This type of Algebra fraction involves replacing one value for
another. It might be an alphabet or a number.
Examples;
1. Given that x : y = 9 : 4, evaluate
Solution
Step
1
Note; The question above simply means that if x = 9 and y = 4
substitute for x and y in;
Step
2
Cancellation Process; 4 cancels each other;
Step
3
Cancellation Process; 6 goes in 60 gives 10;
10.
Note; This question simply means that if x =
,
substitute
for x in
.
Don’t
bother yourself about the word “express” it was just used to twist the question
and make it more technical.
For further explanation, it means anywhere you see x in
,
you
put the whole of
.
Ok,
let’s do this!
Step
1
Step
2
NUMERATOR;
Remove the bracket;
Step
3
Find the L.C.M which is 3a – 2;
Step
4
Collect like terms;
Step
5
DENOMINATOR;
Expand by using 2 to multiply all the values in the bracket;
Step
6
Find L.C.M which is 6a – 4;
Step
7
Collect like terms;
Step
8
Combine Numerator and Denominator together;
Step
9
Expand;
Remember the rule which says that when
dividing two algebra fractions sign must change to multiplication and the
fraction to the right becomes
inverse;
Step
10
Note; 6a – 4 and 10a + 2 are two digit values, so we look for
their common factors;
NUMERATOR;
6a – 4 ---the common
factor will be 2;
2(3a – 2)
Step
11
DENOMINATOR;
10a + 2 ---the common
factor will be 2;
2(5a + 1)
Step
12
Combine all of them together;
Step
13
Cancellation Process; 3a – 2 cancels each other and 2 cancels 2;
Step
1
This question similar to example 1 above, so we follow the same
process;
This means that x = 3 and y = 4.
Step
2
Cancellation Process; 2 goes in 2 gives 1 while 2 goes in 10 gives
5;
Step
1
Note; This question is similar to example 2 above, so we will
follow the same process;
This means that you are to replace x with
;
Step
2
NUMERATOR;
Remove the bracket;
Step
3
Find L.C.M which is 3m + 5;
Step
4
Collect like terms;
Note; 3m – 3m equals 0 and – 5 + 5 also
equals o;
Note; 0 divided by any value must give 0
as the answer, it’s a rule!;
0
Step
5
DENOMINATOR;
Remove the bracket;
Step
6
Find L.C.M which is 3m + 5;
Step
7
Collect like terms;
Step
8
Combine Numerator and Denominator together;
Step
9
Expand;
Step
10
Change sign to multiplication;
Note; 0 multiplied by any value must give
0 as the answer;
0.
Step
1
Simply put, replace P with 9 and q with 5 in
.
Step
2
Cancellation Process; 125 goes in 125 to give 1;
1