Fraction,decimal, ratio

1.2 FRACTIONS
What are fractions?
Fractions are for counting PART of something.
Let's break the hexagon into 6 equal pieces:

What if we just have one of the pieces?

That will be 1 piece out of 6 pieces. Right?
Here's how we write it:

We read this like "one sixth" or "one over six".

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OPERATIONS OF FRACTIONS

Example 1
Evaluate.
a) 5 + 1

88

b) 7 – 2

93

c) 1 1 + 3 2 – 5

2 36

Solution : 5 +1 a c = ac
a) b b
= 88 b
5 +1
=
= 8
63
84
3
4

PRESS 5 a b/c 8 + 1 a b/c 8 = 3
4

b bbb bb
/ /// //
c ccc cc

b) 7 –2 Equate the denominator.
=
= 93
=
7 – 2x3
9 3x3
7 –6
99
1
9

PRESS 7 a b/c 9 – 2 a b/c 3= 1
9
b bbb bb
/ /// //
c ccc cc

2

c) 1 1 + 3 2 – 5

2 36

= 3 + 11 − 5 Change the fraction to improper
236 fraction first

= 33 + 11 2 − 5 Equate the denominator.
23 32 6

= 9 + 22 − 5
666

= 26 = 13
63

or

= 41

3

PRESS 1 a b/c 1 a b/c 2 + 3 a b/c

b2 a b/c 3b – 5 ba b/cb 6b = 41
3
/ / ///
cb bc b b c c bc b
/ /// //

c ccc cc

UNIT EXERCISE 1.3

1. Evaluate each of the following. Verify your answer using calculator.
a) 2 − 1
33
b) 7 + 2
83
c) 1 + 2 3
64
d) 2 5 − 1 1 + 2
6 23

2. There are 455 students at a particular IKM. 3 of the students are
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males. So how many male students are there at that IKM?

3. The length of the rope is 10 m. If Sarah used 1 of the rope, what is
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the length of the rope remaining?

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1.3 DECIMAL NUMBERS

A decimal is a fraction whose denominator is powers of 10.

For examples, 1 Read as ’zero point one’
= 0.1

10

1 Read as ’zero point zero one’
= 0.01

100

1 Read as ’zero point zero zero one’
= 0.001

1000

Decimal point

Do you notice the link between the
number of zeros in the

denominator of a fraction and the
number of digits after the decimal

point of a decimal?

CONVERT DECIMAL NUMBERS TO FRACTIONS AND VICE VERSA

Example 1
Express each of the following decimals as a fraction.
a) 0.49
b) 7.375

Solution :

a) 0.49 = 49
100

PRESS 0 . 49= a b/c 49
b 100
/ bbb
b c/ / /
/
c ccc

b) 7.375 = 7 + 0.375

= 7 + 375

= 1000

= 7 375

1000

73

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Example 2

Express each of the following fractions as a decimal.
a) 39

100

b) 1 7

10

c) 2

5

Solution :

a) 39 = 39 100
100

= 0.39

b) 1 7 = 17
10
10
1.7
=

OPERATIONS OF DECIMAL NUMBERS

Example 1
Simplify the expression :0.821 + 0.63 – 1.2

Solution : 0.821 + 0.63 - 1.2
1.451 - 1.2
= 0.251
=

PRESS 0 •821 +0 . 63

bbbbb bb bbb

-/ 1/ /. 2/ =/ / 0.2/51 / / /

bc bc cb c cb c c c c c

/// /

ccc c

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UNIT EXERCISE 1.4

1. Convert the following decimal numbers to fraction.
a) 1.25
b) 0.008

2. Convert the following fraction to decimal numbers.

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a)

3
8
b) 5

3. Evaluate. b) 8 + 0.6 ÷ 0.2
a) 1 – 0.07 + 0.3 + 0.045

c) 5.32 × 0.4 + 1.25

4. The price of a Mathematics module is RM19.50 and an English
module is RM9.25. If Amin gave a RM50 to the cashier, how much
would he get back?

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1.4 RATIOS AND PROPORTIONS

A RATIOS OF TWO QUANTITIES

A ratio of two quantities is the comparison between two quantities of
the same unit. The ratio is usually written as a : b and read as ‘a is to b’.

Example 1:
Express each of the following as a ratio :
a) 30 m to 50 m
b) 7 weeks to 14 month

Solution :

a) 30 m : 50 m
=
30 : 50
= 3:5

b) 8 weeks : 14 months Equate the units
= 2 months : 14 months
= 2 : 14
= 1:7

Example 2
Given the ratio p : q = 5 : 6.
a) Write the ratio as fraction.
b) State the ratio q : (p + q)

Solution :

a) 5 : 6 = 5
6
b) q : (p + q) = 6 : (5 + 6)
= 6 : 11

B. PROPORTIONS

Two pairs of quantities are a proportion if the two pairs of quantities are
equivalent ratios.

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Example 1
Determine whether the following pairs of ratios are proportion.
a) 3 : 5 and 9 : 15

b) 4 and 24

15 30

Solution :

a) 3 : 5 = 3 x 3 : 5 x 3 = 9 : 15
Since 3 : 5 = 9 : 15, therefore 3 : 5 and 9 : 15 are proportion

b) 24 = 24  6 = 4

30 30  6 5

Since 4  4 , therefore 4 and 4 are not proportion.
15 5 15 5

Example 2
There are 120 bolts in 5 boxes. Find the number of bolts in 3 similar
boxes.

Solution :

The number of bolts in 5 boxes is 120 bolts.

Let the number of bolts in 3 boxes be x.

The ratio of the number of bolts is x : 120 = x .
120

The ratio of the number of boxes is 3 : 5 = 3 .
5

By proportion, 3  24 =x
5  24
120

x = 3 x 24

= 72

Therefore, number of bolts in 3 boxes is 72.

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