CHAPTER ONE
RATIO, PROPORTION AND
PERCENTAGE
Learning Outcomes:
• 1.0 Ratio
1. Converting Ratios from fractions to decimals
2. Ratio in Time Conversions and Speeds
• 2.0 Proportion
1. Direct proportion
2. Inverse proportion
• 3.0 Percentages
1. Percentage change
2. VAT
1.0) RATIO
• Can be expressed in different ways:
 “to” as in 2 to 4
 with a colon, 2 : 4
 as a fraction, “ 2 ”
4
 as a decimal, “0.5”
 as a percentage, 50%
 with “per”
• Often expressed as colon.
GUIDELINES TO KEEP IN
MIND
• Ratio is written with a colon when compare
in two or more numbers or quantities.
• Unit of similar things can be dropped
when write the ratio BUT the terms of the
ratio need to be expressed in the same
unit of measurement.
• Units of measurement can be dropped
although the terms of the ratio represent
different things when rates are expressed as
ratios.
GUIDELINES TO KEEP IN
MIND (CONT.)
• Ratio should not contain decimals
when expressed using “to” or a colon.
• Simplifying a ratio of fractions.
EXAMPLE 1
• At the time of writing, the ratio of
prices in pound sterling to prices in
euros is two to three (2:3). What is the
equivalent price in pounds for a coat
costing 150 euros?
ANSWER
2 Pound : 3 Euro
x Pound : 150 Euro
• Can use Cross Product:
2 * 150 = 300
X * 3 = 3x
• So now just find x:
3x = 300
x = 300 / 3
=100 Pound
1.1) CONVERTING RATIOS FROM
FRACTIONS TO DECIMALS
• Ratios are often expressed as fraction but it
can also be expressed as decimals from
fractions.
• MUST be able to convert between the two
forms.
EXAMPLE 2
22
7
355
113
• How do
and
compare with the
decimal value from 3.141592654? The
fraction are agree with how many
significant figures?
• Significant figures (s.f) is digits that
carry meaning that include all
numbers, even zero.
ANSWER
• 227 = 3.142857143
• Comparing the answer above with this number
3.141592654 will only get us 4 s.f.
355
• 113
= 3.14159292
• Comparing the answer above with this number
3.141592654 will get us 7 s.f.
1.2) RATIO IN TIME CONVERSIONS
AND SPEEDS
• The ratio of time measured in hour to
minutes or in minutes to seconds is one to
sixty (1:60).
• Speed is the ratio of distance travelled to
time taken.
• The formula for speed is:
Speed =
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅
𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏
EXAMPLE 3
•
ANSWER
• 4.5 minutes * 60 seconds = 270 seconds
• So Adam’s grandfather took 270 seconds
compare to Adam who only took 260
seconds.
• Adam is faster than his grandfather.
EXAMPLE 4
• A cheetah is the fastest land
animals over short distances. It can
run 400 meters in 15 seconds.
i. What should be its speed in meters
per second?
ii. What should be its
kilometers per hours?
speed
in
ANSWER
• i) Speed =
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅
𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏
= 400 / 15
= 26.67 meter per second
• ii) Convert meter to kilometer : 400/ 1000 = 0.4km
Convert second to hour: 15/(60*60) = 15/3600
Speed =
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅
𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏
= 0.4/(15/3600)
= 96 km per hour
2.0) PROPORTION
•
PROPORTION (CONT.)
• Use cross product to test whether the
2 ratios are equal.
20
25
=
4
5
• 20 × 5 = 100
• 4 × 25 = 100
EXAMPLE OF SOLVING
PROPORTION
•
2.1) Direct proportion
Two value are different, but the ratio
between the values stays the same.
Relationship between two quantities;
as one increased, same goes to the
other and vice versa.
Example: A recipe of coffee for five
people, calls for teaspoon of 2 coffee
powder. How much should you use for
ten people?
EXAMPLE 5
•
ANSWER
2 litre = 9𝑚2
X litre = 75 𝑚2
• Because she had paint : 75 𝑚2 - 9𝑚2 = 66 𝑚2
• Use cross product:
2 litre *66 𝑚2 = 132
X litre *9 𝑚2= 9x
• So now find x :
x = 132 / 9
x = 14.67 litre
2.2) Inverse proportion
When one quantity increases, the other
decreases instead of increase and vice
versa.
So called “indirect proportion” but no
such commonly recognized thing as
“indirect proportion”.
Example: 3 workers build a wall in 12
hours. How long would it have taken for 2
workers?
EXAMPLE 6
• Suppose that 20 men build a house in
6 days. How many days to build the
same house if:
i. the men increased to 30
ii. the men become 40
ANSWER
i)
20 men = 6 days
1 men = 6 * 20 men
= 120 days
• This is because a man had to do a job of 20 men so
of course he needs more time.
• If the men increase to 30 = 120 / 30
= 4 days
ii) 40 men = 120 / 40
= 3 days
• Inverse proportion because when men increase, the
days needed to build a house decrease.
3.0) PERCENTAGE (%)
• Fractions and decimals can also be
converted to percentages, by multiplying
100%.
• Fractions and decimals that bigger than 1
correspond to percentages greater than
100%.
• Percentage given can increase and decrease
the normal price.
3.1) VAT
• Percentage that can increase (add) normal
price – Value Added Tax (VAT) or service
charge
• Percentage that can decrease
normal price – discount
(minus)
• Formula to get the percentage’s value:
given percentage times the original value
EXAMPLE 7
• If a sport shoe cost RM65.75,
i. How much will the sport shoe cost if
VAT at 20% has to be added?
ii. If the sport shoe is put in sale at 10%
discount. What is the sale price?
ANSWER
i) RM65.75 * 120% = RM 78.90
ii) RM65.75 * 90% = RM 59.18
3.2) PERCENTAGE CHANGE
• Formula for the percentage change:
𝒏𝒆𝒘 𝒗𝒂𝒍𝒖𝒆 − 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒗𝒂𝒍𝒖𝒆
% 𝒄𝒉𝒂𝒏𝒈𝒆 =
× 𝟏𝟎𝟎
𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒗𝒂𝒍𝒖𝒆
• Example: the price of oranges had increased
from 50 cent to 60 cent. Calculate the
percentage change.
% 𝑐ℎ𝑎𝑛𝑔𝑒 = 60−50 × 100 = 20%
50
EXAMPLE 8
• At Tunku Putra School, the enrolment
increased from 1340 students in 2010
to 1766 students in 2011. What is the
percentage change from 2010
to
2011?
ANSWER
• % 𝒄𝒉𝒂𝒏𝒈𝒆 = 𝒏𝒆𝒘 𝒗𝒂𝒍𝒖𝒆−𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒗𝒂𝒍𝒖𝒆 × 𝟏𝟎𝟎
𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒗𝒂𝒍𝒖𝒆
= (1766 – 1340 / 1340) * 100
= 31.79%
End. THANK YOU.