Exercise 2.9
1 Simplify:
a b u u a c 1 1
a --- × --- b --- × --- c --- × --- d --- × ---
3 2 3 4 b d p q
1 1 4c d 9m 3n 5 7
e --- × ------ f ------ × --- g ------- × ------ h ------ × ------
x 4x 5 3 7 4 6x 8x
2 Simplify:
x 4 v 6 t v 1 1
a --- ÷ --- b --- ÷ --- c --- ÷ ---- d --- ÷ ---
5 y 2 v u w g h
1 3e 5 f 10a 3b 4 3h
e --- ÷ 2s f ------ ÷ ------ g --------- ÷ ------ h ------ ÷ ------
s 7 6 11 4 5h 13
■ Consolidation
3 Simplify each of the following by at first cancelling common factors.
n 2 a 8 3 d 3 2x
a --- × --- b --- × --- c --- × ------ d --- × ------
3 n 4 b c 15 x 7
ab cd 5a b 8d 21 4e 5f
e ------ × ------ f ------ × --------- g ------ × ------ h --------- × ---------
e bc 3b 10a 7c 8e 10 f 12e
9t 7u 15w 18x 11i 21h 44r 10 p
i --------- × ----------- j ---------- × ---------- k --------- × ---------- l ------------- × -----------
14v 18tu 27y 25w 12h 22ij 35 pq 99rs
4 Express each of these as a multiplication, then simplify.
x x m n 5 20 6 11s
a --- ÷ --- b ---- ÷ --- c --- ÷ ------ d --- ÷ --------
5 3 2 6 u v r 3r
ef eh 10k 5m 4s 16s 9w 27w
e ----- ÷ ------ f --------- ÷ ------- g ----- ÷ -------- h --------- ÷ ----------
g hi 3 12 7t t 28v 7v
4 p 20 pr 12c 16c 12e 20ef 42xy 49yz
i --------- ÷ ------------ j --------- ÷ --------- k --------- ÷ ----------- l ------------ ÷ -----------
33q 11r 45b 25a 63d 99d 55x 60w
5 Explain why each of the following solutions is incorrect.
1
5a 210 2a 4c 21 3 4
a ------ × --------- = ------ b ------ ÷ ------ = ---
3b 11b 33 71 c 3
6 Simplify each of the following.
p2 q2 5m 2n 2a 2 7b ab 2 pq
a ----- × ----- b --------- × ---------2- c -------2- × ------ d - × ------
--------
q p 4np 3m 3b 5a p 2 q ab
r 2 s rs 8e 24e 2 12x 2 y 28xy 2 24tu 2 36t 2u
e ------2- ÷ -------- f -----------2- ÷ ----------- g -------------- ÷ -------------- h ------------- ÷ -------------
tu tuv 21f 35f 25ab 15bc 33vw 55wx
1 Simplify:
a b u u a c 1 1
a --- × --- b --- × --- c --- × --- d --- × ---
3 2 3 4 b d p q
1 1 4c d 9m 3n 5 7
e --- × ------ f ------ × --- g ------- × ------ h ------ × ------
x 4x 5 3 7 4 6x 8x
2 Simplify:
x 4 v 6 t v 1 1
a --- ÷ --- b --- ÷ --- c --- ÷ ---- d --- ÷ ---
5 y 2 v u w g h
1 3e 5 f 10a 3b 4 3h
e --- ÷ 2s f ------ ÷ ------ g --------- ÷ ------ h ------ ÷ ------
s 7 6 11 4 5h 13
■ Consolidation
3 Simplify each of the following by at first cancelling common factors.
n 2 a 8 3 d 3 2x
a --- × --- b --- × --- c --- × ------ d --- × ------
3 n 4 b c 15 x 7
ab cd 5a b 8d 21 4e 5f
e ------ × ------ f ------ × --------- g ------ × ------ h --------- × ---------
e bc 3b 10a 7c 8e 10 f 12e
9t 7u 15w 18x 11i 21h 44r 10 p
i --------- × ----------- j ---------- × ---------- k --------- × ---------- l ------------- × -----------
14v 18tu 27y 25w 12h 22ij 35 pq 99rs
4 Express each of these as a multiplication, then simplify.
x x m n 5 20 6 11s
a --- ÷ --- b ---- ÷ --- c --- ÷ ------ d --- ÷ --------
5 3 2 6 u v r 3r
ef eh 10k 5m 4s 16s 9w 27w
e ----- ÷ ------ f --------- ÷ ------- g ----- ÷ -------- h --------- ÷ ----------
g hi 3 12 7t t 28v 7v
4 p 20 pr 12c 16c 12e 20ef 42xy 49yz
i --------- ÷ ------------ j --------- ÷ --------- k --------- ÷ ----------- l ------------ ÷ -----------
33q 11r 45b 25a 63d 99d 55x 60w
5 Explain why each of the following solutions is incorrect.
1
5a 210 2a 4c 21 3 4
a ------ × --------- = ------ b ------ ÷ ------ = ---
3b 11b 33 71 c 3
6 Simplify each of the following.
p2 q2 5m 2n 2a 2 7b ab 2 pq
a ----- × ----- b --------- × ---------2- c -------2- × ------ d - × ------
--------
q p 4np 3m 3b 5a p 2 q ab
r 2 s rs 8e 24e 2 12x 2 y 28xy 2 24tu 2 36t 2u
e ------2- ÷ -------- f -----------2- ÷ ----------- g -------------- ÷ -------------- h ------------- ÷ -------------
tu tuv 21f 35f 25ab 15bc 33vw 55wx
