Adding and subtracting algebraic fraction
Exercise 2.8
1 Simplify:
3a 2a 5m m 9h 8h x x
a ------ + ------ b ------- – ---- c ------ – ------ d --- + ---
7 7 9 9 13 13 4 4
3n 3n 11k 3k 5c 2c 9d 3d
e ------ + ------ f --------- – ------ g ------ – ------ h ------ + ------
8 8 12 12 3 3 10 10
6b 8b 14w 4w 19e 9e 13s 9s
i ------ + ------ j ---------- – ------- k --------- – ------ l -------- + ------
7 7 15 15 24 24 16 16
2 Simplify:
5 2 8 7 10 4 12 3
a --- + --- b --- – --- c ------ + ------ d ------ – ------
x x p p 3y 3y 7q 7q
1 1 3 5 11 9 13 4
e ----- + ------ f ----- + ------ g ------ + ------ h -------- – ---------
2n 2n 4c 4c 5g 5g 12k 12k
17 a 9 a 4m 2m 7e 8e 19 t 15 t
i --------- – -------- j --------- + --------- k -------- + --------- l -------- – --------
10r 10r 15b 15b 20v 20v 16z 16z
■ Consolidation
3 Express these fractions with a common denominator, then simplify.
n n a a k k d d
a --- + --- b --- – --- c --- + ------ d --- – ------
2 4 3 9 3 12 5 15
y y t t b b h h
e --- + --- f --- – --- g --- – --- h ----- + ---
5 2 3 4 4 7 12 5
2c 3c 5m m 3r 4r 3u 6u
i ------ + ------ j ------- – ---- k ----- + ----- l ------ – ------
5 10 12 3 5 3 2 7
w 5w 7x 2x 3f 5f 11 s 8 s
m ---- + ------- n ------ – ------ o ------ + ------ p -------- – -----
4 6 6 9 10 8 12 9
4 Explain why each of the following answers is not correct.
5m 2m 7m 3w 2w 5w 4 3
a ------- + ------- = ------- b ------- + ------- = ------- c ----- + ----- = 1 2--5- a
9 9 18 5 3 8 5a 5a
5 Simplify each of the following.
1 3 2 1 17 2 13 2
a --- + ------ b ------ + ----- c -------- – ------ d --------- – ------
x 2x 3a 6a 20e 5e 12 p 3 p
3 2 4 3 2 4 3 5
e ----- + ------ f ------ – ------ g ----- – ----- h ----- + ------
2u 3u 5f 4f 3t 7t 5h 9h
5 c 11 c 9m 5m 9a 3a 5k 7k
i ------ + --------- j ------- – ------- k -------- – ------ l -------- + ------
4j 6j 8z 6z 10g 4g 12n 8n
Exercise 2.8
1 Simplify:
3a 2a 5m m 9h 8h x x
a ------ + ------ b ------- – ---- c ------ – ------ d --- + ---
7 7 9 9 13 13 4 4
3n 3n 11k 3k 5c 2c 9d 3d
e ------ + ------ f --------- – ------ g ------ – ------ h ------ + ------
8 8 12 12 3 3 10 10
6b 8b 14w 4w 19e 9e 13s 9s
i ------ + ------ j ---------- – ------- k --------- – ------ l -------- + ------
7 7 15 15 24 24 16 16
2 Simplify:
5 2 8 7 10 4 12 3
a --- + --- b --- – --- c ------ + ------ d ------ – ------
x x p p 3y 3y 7q 7q
1 1 3 5 11 9 13 4
e ----- + ------ f ----- + ------ g ------ + ------ h -------- – ---------
2n 2n 4c 4c 5g 5g 12k 12k
17 a 9 a 4m 2m 7e 8e 19 t 15 t
i --------- – -------- j --------- + --------- k -------- + --------- l -------- – --------
10r 10r 15b 15b 20v 20v 16z 16z
■ Consolidation
3 Express these fractions with a common denominator, then simplify.
n n a a k k d d
a --- + --- b --- – --- c --- + ------ d --- – ------
2 4 3 9 3 12 5 15
y y t t b b h h
e --- + --- f --- – --- g --- – --- h ----- + ---
5 2 3 4 4 7 12 5
2c 3c 5m m 3r 4r 3u 6u
i ------ + ------ j ------- – ---- k ----- + ----- l ------ – ------
5 10 12 3 5 3 2 7
w 5w 7x 2x 3f 5f 11 s 8 s
m ---- + ------- n ------ – ------ o ------ + ------ p -------- – -----
4 6 6 9 10 8 12 9
4 Explain why each of the following answers is not correct.
5m 2m 7m 3w 2w 5w 4 3
a ------- + ------- = ------- b ------- + ------- = ------- c ----- + ----- = 1 2--5- a
9 9 18 5 3 8 5a 5a
5 Simplify each of the following.
1 3 2 1 17 2 13 2
a --- + ------ b ------ + ----- c -------- – ------ d --------- – ------
x 2x 3a 6a 20e 5e 12 p 3 p
3 2 4 3 2 4 3 5
e ----- + ------ f ------ – ------ g ----- – ----- h ----- + ------
2u 3u 5f 4f 3t 7t 5h 9h
5 c 11 c 9m 5m 9a 3a 5k 7k
i ------ + --------- j ------- – ------- k -------- – ------ l -------- + ------
4j 6j 8z 6z 10g 4g 12n 8n
