CHAPTER 1
DIRECTED NUMBERS
1.1
Multiplication and division of integers
1.2
Combined operations ( Addition, Subtraction,
Multiplication and Division )
1.3
Positive and Negative Fractions
1.4 Positive and Negative Decimals
1.5
Computations involving Directed Numbers
KEYWORDS
 POSITIVE SIGN
 NEGATIVE SIGN
 ADDITION
 SUBTRACTION
 GREATER THAN
 LESS THAN
(+)
(-)
(+)
(-)
(>)
(<)
1.1
MULTIPLICATION AND DIVISION OF INTEGERS
Learning Outcome :
a)
Multiply integers and solve problems involving of multiplication
of integers.
b)
Divide integers and solve problems involving division of integers.
The positive numbers such as 1, 2, 3, 4, …. are positive integers.
The negative numbers such as -1, -2, -3, -4, …. are negative integers
MULTIPLICATION
DIVISION
(+ ) × (+) = (+)
(+ ) ÷ (+) = (+)
(- ) × (-) = (+)
(- ) ÷ (-) = (+)
(+ ) × (-) = (-)
(+ ) ÷ (-) = (-)
(- ) × (+) = (-)
(- ) ÷ (+) = (-)
THE PRODUCT /QUOTIENT OF TWO INTEGERS WITH LIKE SIGNS IS +VE INTEGERS
THE PRODUCT/QUOTIENT OF TWO INTEGERS WITH UNLIKE SIGNS IS –VE INTEGERS
EXAMPLE FOR THIS SUB TOPIC
TIPS !!!
1) 6×(-7) × (-2)
Solution:
=6×(14)
=84
2)-27 ÷ 9 ÷ 3
Solution:
=-3 ÷ 3
=-1
the +ve sign is usually
omitted
+30 is written as 30
!!!
a×b=b×a
1.2
COMBINATION OPERATION ( + - × ÷ )
REMEMBER!!!
B
()
O
of
D
÷
M
×
A
+
S
-
To perform computations involving combined operations, you
must abide by BODMAS rule. Calculation within brackets must
be performed first, followed by division or multiplication, then
addition or subtraction, from left to right.
Eg:
125 ÷ (-5) + 6 × (-2)
SOLUTION:
1) Solve the division or multiplication
first
2) Then solve the addition
= ( -25 ) + ( - 12 )
= - 37
1.3
POSITIVE AND NEGATIVE FRACTION
 +VE (POSITIVE FRACTION)
A fraction with a value greater than zero ( > 0) is a positive fraction
eg: ½, 2/5, 6/5, 1/6, …
 -VE (NEGATIVE FRACTION)
A fraction with a value less than zero ( < 0 ) is a negative fraction
eg: -1/3, -5/6, -9/10, -4/7, …
COMPARE AND ORDER FRACTION
<0
>0
--------l---------l---------l---------l---------l----------l---------l-------
-3/4
-1/2
-ve fraction
-1/4
0
zero
¼
½
+ve fraction
¾
 A fraction is always greater than the fraction to its left
For example :
½ is greater than ¼
-1/4 is greater than -1/2
¼ is greater than -1/4
 A fraction is always less than the fraction to its right
For example :
¼ is less than ½
-1/2 is less than -1/4
-1/4 is less than ¼
TIPS
+ (+a) = +a
-(-a) = +a
+ (-a) = -a
-(+a) = -a
SEE THE
SYMBOL
CAREFULLY
EXAMPLE FOR THIS SUB TOPIC
 Arrange the following fractions in ascending and
descending order
1/6, -1/3, -3/8, 1/8, -3/4
Solution :
1/6, -1/3, -3/8, 1/8, -3/4
The LCM of 3, 4, 6, and 8 is 24
Change the fraction to their respective
equivalent fractions with the
denominator of 24
Ascending order : -3/4, -3/8, -1/3, 1/8, 1/6
Descending order : 1/6, 1/8, -1/3, -3/8, -3/4
1.4
POSITIVE AND NEGATIVE DECIMALS
 A decimal with a value greater than zero is a positive
decimal such as 0.21, 7.89, 9.54, 8.88, …
 A decimal with a value less than zero is a negative
decimal such as -0.05, -4.45, -9.90, -3.54, …
COMPARE AND ORDER DECIMAL
---l------------l-------------l-------------l------------l---
-2.22
-1.11
o.00
1.11
2.22
negative decimal
DID YOU
KNOW???
zero
positive decimal
ascending means increasing
Descending means decreasing
1.5
COMPUTATIONS INVOLVING DIRECTED NUMBERS
 As integers, computation involving directed numbers
follow the BODMAS rule.
a)
Eg:
Involving two directed numbers
4/5 × (8.2)
solution:
= - (4/5 × 82/10)
= -328/50
= - 6/14/25
b) Involving the combination of two or more operations on directed
numbers
Eg:
[ 55 + (-37)] × 6
solution:
= 18 × 6
= 108
 LET SEE THIS VIDEO…
SUMMARY
SKILL CHECKLIST
 Can you multiply and divide integers?
 Can you solve problem involving multiplication and




division of integers?
Can you perform computation and solve the problem
involving combined operation of integers?
Can you compare, order and perform computation
involving fraction and decimals?
Can you perform computations involving combined
operations of directed numbers?
Can you pose and solve problems involving directed
numbers.
EXERCISE