DIRECTED NUMBERS

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

1. (-2_+(-4)
2. (-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

1. (+6)-(+10)
2. 12-(+3)-8
3. (-5)+(-5)+(-5)
4. (-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

1. (+a) ÷ (+b)=+(a/b)
2. (-a) ÷ (-b)=+(a/b)

iii.  (+a) ÷ (-b) = -(a/b)

1. (-a)÷(+b) = -(a/b)

Class work

1. Simplify the following

1. (-36) ÷ (+4)
2. (-4) ÷(-12)
3. (-6) x (-5)

-10 x 3

 

2. Complete the following
3. (+6) + (5) =
4. (+6) + (9) =
5. (-6) + (=5) =
6. (+7) + (=4) =
7. (+8) – (+6) =

 

WEEKEND ASSIGNMENT

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

 

THEORY

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

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

2    Simplify

6. a) 7 x (-6.2)

      b)   -112 ÷ -4

 

See also

APPROXIMATION OF NUMBERS ROUNDING

SIMPLE INTEREST

FRACTIONS

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

WHOLE NUMBERS AND DECIMAL NUMBERS