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

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 = 6 + 7 = 13

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

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 = 35 + 24 = 9 + 40 – 7 = 59 = 42

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

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

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