1. Substitution 1. Calculate a + b – c If a = 10 b = 8 and c = 12 When g = 6 and h = 14 2t 2 – 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 a = 6b = 7 a + b = 6 + 7 = 13 Because we have substituted numbers for letters we call this process : Substitution

3. Now look at the problems below: Example 1. Calculate a + b – c If a = 10 b = 8 and c = 12 Solution. a + b – c =10+ 8– 12 = 18 – 12 = 6 Example 2. Calculate r t If r = 4 and t = 8 Solution. r tr t means r times t =4x8 = 32

4. Example 3 Calculate 5w + 6t If w = 7 and t = 4 Solution. 5w + 6t =(5 x 7)+(6 x 4) = 35 + 24 = 59 Example 4 Calculate 3h + 5j - 7 If h = 3 and j = 8 Solution. 3h + 5j - 7 =(3 x 3)+(5 x 8)- 7 = 9 + 40 – 7 = 42

5. Fractions & Squares. Consider the expression : It means add g and h together then divide by 4 Example 1 Calculate: When g = 6 and h = 14 Solution. = 5 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.

6. Consider the expression : This means square r by multiplying r times itself. Example 2 Calculate : When r = 3 Solution. =5 x3 x3 = 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 (2) 3r + 6w r = 5 and w = 4 (3) 4g – 2h + 7 g = 8 and h = 9 (4) ½ w + ¼ h w = 12 and h = 20 (5) 5r 2 – 2f r = 5 and f = 10 (6) 2t 2 – 4t 2 t = 4 and t =6 20 39 21 11 105 4