This document provides an overview of fundamental arithmetic operations including fractions, ratios, proportions, and percentages. It defines key terms such as numerator, denominator, proper/improper fractions, equivalent fractions, and operations involving addition, subtraction, multiplication, division, and powers of fractions. It also defines ratios and proportions, including using cross multiplication to solve proportion problems. Finally, it discusses percentages and how to convert between fractions, decimals, and percentages by moving the decimal point.

1. CHAPTER 1 :
Fundamental Operation
of Arithmetic
1.1 Fraction
1.2 Ratio and Proportion
1.3 Percentage

2. 1.1 FRACTION


WHAT IS
FRACTION?
Two numbers separated by a horizontal or
sloping line.
Numerator, N
2
E.g. Two seventh = 2/7 =
7
Denominator, D
Types of fraction
Types
Definition
Proper fraction
Numerator < denominator
Improper fraction
Numerator = or >
denominator
Mixed fractions
Whole number + common
fraction
Equivalent fractions
Two fractions that have
equals values
Examples

3. 1.1 FRACTION
IMPROPER
Divide N by D as far as possible
and express remainder as a proper fraction
Conversion
improper to
mixed
MIXED
Multiply the whole number by D,
add N. Place the total over N.

4. 1.1 FRACTION
OPERATION ON FRACTIONS
1. ADDITION & SUBTRACTION
Same Denominators
 Just add / minus the numerator
Different Denominators
 Find a common denominator, then add / minus and
simplified the answer to the lowest term.
 Example: Evaluate the followings; a) 1 + 3 + 6
5 5 5
3 1
b) +
7 5
2 2
c) −
5 3
3
2
d) 2 + 5
4
5

5. PRACTICE 1
1. Add together :
2 1
a) +
3 5
5 1
b) +
8 9
3 2 1
c) + +
8 5 3
2
3
d) 3 + 4
3
5
1
1
1
e) 5 + 4 + 3
2
3
5
2. Subtract the following:
2 1
a) −
3 4
3 2
b) −
4 5
7
1
c) 5
−3
16
3
1
3
d) 5 − 2
3
4
1
3
e) 7 − 3
2
5

6. 1.1 FRACTION
OPERATION ON FRACTIONS
2. MULTIPLICATION

3. DIVISION
Product of the numerators  Invert the divisor and
divide by the product of the change the division sign to
denominators.
multiplication.
p r p×r
× =
q s q×s


Can be simplified if possible
before multiplying.
Mixed fractions have to be
converted into improper
fractions before multiply.
p r p s p× s
÷ = × =
q s q r q× r

7. PRACTICE 2
Calculate each of the following:
5 4
1) ×
8 7
5
2
2)
÷
6 3
1 3
3) ×
4 5
3 5
4) 1 ×
4 8
7
3
5) ÷
8
4
1 3
÷
8 4
1  1 2
7) ÷ 1 × 
4  8 5
6)1
2
2
 7
8) 1 × 2  − 3
5
5
 8
2 2 1 1
9) ×  −  +
5 3 4  2
1
4
 2
10)  2 + 1  ÷ 5
5
5
 3

8. 1.1 FRACTION
OPERATION ON FRACTIONS
4. POWERS


5. SQUARE ROOTS
Raise both the numerator &
the denominator to that
power.  a  n a n
  = n
b
b
3
Example;  2  = 23 = 8
 
3
5
5
125


Invert the divisor and
change the division sign to
multiplication.
a
a
=
b
b
Example; 16 = 16 = 4
81
81
9

9. 1.1 FRACTION
OPERATION ON FRACTIONS
6. PRACTICAL APPLICATION

A girl spends 3/4 of her pocket money and has 90cents left. How
much did she have to start with?
3 1
1 − = = 90 cents
4 4
1 = 4 × 90 = 360 cents
∴ The girl had RM 3.60 to start with.

A group, of school children went to a hamburger bar, 2/5 of them bought
hamburgers only, 1/4 bought chips only and the remainder bought drinks only
What fraction bought food?
2 1
 What fraction bought drinks? 1)Food =
+

5 4
8 + 5 13
=
=
20
20
13
20
20 − 13
7
=
=
20
20
2)Drink = 1 −

10. PRACTICE 3
1.
2.
3.
4.
5.
Jane takes 5 ¾ minutes to iron a blouse. How
many blouses can she iron in 23 minutes?
The profit of a business are RM 29 000. It is
shared between two partners A & B. If A
receives 9/20 of the profits, how much money
does B receive?
A man sells his car for RM 16 200 and as a
result, loses one tenth of the price he paid for it.
What price did he pay for it?
5/8 of a fence has been built. If there is still 40
feet to be built, how long will the fence be?
A man left three eight of his money to his wife &
half the remainder to his son. The rest was
divided equally between his five daughters.
Determine what fraction of the money each
daughter received.

11. 1.2 RATIO &
PROPORTION






WHAT IS
RATIO ?
Comparison of 2 numbers or quantities as quotient.
Represent by x/y or x : y.
Generally reduced to lowest terms like fraction (by
dividing the HCF of the numbers).
Derived from quantities measured in the same units
Its just number, don’t have unit.
Its express the relationship between 2 or more
factors (or numbers)

12. 1.2 RATIO &
PROPORTION


WHAT IS
RATIO ?
E.g. Simplify the ratio 200g : 1 kg (different units)
= 200g : 1000g
=1:5
Example: Expressed the following ratio to the lowest
78 3
term;
a) 78 : 52 =
=
52
2
5 3
: =
8 8
12
8
c)
to
13 13
d) 10 cm 2 : 10 mm 2
b)

13. 1.2 RATIO &
PROPORTION




1.


WHAT IS
PROPORTION ?
The equality of 2 ratios
E.g. 5 : 2 = 25 : 10
To solve problems dealing with proportion, we use
cross multiplication.
Types of proportion:
Direct proportion
2.
If increase or decrease at the 
same rate.
E.g. If we buy rice at RM 2 for 2
kg, then we expect to pay RM 4

for 4 kg.
Inverse proportion
If an increase (decrease) in one
quantity produces a decrease
(increase) in a second quantity
in the same time.
E.g. 5 men building a wall take
20 days. If 4 men, it will take
only 25 days.

14. 1.2 RATIO &
PROPORTION

WHAT IS
PROPORTION ?
Examples:
5 x = 75
1. Find the value of x for 5 : 25 = 3 : x. 5 = 3 ⇒
25
2.
If a : b = 5 : 3, find
a. b : a
b. a : (a – b)
c. b : (a + b)
d. (a – b) : (a + b)
1.
If a : c = 3 : 4, and a : b = 4 : 5, find b : c
x
x = 15

15. 1.3 PERCENTAGE



WHAT IS
PERCENTAGE
?
Express a quantity as the number of parts in 100 parts.
Written as fraction, e.g. 20 percent = 20 % = 20/100 = 0.20
Conversion:
Then move dec. point
2 places to the right
x 100%
÷ 100%
Fractions
Percentage
x 100%
Decimal
÷ 100%
Then move dec. point
2 places to the left

16. 1.3 PERCENTAGE

Example: Express each number as a fraction, decimal
and percent.
a. 86%
b. 5.6%
c. 8 ½%
d. 0.025
e. 1.5
f.
9/8
g. 17/1000