HOW TO SIMPLIFY RATIOS WITH DECIMALS

Example 1 :

Express the ratio in simplest form :

(2) 1.3 : 1.8

(3)  0.1 : 0.9

(4)  0.2 : 0.6

(5)  0.4 : 0.2

(6)  1.4 : 0.7

(7)  0.03 : 0.15

(8)  0.02 : 0.12

(9) 0.18 : 0.06

(10)  0.05 : 0.15

(2)  Solution :

1.3 : 1.8

Multiply both parts of ratio by 10, we get

=  1.3(10) : 1.8(10)

=  13 : 18

It is not possible to simplify hereafter, so the answer is 13 : 18.

(3)  Solution :

0.1 : 0.9

Multiply both parts of ratio by 10, we get

=  0.1(10) : 0.9(10)

=  1 : 9

So, the answer is 1 : 9.

(4)  Solution :

0.2 : 0.6

Multiply both parts of ratio by 10, we get

=  0.2(10) : 0.6(10)

=  2 : 6

=  2/6

=  1/3

So, the answer is 1 : 3.

(5)   Solution :

0.4 : 0.2

Multiply both parts of ratio by 10, we get

=  0.4(10) : 0.2(10)

=  4 : 2

=  4/2

=  2/1

So, the answer is 2 : 1.

(6)  Solution :

1.4 : 0.7

Multiply both parts of ratio by 10, we get

=  1.4(10) : 0.7(10)

=  14 : 7

=  14/7

=  2/1

So, the answer is 2 : 1.

(7)  Solution :

0.03 : 0.15

Multiply both parts of ratio by 100, we get

=  0.03(100) : 0.15(100)

=  3 : 2

=  4/2

=  2/1

So, the answer is 2 : 1.

(8)  Solution :

0.02 : 0.12

Multiply both parts of ratio by 100, we get

=  0.02(100) : 0.12(100)

=  2 : 12

=  2/12

=  1/6

So, the answer is 1 : 6.

(9)  Solution :

0.18 : 0.06

Multiply both parts of ratio by 100, we get

=  0.18(100) : 0.06(100)

=  18 : 6

=  18/6

=  3/1

So, the answer is 3 : 1.

(10)  Solution :

0.05 : 0.15

Multiply both parts of ratio by 100, we get

=  0.05(100) : 0.15(100)

=  5 : 15

=  5/15

=  1/3

So, the answer is 1 : 3.

Example 2 :

A train normally complete a 270 mile journey in 4 1/2 hours. How much faster would it have to travel to complete the journey in 4 hours.

Solution :

Distance covered = 270 miles

Time taken = 4   1/2 hours

= 4.5 hours

The ratio between the distance covered and time taken 

= 270 : 4.5

Converting it as fraction

= 270/4.5

= 2700 / 45

= 60/1

= 60 : 1

From this ratio we understand that, 60 miles is covered in 1 hour.

To find the distance covered in 4 hours, we have to multiply each part by 4.

= 240 : 4

So, the distance covered in 4 hours is 240 miles.

Example 3 :

On a certain day the exchange rate was such that £1 was worth $1.63. Use a calculator to convert the following amount to £, giving each answer correct to the nearest place.

a)  $100

b)  $250

c)  $75

Solution :

£1 = $1.63

By dividing 1.63 on both sides,

£1/1.63 = $1

$1 = £0.613 -----(1)

a)  $100

Multiplying (1) by 100 on both sides

$100 = £61.3

So, value of $100 is £61.3.

b)  $250

Multiplying (1) by 250 on both sides

$250 = £153.25

So, value of $250 is £153.25

c)  $75

Multiplying (1) by 75 on both sides

$75 = £45.97

So, value of $250 is £45.97

Example 4 :

There are 8 pints in one gallon. One gallon is equivalent to approximately 4.55 liters. Use a calculator to convert.

a)  12 pints to liters

b)  20 liters to pints

Give your answer to correct one decimal places.

Solution :

1 gallon = 8 pints = 4.55 liters

a)  12 pints to liters

To convert pints to liters, we have to find the value of 1 pint in liters.

8 pints = 4.55 liters

1 pint = 4.55/8

1 pint = 0.57 liters -----(1)

Multiplying by 12 on both sides

12 pints = 6.84 liters

b)  20 liters to pints

To convert liters to pints, we have to find the value of 1 liter in pints.

4.55 liters = 8 pints

1 liter = 8/4.55 pints

1 liter = 1.76 pints

Multiplying 20 on both sides

20 liters = 35.2 pints

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