This document provides instruction on adding, subtracting, multiplying, and dividing numbers with negative signs. It begins by defining positive and negative numbers on a number line. It then demonstrates how to perform each operation with positive and negative numbers through examples. Rules are provided for multiplying and dividing with signs, such as two positives or a positive and negative multiplying to a positive or negative. The document encourages practicing these concepts through exercises in a textbook. Overall, it teaches the essential rules and mechanics for performing the basic arithmetic operations with positive and negative numbers.

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