Multiplying and Dividing Algebraic Fractions
Y10
To multiply algebraic fractions, multiply the numerator by themselves and the denominator by themselves.
Examples.
3ac
10
=
2v
2a + 2b
×
(a + b)
4uv
6p 10c
×
5
2pq
3a
c
×
5
2
=
6p1 210c
× 1
15
1 2pq
3
=
6c
q
=
1
1 2v1
(a + b)
×
1
2(a + b) 1
2
1 4uv
1
u
=
A.
Simplify the following.
1).
2a
b
×
5
3
2).
2u
v
×
3
4
3).
y
3x
×
6
2y
4).
8a
2b
×
3
12
5).
6).
10
3p
×
5
2pq
7).
8c
9c
×
4
3cd
8).
5v
18u2
×
6
3uv
9).
6p2 10q
×
q
20p
10). 5b × 14a
2
7a2b
12x
y
×
5
2x
11).
2v
3u + 3v
×
6(u + v)
4uv
12).
6r
5s + 5t
×
3s + 3t
2rt
13).
2
(2u + 1)
×
4u + 2
u2
14).
15a2
4a + 2b
×
2a + b
10a
15).
2wx
2u + 2v
×
2
2
u ‒v
4w
16).
2a
a2 ‒ b2
×
a‒b
6ab
To divide algebraic fractions multiply by the reciprocal of the divisor.
Examples
=
3
2a
÷
7
c
3p 2pq
÷
4
12c
2v
8v
÷
3 (a ‒ b) 6a ‒ 6b
2a
c
×
7
3
3p 12c
×
4
2pq
2v
6a ‒ 6b
×
3(a ‒ b) 8v
2ac
21
=
=
3p1 312c
× 1
2pq
14
=
9c
2q
2v 1 1 2 6(a ‒ b) 1
× 24 1
1 3(a ‒ b) 1
8v
1
=
1
2
B.
Simplify the following.
1).
2a
a
÷
7
14
2).
4
2x
÷
3
y
3).
2
6
÷ 2
a
a
4).
uv
v
÷
5
15
5).
6).
3p 6pq
÷
4
12q
7).
2s
8s2
÷
t
5t
8).
2p
p2q
÷
5
10q
9).
bd 2bd2
÷
4c 12c2
10). 9g2 6gh
÷
8f 12f
2a2 ab
÷
8
4
11).
8a
6a
÷
(a ‒ b)
3a ‒ 3b
12).
3x
6x
÷
4(p + 2)
3p + 6
13).
2p ‒ 4
7p ‒ 14
÷
3p ‒ 9
5p ‒ 15
14).
6x
x ‒ y
12x2
x2 ‒ y2
15).
2p2
12pq
÷
2
2
p ‒q
6p + 6q
16).
5
2x ‒ 1
÷
2x + 1
4x2 ‒ 1
÷
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