EXPRESS THE FOLLOWING AS RATIO IN SIMPLEST FORM

Example 1 :

Express as a ratio:

a) 65 g is to 1 kg

b) 87 pence is to $1:00

c) 5 months is to 2 years

d) 60 cents is to $2:40

e) $2:00 is to 80 cents

f) 200 kg is to 1 tonne.

Solution :

a) 65 g is to 1 kg

To write the given as ratio, represent both quantities in same unit.

1 kg  =  1000 g

=  65 : 1000

=  13 : 200

So, the required ratio is 13 : 200.

b) 87 pence is to $1:00

$1  =  100 pence

Required ratio is 87 : 100.

c) 5 months is to 2 years

1 year  =  12 months

2 years  =  12 (2)  ==>  24 months

So, the required ratio is 5 : 24.

d) 60 cents is to $2:40

$2.40  =  240 cents

=  60 : 240

Dividing both parts by 60, we get

=  1 : 4

So, the required ratio is 1 : 4.

e) $2:00 is to 80 cents

$2  =  200 cents 

=  200 : 80

By simplifying, we get

=  5 : 2

So, the required ratio is 5 : 2

f) 200 kg is to 1 tonne.

1000 kg  =  1 tonne

=  200 : 1000

=  1 : 5

So, the required ratio is 1 : 5.

Example 2 :

Write as a ratio:

a) Peter has $11 and Jacki has $9.

b) In a theatre there are 3 girls for every boy.

c) There are 2 Japanese made cars for every 5 European made cars.

d) For every 15 km that you travel by car, I can travel 4 km by bicycle.

e) There are 2 blue-fin tuna for every 5 schnapper.

f) Mix 50 mL of liquid fertilizer with 2 liters of water.

g) Take 5 mg of medicine for every 10 kg of body weight.

Solution :

(a)  Ratio between Peter and Jacki is 11 : 9.

(b)  Ratio between girls and boys is 3 : 1.

(c)  Ratio between Japanese cars and European cars is

2 : 5

(d)  Ratio of distance covered by car to bicycle is 15 : 4

e)  Ratio of blue-fin tuna to schnapper is 2 : 5.

f) 50 ml to 2 liters

1 liter  =  1000 ml

2 liters  =  2000 ml

50 : 2000

By simplifying, we get

1 : 40

g) Take 5 mg of medicine for every 10 kg of body weight.

1000 g  =  1 kg

1000 mg    =  1 g

=  5 : 1000000

Example 3 :

Express 96 : 72 as a ratio in simplest form.

Solution :

Writing the given ratio as fraction, we get

= 96/72

= 16/12

= 4 / 3

So, the simplified form is 4 : 3.

Example 4 :

Write 750 mL is to 2 litres as a ratio in simplest form.

Solution :

1 liter = 1000 ml

2 liters = 2(1000)

= 2000 ml

= 750 : 2000

= 750/2000

= 15/40

= 3 : 8

So, the ratio is 3 : 8.

Example 5 :

Write as a ratio: “I saw five Audis for every six BMWs”.

Solution :

Number of Audis = 5

Number of BMW = 6

So, the ratio between them = 5 : 6.

Example 6 :

Find the ratio of the shaded area : total area in the figure shown.

Solution :

Total number of triangles = 25

Number of triangles shaded = 13

Ratio between shaded to unshaded = 25 : 13.

Example 7 :

Express 0.4 : 0.9 as a ratio in simplest form.

Solution :

= 0.4 : 0.9

The ratio is in decimal. By multiplying 10 on both sides, we get

= 4 : 9

Example 8 :

Express 2 hours 20 minutes : 4 hours in simplest form.

Solution :

1 hour = 60 minutes

2 hours = 2(60)

= 120 minutes

2 hours 20 minutes = 120 + 20

= 140 minutes

4 hours = 4(60)

= 240 minutes

= 140 : 240

= 140/240

= 14 / 24

= 7 : 12

So, the required ratio is 7 : 12.

Example 9 :

 Express the ratio 3 : 2 1/2 in simplest form.

Solution :

= 3 : 2  1/2

Converting the mixed fraction as improper fraction, we get

= 3 : 5/2

= 3/(5/2)

= 3 x (2/5)

= 6/5

= 6 : 5

So, the required ratio is 6 : 5.

Example 10 :

A farm has 6000 animals. 2500 are sheep and the rest are cattle. Find the ratio of:

a) number of sheep : number of cattle

b) number of sheep : total number of animals.

Solution :

a) number of sheep : number of cattle

Total number of animals = 6000

Number of sheep = 2500

Number of cattle = 6000 - 2500

= 3500

a) Number of sheep : number of cattle 

= 2500 : 3500

= 5 : 7

b)  Number of sheep : total number of animals

= 2500 : 6000

= 5 : 12

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