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RATIOS
DEFINITION:
A ratio is a comparison of two or more
similar quantities It is denoted by the symbol:
For example if a farmer divides his orange harvest so that for every 10 oranges,
3 are kept and sends 7 to the market, we say he divides the oranges in the
ratio of 3:7.
The quantities compared in a ratio must
always be in the same unit of measurement. If two quantities are given in
different units, before we can write a ratio for the quantities we must first
convert the units so they are the same.
EXAMPLE 1. A car dealer sales two types
of car batteries called incoe and bravo. Each incoe weighs 60kg while each
bravo weighs 1200g. A Toyota pickup uses all two batteries for proper
functioning. Express this as a ratio.
Solution
Convert
all grams (g)
Weight of
incoe= 60kg=60×1000g=60,000g
Weight of
bravo= 1200g
Ratio;
weight of incoe: weight of bravo= 60000g: 1200g
Weight of incoe: weight of bravo=
60000:1200
Weight of incoe: weight of bravo=
50:1
A ratio is
another way of expressing a fraction as a whole. That is 50:1= 50
1
EXAMPLE 2
A woman has
7 mangoes to share between her two daughters Bih and Abigail. Bih receives 3
mangoes and Abigail receives 4 . Bih has 3 out of 7 mangoes – in words, 3 of the mangoes. Abigail has 4 out of
the 7 mangoes, 4 of the mangoes.
7
7
The ratio of
Bih’s mangoes to Abigail’s mangoes can be written as 3:
4 or simply as 3: 4.
7 7
Note that if you are given a ratio of one
part to another part; find the whole by adding the ratios together. In example
2 above, 3parts +4parts = 7parts which is the total or whole.
From this example, Bih gets 3parts of the
whole (3) and Abigail gets 4 parts of the whole (4).
7 7
SIMPLIFYING RATIOS
To simplify
ratios, cancel out common factors as for fractions to write the ratio in its
lowest form.
EXAMPLE1: Simplify the following the ratios
to the lowest term.
i)
8:16
ii)
28:7
iii)
15:25
iv)
45minutes: 2 hours
v)
7days:3weeks
vi)
1 :
3
3 5
Solution
i)
8:16; the number 8 is the common factor of 8 and
16
8:16
= 8 : 16
8
8
8:16
= 1: 2
ii)
28:7 ; the number 7 is the factor of 28 and 7.
28:7
= 28: 7
7 7
28:
7 = 4: 1
iii)
15: 25; the number 5 is the common factor of 15
and 25.
15:
25= 15 : 25
5 5
15:
25 = 3 : 5
iv)
45minutes: 2hours; change all to either hours
or minutes. It is preferable to convert in the lower unit that is minutes.
45minutes:
2hours= 45minutes: 2×60minutes
45minutes:
2hours=45: 120; the number 5 is a common factor.
45minutes:
2hours= 45 : 120
5 5
45minutes:
2hours= 9: 24; another common factor here is 3.
45minutes:
2hours= 9 : 24
3 3
45minutes:
2hours= 3:8
v)
7days : 3weeks = 7days : 3×7days
7days:
3weeks= 7days: 21 days (common factor is 7)
7days:
3weeks = 7 : 21
7 7
7days:
3weeks = 1: 3
vi)
1 : 3 ; multiply through by the lowest common
multiple of the denominators that is 15.
3 5
1:
3 = 15× 1 : 15× 3
3 5 3 5
1: 3 = 5: 9
3 5
A ratio can be a comparison of more than two quantities,
as long as they are of the same kind. From this, you can solve a number of
problems with ease.
EXAMPLE 1: Maurice sells three brands of car tyres. He finds that
for every 3 Michelin tyres he sells, he sells 7 Continental tyres and 5
Goodyear tyres. The ratio of sales for the different tyre brands is therefore
3:7:5. If he sells 30 tyres altogether in a week, how many of each brand does
he sell?
Solution
Ratio; 3:7:5
Sum of parts;
3+7+5=15 whole
Total number
of these tyres sold per week= 30
Ø
3 of total tyres will be Michelin
15
Number of
Michelin tyres sold= 3 ×30
15
Number of Michelin tyres sold=6.
Ø
7 of
total tyres will be Continental
15
Number of
Continental tyres sold= 7 ×30
15
Number of Continental tyres sold=14
Ø
5 of total tyres will be Goodyear
15
Number of
Goodyear tyres sold = 5 ×30
15
Number of Goodyear tyres sold=10.
If you the
individual brands sold, you will have 30. That is 6+14+10=30.
EXAMPLE 2
A bag contains blue, green and yellow balls
in the ratio 2:2:3. If there are 35 balls all together, how many balls of each
color are there?
Solution
Ratio; 2:2:3
Sum of
parts; 2+2+3=7 whole
Total number
of balls= 35
Ø
2 of the total balls will be blue
7
Number of blue balls= 2 × 35
7
Number of blue balls = 10
Ø
2 of the total balls will be green
7
Number of
green balls = 2 × 35
7
Number of green balls= 10
Ø
3 of the total ball will be yellow
7
Number of
yellow balls = 3 ×35
7
Number of yellow balls= 15
EXERCISE
1)
Simplify these ratios
a)
2cm: 5cm, b) 1.5kg: 500g, c) 100cm:6m, d) 11%:
22%, e) 1: 2 , f) 0.5:0.75
4 7
2)
Mr. John has 15 domestic animals of which 6 are
cats, 4 are dogs and 5 are goats. Write down in its simplest form the ratio of:
a)dogs to goats, b) cats to dogs, c) cats to goats, d) goats
to dogs, e) dogs to cats to goats, f) write the ratios from a to e as proper fractions.
3) In a class of 60 students, there are
28girls and 32 boys.
a) What is the ratio of :
i) Boys to girls?
ii) Girls to the total number of
students?
b)
Write the ratio in a as a percentage of the
whole class.
3)
John and Mary are 14y years and 12 years old
respectively. Their father share 52000F CFA between the two of them in the
ratio of their ages.
a)
How much does each receive?
b)
Write these two amounts as :
i)
Proper fractions
ii)
Decimal fractions
iii)
Percentages of the total amount of money.
4)
A man’s wage in a month is divided as follows:
savings= 30%, Food=40%, health care 10%. He gives the rest of the money to his
parents.
a)
Write down the ratios of:
i)
Savings to food
ii)
Health care to food
b)
If the amount for health care is 15000 F CFA,
find his wage per month.
c)
What percentage did he give to his parents?
d)
What amount did he give to his parents?
5)
In the school Library, 2 of the books are
science books.
3
a)
What is the ratio of science books to
non-science books
b)
There are 7131 books in the library. How many of
them are non-science books?
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