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