1. Substitution 1. Calculate a + b – c If a = 10 b = 8 and c = 12
When g = 6 and h = 14
2t2 – 4t 2
t = 4 and t =6
½ w + ¼ h
w = 12 and h = 20

2. Letters For Numbers. Consider the algebraic expression below: a + b
If a = 6 and b = 7 , what would a + b equal ?
a + b
Because we have substituted numbers for letters we call this process :
a = 6
b = 7
a + b
Substitution =
= 13

3. Now look at the problems below:
Example 1.
Example 2.
Calculate a + b – c
Calculate r t
If a = 10 b = 8 and c = 12
If r = 4 and t = 8
Solution.
Solution.
a + b – c
r t
r t means r times t = 10
+ 8
– 12 = 4 x 8
= 18 – 12
= 32
= 6

4. Example 3
Example 4
Calculate 5w + 6t
Calculate 3h + 5j - 7
If w = 7 and t = 4
If h = 3 and j = 8
Solution.
Solution.
3h + 5j - 7
5w + 6t =
(5 x 7) +
(6 x 4) =
(3 x 3) +
(5 x 8)
- 7 =
= – 7
= 59
= 42

5. Fractions & Squares. Consider the expression : Example 1 Calculate:
It means add g and h together
When g = 6 and h = 14
then divide by 4
Solution.
Note : an expression such as
½ a or ¼ b means calculate a half a or a quarter of b by dividing in the usual way.
= 5

6. Consider the expression :
Example 2
Calculate :
This means square r by multiplying r times itself.
When r = 3
Solution. =
5 x
3 x 3
= 45

7. What Goes In The Box ? 1.
Calculate the value of the expressions below for the given substitutions .
(1) f + g
f = 6 and g = 14
(4) ½ w + ¼ h
w = 12 and h = 20 11 20
(2) 3r + 6w
r = 5 and w = 4
(5) 5r2 – 2f
r = 5 and f = 10 39
105
(3) 4g – 2h + 7
g = 8 and h = 9
(6) 2t2 – 4t 2
t = 4 and t =6 21 4