1. Simplifying Algebra • Multiplication and Division

2. Multiplication Start with what we know about numbers… is lots of and can be written as So if we had that is just In algebra, we do not need the times between letters and numbers, so we would say

3. Multiplication Just like numbers and letters, two different letters do not need the times symbol between them. So Numbers multiply as you would expect:

4. Multiplication Summing up: To multiply algebraic terms: • Multiple the numbers together first e.g. 3p x 4 = 12p • Then multiply the variables e.g. a x b = ab • Add the power of the same variable e.g. a2 x a3 = a5 • Two negatives cancel e.g. -2 x -a = 2a Remember: • numbers go before the letters • letters go in alphabetic order

5. Multiplication Practice: 1) 3m x 6 =   2) -4w x 5q = 3) -3p x-2 = 4) 4p x p = 5) 2 x p x p = 6) q x q2 = 7) 2m2 x 4m3 8) 2q2 x 3q x 2q =   9) 6m2 x 3d2 x 2m =  10) -3q x 4t2 x 8t x -q =

6. Division Division in algebra works in the same way as it did in number. We just do not always end up with a number for an answer. is usually written as to avoid the use of decimals. We will use the same idea in algebraic division. i.e. always write in fraction form

7. Division The order matters! The above is divided by . This is divided by : i.e. is not the same as

8. Division Numbers here only change if the number fraction can be simplified.

9. Division Review = = = = 3 = = = -3 = 3 = 3-1 = = a-1 a

10. Summing up: To divide algebraic terms: • Divide the numbers together first (simplify)e.g. 12p ÷ 4 = 3p • Simplify the variables e.g. a2÷ ab = • Subtract the powers of the same variable e.g. a5÷ a2= a3 • Two negatives cancel e.g. -2a ÷-a = 2 Division

11. Division Practice: 1) 10b ÷ 2 =   2) 15c ÷ 5c = 3) 24de ÷ 6d = 4) 4p ÷p = 5) 20p2÷ 4p = 6) q2÷ q = 7) 4m2÷ 8m = 8) 8m ÷ 24 =   9) 6pq ÷ 3qr =  10) 7pq ÷ 2q =