1. Directed Number Using Negative Numbers

2. Objective To able to –Add & Subtract negative numbers –Multiply & Divide negative numbers

3. A Directed Number… Is one which has a + or – sign attached To show its direction +2+2 -2-2 Positive & Negative numbers NOT Plus & Minus numbers Yes! NO!

4. From 0 on a number line 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 +3+3 +5+5 -5-5 3 to right 5 to right 5 to left

5. Adding numbers 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 +3+3 +2+2 + 3 + + 2 +5+5 = + 5

6. Adding numbers 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 -3-3 -2-2 - 3 + - 2 -5-5 = - 5

7. Adding numbers 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 +5+5 + 5 + - 2 +3+3 = + 3 -2-2

8. Adding numbers 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 + 2 + - 5 +2+2 = - 3 -3-3 -5-5

9. Try these 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 a) + 3 + - 7 b) + 6 + - 3 c) - 2 + - 4 d) - 1 + + 6 -4-4 +3+3 -6-6 +5+5 Think of 1 st number as a starting point Think of 2 nd number as a move left or right

10. Subtracting numbers 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 +5+5 + 5 - + 2 = + 3 +2+2 +3+3

11. Subtracting numbers 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 +5+5 + 5 - + 2 = + 3 +3+3 -2-2 - + 2 is just -2

12. Subtracting numbers 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 +3 + 3 - + 5 = - 2 -5-5 -2-2

13. 4 Volunteers with WHITEBOARDS How good a teacher am I? Give a mark between 1 and 10 Hold up your boards – show class SUBTRACT a NEGATIVE means ADD

14. Subtract a NEGATIVE number 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 +3 + 3 + - 2 = + 1 -2-2 +1+1 So + 1 - - 2 = + 3

15. Try these 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 a) +3 - -2 b) +1 - -3 c) -2 - +4 +5+5 +4+4 -6-6 Think of 1 st number as a starting point Think of 2 nd number as a move left or right Think of SUBTRACT as a REVERSE of DIRECTION

16. Basic Rules ADD a POSITIVE means ADD ADD a NEGATIVE means SUBTRACT SUBTRACT a POSITIVE means SUBTRACT SUBTRACT a NEGATIVE means ADD + + 3 = + 3 + - 3 = - 3 - + 3 = - 3 - - 3 = + 3

17. Sometimes Textbooks give a number in a bracket 5 - ( + 2)= 5 - + 2 5 - (+2) Sometimes Textbooks give the sign NOT raised = 5 - ( + 2)= 5 - + 2

18. Task AQA Intermediate Text [Green] –Page 36 Exercise 4.3 –Write Questions and answers

19. Multiply & Divide with Negative numbers

20. Multiplication 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 +2+2 + 3 x + 2 +2+2 +2+2 = + 6

21. -2-2 Multiplication 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 + 3 x - 2 = - 6 -2-2 -2-2

22. -2-2 Multiplication 0 124 56 3 -6-6 -5-5 -4-4 -3-3 -2-2 -1 - 3 x - 2 = + 6 -2-2 -2-2 +2+2 +2+2 +2+2

23. Rule for Multiplication POSITIVE x POSITIVE = POSITIVE + 2 x + 3 = + 6 + 2 x - 3 = - 6 POSITIVE x NEGATIVE = NEGATIVE - 2 x - 3 = + 6 NEGATIVE x NEGATIVE = POSITIVE NEGATIVE x POSITIVE = NEGATIVE - 2 x + 3 = - 6 If SAME SIGN, answer is POSITIVE

24. Rule for Division POSITIVE ÷ POSITIVE = POSITIVE + 18 ÷ + 3 = + 6 + 18 ÷ - 3 = - 6 POSITIVE ÷ NEGATIVE = NEGATIVE - 18 ÷ - 3 = + 6 NEGATIVE ÷ NEGATIVE = POSITIVE NEGATIVE ÷ POSITIVE = NEGATIVE - 18 ÷ + 3 = - 6 If SAME SIGN, answer is POSITIVE Inverse of Multiplication

25. Task Exercise 4.4 page 38 Review Exercise

26. Puzzle Can you complete this puzzle? Click Here

27. Using negative numbers in formulae We call putting a number into an expression Substitution

28. Examples If t = f + 7 If f = 5 If f = - 5 t = 5 + 7 t = f + 7 t = 12 t = - 5 + 7t = 2

29. Examples If t = 3q + 4 If q = 5 If q = - 5 t = 3x5 + 4 t = 3q + 4 3q = 3 x q t = 15 + 4t = 19 t = 3x - 5 + 4t = - 15 + 4t = - 11 NOT t = 35 + 4 = 39

30. Examples If t = 5 If t = - 5 S = 5x5 S = t 2 t 2 = t x t S = 25 S = - 5x - 5S = 25

31. Exercises Referring to your notes on negatives Attempt Exercises in Keymaths 8/3 page 126 onwards –6:5 –6:6 –6:7 –6:8