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```Directed
Number
Using Negative
Numbers
Objective
• To able to
– Add & Subtract negative numbers
– Multiply & Divide negative numbers
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!
From 0 on a number line
+5
-5
5 to right
+3
5 to left
-6 -5
-4 -3
-2 -1
0
1
3 to right
2
3
4
5
6
+3
+
+2
=
+5
+5
+3
-6 -5
-4 -3
-2 -1
0
1
+2
2
3
4
5
6
+
-2
2
3
=
-5
-5
-2
-6 -5
-4 -3
-3
-2 -1
0
1
4
5
6
+5
+
-2
=
+3
+3
+5
-6 -5
-4 -3
-2 -1
0
1
2
-2
3
4
5
6
+2
+
-5
2
3
=
-3
-3
-5
-6 -5
-4 -3
-2 -1
0
+2
1
4
5
6
Try these
+3
-7
a) +
b) +6 + -3
c) -2 + -4
+
d) 1 + 6
-6 -5
-4 -3
Think of 1st number as a starting point
Think of 2nd number as a move left or right
-4
+3
-6
+5
-2 -1
0
1
2
3
4
5
6
Subtracting numbers
+5
-
+2
=
+3
+2
+5
+3
-6 -5
-4 -3
-2 -1
0
1
2
3
4
5
6
Subtracting numbers
+5
-
+2
=
+3
+3
+5
- +2 is just -2
-6 -5
-4 -3
-2 -1
-2
0
1
2
3
4
5
6
Subtracting numbers
+3
-
+5
=
-2
-2
-5
-6 -5
-4 -3
-2 -1
0
+3
1
2
3
4
5
6
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 number
+3
+
-2
=
+1
=
+3
So
+1
-
-2
+1
+3-2
-6 -5
-4 -3
-2 -1
0
1
2
3
4
5
6
Try these
a) +3 - -2
b) +1 - -3
c) -2 - +4
-6 -5
-4 -3
Think of 1st number as a starting point
Think of 2nd number as a move left or right
+5
+4
-6
-2 -1
Think of SUBTRACT as a
REVERSE of DIRECTION
0
1
2
3
4
5
6
Basic Rules
+ +3 = + 3
ADD a NEGATIVE means SUBTRACT + -3 = - 3
SUBTRACT a POSITIVE means SUBTRACT - +3 = - 3
- -3 = + 3
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
• AQA Intermediate Text [Green]
– Page 36 Exercise 4.3
Multiply &
Divide with
Negative
numbers
Multiplication
+3
x
+2
=
+6
+2
-6 -5
-4 -3
-2 -1
0
1
+2
2
3
+2
4
5
6
Multiplication
+3
-2
-6 -5
x
-2
-2
-4 -3
=
-6
-2
-2 -1
0
1
2
3
4
5
6
Multiplication
-3
x
-2
=
+6
+2
+2
+2
-2
-2
-2
-6 -5
-4 -3
-2 -1
0
1
2
3
4
5
6
Rule for Multiplication
POSITIVE x POSITIVE = POSITIVE
+2
x +3 = +6
POSITIVE x NEGATIVE = NEGATIVE
+2
x -3 = -6
NEGATIVE x POSITIVE = NEGATIVE
-2
x +3 = -6
NEGATIVE x NEGATIVE = POSITIVE
-2
x -3 = +6
If SAME SIGN, answer is POSITIVE
Rule for Division
Inverse of Multiplication
POSITIVE ÷ POSITIVE = POSITIVE
+18
÷ +3 = +6
POSITIVE ÷ NEGATIVE = NEGATIVE
+18
÷ -3 = -6
NEGATIVE ÷ POSITIVE = NEGATIVE
-18
÷ +3 = -6
NEGATIVE ÷ NEGATIVE = POSITIVE
-18
÷ -3 = +6
If SAME SIGN, answer is POSITIVE
• Exercise 4.4 page 38
• Review Exercise
Puzzle
• Can you complete this puzzle?
Using negative numbers in
formulae
• We call putting a number into an
expression Substitution
Examples
t=f+7
If t = f + 7
If f = 5
t=5+7
If f = -5 t = -5 + 7
t = 12
t=2
Examples
t = 3q + 4
If t = 3q + 4
If q = 5 t = 3x5 + 4
3q = 3 x q
t = 15 + 4 t = 19
If q = -5 t = 3x-5 + 4 t = -15 + 4 t = -11
NOT t = 35 + 4 = 39
Examples
S = t2
t2 = t x t
If t = 5
S = 5x5
If t = -5 S = -5x-5
S = 25
S = 25
Exercises
• Referring to your notes on negatives
• Attempt Exercises in Keymaths 8/3 page
126 onwards
– 6:5
– 6:6
– 6:7
– 6:8
```
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