We have seen we can form expressions using numbers, mathematical operations and variables. If an expression contains a variable and we replace the variable with a particular number, this is called substitution. For example, if we had $4$4 full boxes of matches and $12$12 additional loose matches, then the expression $4m+12$4m+12 would give us the total number of matches where $m$m was the number of matches in a full box. If we were then told the additional information that there are $50$50 matches in a full box, we could evaluate the expression to find the total number of matches by making the substitution $m=50$m=50 in the expression:
$4m+12$4m+12  $=$=  $4\times50+12$4×50+12 
$=$=  $200+12$200+12  
$=$=  $212$212 
If $x=3$x=3, evaluate the expression $6x4$6x−4.
Think: This means that everywhere the letter $x$x has been written, we will replace it with the number $3$3.
Do:
$6x4$6x−4  $=$=  $6\times34$6×3−4 
$=$=  $184$18−4  
$=$=  $14$14 
If $x=6$x=6 and $y=0.5$y=0.5, evaluate the expression $6x2y12$6x−2y−12.
Think: The same process applies even if there is more than one unknown value, we will replace the letter $x$x with the number $6$6, and the letter $y$y with the number $0.5$0.5. We also need to keep the order of operations in mind when we do these kinds of calculations!
Do:
$6x2y12$6x−2y−12  $=$=  $6\times62\times0.512$6×6−2×0.5−12 
Replacing $x$x with $6$6, and $y$y with $0.5$0.5. 
$=$=  $36112$36−1−12 
Evaluating multiplication before subtraction. 

$=$=  $23$23 
If $a=3$a=3 and $b=4$b=−4, evaluate the expression $a\left(102b\right)$a(10−2b).
Think: Just like before, we will replace the letter $a$a with the number $3$3, and the letter $b$b with the number $4$−4. To avoid confusion with the operations in the expression we will place the negative number within brackets.
Do:
$a\left(102b\right)$a(10−2b)  $=$=  $3\left(102\times\left(4\right)\right)$3(10−2×(−4)) 
Replace $a$a with $3$3, and $b$b with $\left(4\right)$(−4). 
$=$=  $3\left(10+8\right)$3(10+8) 
Simplify the terms within the bracket. 

$=$=  $3\left(18\right)$3(18) 
Evaluate the bracket before multiplication. 

$=$=  $54$54 
When making a substitution and evaluating an expression be careful to follow order of operations, just as we did in our first chapter.
When substituting a negative value, place brackets around the value so the sign is not confused with operations in the expression.
Evaluate $8x+4$8x+4 when $x=2$x=2.
If $m=3$m=−3 and $n=4$n=4, evaluate the following:
$mn\left(mn\right)$mn−(m−n)
$m^2+9n$m2+9n
Evaluate $\frac{2a\times9}{5b}$2a×95b when $a=25$a=25 and $b=2$b=−2.
Find the exact value in simplest form.
Evaluate $7a^2$7a2 for $a=3$a=−3.
substitute values for the variables in a mathematical formula in given form to calculate the value of the subject of the formula