Algebraic Processes

Substituting Numbers:

The value of an expression such as x + 8  can be found by replacing x with a given number. This is called substitution. For example:  

For the expression x + 8 

If  x = 8,  then  8 + 8  = 16

If x = 10, then 10 + 8  =  18

Example 1

Find the value of each of the following mentally when  x = 3

i. \( \scriptsize x + 10 \\ \rightarrow \scriptsize 3 + 10 \\ = \scriptsize 13 \)

ii. \( \scriptsize x\: – \: 1 \\ \rightarrow \scriptsize 3\: – \: 1 \\ = \scriptsize 2 \)

iii. \( \scriptsize x \: \times \: 8 \\ \rightarrow \scriptsize 3 \: \times \: 8 \\ = \scriptsize 24 \)

iv. \( \scriptsize x \: \div \: 9 \\ \rightarrow \scriptsize 3 \: \div\: 9 \\ = \frac{3}{9} \\ = \frac{1}{3} \)

v. \( \scriptsize x \: \times \: 3 + 1 \\ \rightarrow \scriptsize 3 \: \times \: 3 + 1 \\ = \scriptsize 10 \)

Example 2

Find the value of each of the following mentally when  y = 20

i. \( \scriptsize y + y + 2 \\ \rightarrow \scriptsize 20 + 20 + 2 \\ = \scriptsize 42 \)

ii. \( \scriptsize (y \: – \: y ) \: + \: 5 \\ \rightarrow \scriptsize (20 \: – \: 20) \: + \: 5 \\ \scriptsize = 0 \: + \: 5 \\ \scriptsize = 5 \)

iii. \( \scriptsize (y \: – \: 10) \: \times \: 8 \\ \rightarrow \scriptsize (20 \: – \: 10) \: \times \: 8 \\ = \scriptsize 10 \: \times \: 8 \\ \scriptsize = 80 \)

iv. \( \scriptsize y \: \div \: y \: + \: 25 \\ \rightarrow \scriptsize 20 \: \div \: 20 \: + \: 25 \\ = \scriptsize 1 + 25 \\= \scriptsize 26 \)

v. \( \scriptsize y \: – \: y \: + \: 8 \\ \rightarrow \scriptsize 20 \: – \: 20 \: + \: 8 \\ \scriptsize = 20 \: – \: 28 \\ \scriptsize = \; – 8 \)