NOTE

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
Positive & Negative numbers
NOT Plus & Minus numbers
Yes!
NO!

4. From 0 on a number line
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+
3
+
5
-
5
3 to right
5 to right
5 to left

5. Adding numbers
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+
3 +
2
+
3 + +
2 +
5
= +
5

6. Adding numbers
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
-
3-
2
-
3 + -
2
-
5
= -
5

7. Adding numbers
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+
5
+
5 + -
2 +
3
= +
3
-
2

8. Adding numbers
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+
2 + -
5
+
2
= -
3
-
3
-
5

9. Try these
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
a) +
3 + -
7
b) +
6 + -
3
c) -
2 + -
4
d) -
1 + +
6
-
4
+
3
-
6
+
5
Think of 1st
number as a starting point
Think of 2nd
number as a move left or right

10. Subtracting numbers
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+
5
+
5 - +
2 = +
3 +
2
+
3

11. Subtracting numbers
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+
5
+
5 - +
2 = +
3 +
3 -
2
- +
2 is just -2

12. Subtracting numbers
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+3
+
3 - +
5 = -
2
-
5
-
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 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+3
+
3 + -
2 = +
1
-
2
+
1
So
+
1 - -
2 = +
3

15. Try these
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
a) +3 - -2
b) +1 - -3
c) -2 - +4
+
5
+
4
-
6
Think of 1st
number as a starting point
Think of 2nd
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 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+
2
+
3 x +
2
+
2 +
2
= +
6

21. -
2
Multiplication
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
+
3 x -
2 = -
6
-
2 -
2

22. -
2
Multiplication
0 1 2 4 5 63-
6 -
5 -
4 -
3 -
2 -
1
-
3 x -
2 = +
6
-
2 -
2
+
2+
2+
2

23. Rule for Multiplication
POSITIVE x POSITIVE = POSITIVE +
2 x +
3 = +
6
+
2 x -
3 = -
6POSITIVE x NEGATIVE = NEGATIVE
-
2 x -
3 = +
6NEGATIVE 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 = -
6POSITIVE ÷ NEGATIVE = NEGATIVE
-
18 ÷ -
3 = +
6NEGATIVE ÷ 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 + 7 t = 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 + 4 t = 19
t = 3x-
5 + 4 t = -
15 + 4 t = -
11
NOT t = 35 + 4 = 39

30. Examples
If t = 5
If t = -
5
S = 5x5
S = t2
t2
= t x t
S = 25
S = -
5x-
5 S = 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