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
NOT Plus & Minus numbers
Yes!
NO!
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
Adding numbers
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+3 +2
+3 + + 2 +5= + 5
Adding numbers
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
-3-2
-3 + - 2
-5
= - 5
Adding numbers
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+5
+5 + - 2+3
= + 3
-2
Adding numbers
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+2 + - 5
+2
= - 3-3
-5
Try these
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
a) +3 + -7b) +6 + -3c) -2 + -4d) -1 + +6
-4+3-6
+5
Think of 1st number as a starting point
Think of 2nd number as a move left or right
Subtracting numbers
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+5
+5 - + 2 = + 3 +2
+3
Subtracting numbers
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+5
+5 - + 2 = + 3 +3 -2
- +2 is just -2
Subtracting numbers
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+3
+3 - + 5 = - 2
-5
-2
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SUBTRACT a NEGATIVE means ADD
Subtract a NEGATIVE number
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+3
+3 + - 2 = +1
-2
+1So
+1 - - 2 = +3
Try these
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
a) +3 - -2b) +1 - -3c) -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
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
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
Task
• AQA Intermediate Text [Green]– Page 36 Exercise 4.3– Write Questions and answers
Multiply & Divide with Negative numbers
Multiplication
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+2
+3 x + 2
+2 +2
= + 6
-2
Multiplication
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
+3 x - 2 = - 6
-2 -2
-2
Multiplication
0 1 2 4 5 63-6 -5 -4 -3 -2 -1
-3 x - 2 = + 6
-2 -2
+2+2+2
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
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
Task
• Exercise 4.4 page 38
• Review Exercise
Puzzle
• Can you complete this puzzle?
Click Here
Using negative numbers in formulae
• We call putting a number into an expression Substitution
Examples
If t = f + 7
If f = 5
If f = -5
t = 5 + 7
t = f + 7
t = 12
t = -5 + 7 t = 2
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
Examples
If t = 5
If t = -5
S = 5x5
S = t2
t2 = t x t
S = 25
S = -5x-5 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