# Lesson Notes By Weeks and Term - Junior Secondary School 2

DIRECTED NUMBERS

SUBJECT: MATHEMATICS

CLASS:  JSS 2

DATE:

TERM: 1st TERM

WEEK SEVEN

TOPIC: DIRECTED NUMBERS

CONTENT

(i)    Addition and subtraction of directed numbers

(ii)   Multiplication of directed numbers

(iii)  Division of 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

-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. 1)     (-2)+(-4)=2+4=-6

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

1.  (-6)+(-6)+0= 6+6+0 =- 0

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

1. -(-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. 3x4=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

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

1. a) 7 x (-6.2)
2. b)   -112 ÷ -4