3

£x h

x

4

£

8

y

i

n

2

£

1

n^2

j

6

p

£

p

2

k

m

x

£

x

n

l x£

2

x

m

5

t

£t^2 n

μ

x

y

¶ 2

o

μ

4

d

¶ 2

p

a

b

£

b

c

£

c

a

2 Simplify:

a

x

3

¥

x

2

b

3

y

¥

6

y

c 3 ¥

1

x

d 6 ¥

2

y

e

3

p

¥

1

p

f

c

n

¥n g d¥

5

d

h x¥

x

3

i 1 ¥

a

b

j

3

d

¥ 2 k

4

x

¥

x^2

2

l

4

x

¥

8

x^2

m a¥

a^2

3

n

x

y

¥

x^2

y

o

5

a

¥

a

2

p

a^2

5

¥

a

3

1

3

11

(^111)
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