Directed Number

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
Yes!
NOT Plus Minus numbers
NO!
4
From 0 on a number line
5 to right
5 to left
3 to right
5
Adding numbers
5
3 2
6
Adding numbers
- 5
-3 - 2
7
Adding numbers
3
5 - 2
8
Adding numbers
- 3
2 - 5
9
Try these
Think of 1st number as a starting point
Think of 2nd number as a move left or right

• 3 -7
• 6 -3
• -2 -4
• -1 6

-4
3
-6
5
10
Subtracting numbers
3
5 - 2
11
Subtracting numbers
3
5 - 2
12
Subtracting numbers
- 2
3 - 5
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
3 - 2 1
So 1 - - 2
3
15
Try these
Think of 1st number as a starting point
Think of 2nd number as a move left or right

• 3 - -2
• 1 - -3
• -2 - 4

5
Think of SUBTRACT as a REVERSE of DIRECTION
4
-6
16
Basic Rules
3 3
ADD a POSITIVE means ADD
-3 - 3
ADD a NEGATIVE means SUBTRACT
- 3 - 3
SUBTRACT a POSITIVE means SUBTRACT
- -3 3
SUBTRACT a NEGATIVE means ADD
17
Sometimes Textbooks give a number in a bracket
5 - (2)
5 - 2
Sometimes Textbooks give the sign NOT raised
5 - (2)
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
6
3 x 2
21
Multiplication
- 6
3 x - 2
22
Multiplication
6
-3 x - 2
23
Rule for Multiplication
2 x 3 6
POSITIVE x POSITIVE POSITIVE
2 x -3 -6
POSITIVE x NEGATIVE NEGATIVE
NEGATIVE x POSITIVE NEGATIVE
-2 x 3 -6
-2 x -3 6
NEGATIVE x NEGATIVE POSITIVE
If SAME SIGN, answer is POSITIVE
24
Rule for Division
Inverse of Multiplication
18 3 6
POSITIVE POSITIVE POSITIVE
18 -3 -6
POSITIVE NEGATIVE NEGATIVE
NEGATIVE POSITIVE NEGATIVE
-18 3 -6
-18 -3 6
NEGATIVE NEGATIVE POSITIVE
If SAME SIGN, answer is POSITIVE
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
t f 7
If t f 7
If f 5
t 5 7
t 12
t -5 7
t 2
If f -5
29
Examples
t 3q 4
If t 3q 4
If q 5
t 3x5 4
t 15 4
t 19
t 3x-5 4
t -15 4
t -11
If q -5
30
Examples
S t2
If t 5
S 5x5
S 25
S -5x-5
S 25
If t -5
31
Exercises

• Referring to your notes on negatives
• Attempt Exercises in Keymaths 8/3 page 126
  onwards
• 65
• 66
• 67
• 68