**ADDITION AND SUBTRACTION OF DIRECTED NUMBERS**

Directed numbers are the positive and negative numbers in any given number line e.g

-4 -3 -2 -1 0 1 2 3 4

The (+) and (-) signs show the direction from the origin (o). To add a positive number move to the right on the number line

Addition

-2 -1 0 +1 +2 +3 +4

To subtract a positive number, move to the left on the number line

Subtraction

-2 -1 0 +1 +2 +3 +4

* *

**Worked examples**

Simplify the following

- (-2_+(-4)
- (-6)+(+6)+0

iii. 6-(-3)-(-4)

** **

**Solution **

- 1) (-2)+(-4)=2+4=-6

-6 -5 -4 -3 -2 -1 +1 +2

- (-6)+(-6)+0= 6+6+0 =- 0

-6 -5 -4 -3 -2 -1 0 +1 +2 +3

- -(-3)-(-4)= 6+3+4 =- 13

-1 0 +1 +2 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13

** **

**EVALUATION **

Simplify the following

- (+6)-(+10)
- 12-(+3)-8
- (-5)+(-5)+(-5)
- (-8)-(-2)+(-2)

** **

**MULTIPLICATION OF DIRECTED NUMBERS**

Multiplication is a short way of writing repeated addition e.g. 3×4=4+4+4 =12.

When directed numbers are multiplied together, two like signs give a positive result, while two unlike signs give a negative result in general

(i) (+a) x (-b) =+ab

(ii) (-a) x (-b) =+ab

(iii) (+a) x(-b)=-ab

(iv) (-a) x (+b) =-ab

* *

**Worked examples**

Simplify the following

(a) (+1/2) x (+1/4) = +1/8

(b) (+17) x (-3) = -51

(c ) (- 91/3) x (+2/5) = -56/15 = -311/15

**DIVISION OF DIRECTED NUMBERS**

The rules of multiplication of directed numbers also apply to the division of directed numbers

- (+a) ÷ (+b)=+(a/b)
- (-a) ÷ (-b)=+(a/b)

iii. (+a) ÷ (-b) = -(a/b)

- (-a)÷(+b) = -(a/b)

**Class work**

- Simplify the following

- (-36) ÷ (+4)
- (-4) ÷(-12)
__(-6) x (-5)__

-10 x 3

** **

- Complete the following
- (+6) + (5) =
- (+6) + (9) =
- (-6) + (=5) =
- (+7) + (=4) =
- (+8) – (+6) =

** **

**WEEKEND ASSIGNMENT**

- Simplify 12 – (+3) – 8= ____ a) -1 (b) +1 (c)-2 (d)+2
- Simplify (-3) (-1)= ____ a) -2 (b) -1 (c)+1 (d) +2
- Simplify (+15) x (-4)= ____ a) -20 (b) -60 (c)+20 (d) +60
- Divide -18 by -3 = ____ a) -6 (b) +6 (c)-21 (d) +15
- Divide -5 by -15 = ____ a) +1/3 (b) -1/3 (c) +1/5 (d) -1/5

**THEORY **

1a). Simplify 4/9 of (-2 __4__)

- b) Simplify (-2) + (-7) using number lines.

2 Simplify

- a) 7 x (-6.2)

** **b) -112 ÷ -4

**See also**

APPROXIMATION OF NUMBERS ROUNDING

H.C.F & L.C.M AND PERFECT SQUARES

WHOLE NUMBERS AND DECIMAL NUMBERS

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