2. CHAPTER 1
DIRECTED NUMBERS
Subtopics in this chapter:
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
3. KEYWORDS
POSITIVE SIGN (+)
NEGATIVE SIGN (-)
ADDITION (+)
SUBTRACTION (-)
GREATER THAN (>)
LESS THAN (<)
4. 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.
5. • 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
(+ ) × (+) = (+) (+ ) ÷ (+) = (+)
(- ) × (-) = (+) (- ) ÷ (-) = (+)
(+ ) × (-) = (-) (+ ) ÷ (-) = (-)
(- ) × (+) = (-) (- ) ÷ (+) = (-)
LIKE SIGNS ARE +VE INTEGERS
UNLIKE SIGNS ARE –VE INTEGERS
6. EXAMPLES
1) 6×(-7) × (-2) TIPS !!!
Solution: the +ve sign is usually
=6×(14) omitted
=84 +30 is written as 30
2)-27 ÷ 9 ÷ 3 !!!
Solution: a×b=b×a
=-3 ÷ 3
=-1
7. REMEMBER!!!
B O D M A S
() of ÷ × + -
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.
8. EXAMPLE
125 ÷ (-5) + 6 × (-2)
Solution:
1) Solve the division or multiplication first
2) Then solve the addition
= ( -25 ) + ( - 12 )
= -37
9. 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, …
10. Compare and Order Fraction
<0 >0
--------l---------l---------l---------l---------l----------l---------l-------
-3/4 -1/2 -1/4 0 ¼ ½ ¾
-ve fraction zero +ve fraction
11. 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
12. 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
13. TIPS +(+a) = +a -(-a)= +a
+(-a)= -a -(+a)= -a
See the symbols
CAREFULLY
14. EXAMPLE
Arrange the following fractions in ascending and
descending order
1/6, -1/3, -3/8, 1/8, -3/4
15. Solution :
1/6, -1/3, -3/8, 1/8, -3/4 i) The LCM of 3, 4, 6,
and 8 is 24.
ii) 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
16. 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, 8.74, …
A decimal with a value less than zero is a negative
decimal such as -0.05, -4.45, -9.90, -3.54, …
17. COMPARE AND ORDER DECIMAL
<o >0
---l------------l-------------l-------------l------------l---
-2.22 -1.11 0.00 1.11 2.22
negative decimal zero positive decimal
DID YOU Ascending means increasing
KNOW??? Descending mean decreasing
18. 1.5 COMPUTATIONS INVOLVING DIRECTED
NUMBERS
As integers, computation involving directed numbers
follow the BODMAS rule.
a) Involving two directed numbers
Eg: 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
21. 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.
