EXPRESS THE FOLLOWING 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

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