Worksheet: Adding And Subtracting Algebraic Fractions Page 2
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1
2
33.
Multiplying together the denominators always gives a usable common denominator.
However if the two denominators have common factors you can find a simpler
common denominator by finding the common factors of them and then multiplying
this by the remaining factors. This can be thought of as the simplest common
multiple of the two denominators. For example the simplest common multiple of t 4
and t 2 is t 4 .
Find the simplest common multiples for the following expressions:
2
(a)
2 and 2
x
(b)
2 and x
x
(c)
x and x
2
5
4
2
3
(d)
9 and 3
(e)
abc and ab and a
(f)
and
a
bc
a
b
c
4.
If you do not use the simplest common denominator then you will still get the right
answer, but your answers will have to be cancelled down. Therefore it is more
effective to use the simplest common multiple when adding or subtracting fractions.
Using the simplest common multiples you found in question 3 to calculate:
1
1
1
1
1
1
(a)
(b)
(c)
2
2
x
2
2
x
x
x
x
7
y
x
2
d
3
f
1
5
1
(d)
(e)
(f)
2
5
4
2
3
9
3
abc
ab
a
a
bc
a
b
c
5.
Remember you may only cancel down a fraction if the same letter or number is a
2
x
factor of both the numerator and the denominator. For example
cannot be
2
x
cancelled down as neither 2 nor x are factors of the numerator.
Bearing this in mind, add or subtract:
1
1
1
1
1
x
x
1
x
1
x
3
(a)
(b)
(c)
(d)
2
x
x
1
2
2
x
x
x
2
x
1
ab
a
b
x
y
ab
a
(e)
(f)
(g)
2
3
2
2
3
2
2
2
c
d
bc
d
c
d
bc
d
c
d
y
x
6.
When adding a non-fraction to a fraction, it may be helpful to think of the non-fraction
as a fraction with denominator 1.
Add the following:
1
1
1
1
5
(a)
1
(b)
x
(c)
x
(d)
x
1
x
2
5
x
x
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