Substitution in Algebra Fractions

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