Multiplication of Algebraic Fractions
Simplify by 'reducing' the numbers and variables
=> "Crossing out " same variables and numbers from numerator/denominator of the algebraic Expression
Example
Simplify the algebraic Expression
a x 3b
9 a
Step 1 : Look for numbers that can be reduced => 3 and 1/9 can be reduced by 3
: a and 1/a can be reduced a/a = 1
(1a) a x 3b
3 9 a
(1b) a x b
3 a
Step 2 : Simplify
1 x b
3
= 1 b or b
3 3
Example
Simplify 3a x 2b
4 a
= 5a x 2b (Step 1 : Look and "cross" same variables/numbers)
2 4 a (Step 2 : Simplify)
= 5b
2
Example
Simplify 3a x 14b
7b 9a
= 3a x 214b = 2a
7b 39c 3c
Example
Simplify 2a2 x 5b
15b2 a
= 2a2 x 5b
315b2 a
= 2a
3b
Division of Algebraic fraction
First, to 'convert' the expressions to multiplication before simplifying the expression.
=> a ÷ c = a x d
b d b c
Example
Simplify 3b ÷ 2b
4 a
= 3b x a (Step 1 : Change the ÷ to multiply by 'flipping' the fraction)
4 2b (Step 2 : Look and "cross" same variables/numbers)
= 3a (Step 3 : Simplify)
8
Example
Simplify 3a ÷ 9a2
8 10
= 3a x 10 (Step 1 : Change the ÷ to multiply by 'flipping' the fraction)
8 9a
= 13ax 510 (Step 2 : Look and "cross" same variables/numbers)
48 39a2 (Step 3 : Simplify)
= 5a
12
Practice
Simplify the following
(a) 2a x 3a (b) b2 x 6b
9 16 2
(c) 3y x 4x2 (d) -3a2 x 4a
(e) 10y ÷ 4 (f) 4a ÷ 2
(g) -2a ÷ -a (h) b2 ÷ b
5 10 3
