HOW TO SIMPLIFY RATIOS WITH DECIMALS

To simplify the ratio in decimals, we follow the steps given below :

(i)  Multiply both parts of ratio by 10, 100, 1000...... etc

(ii)  After changing the decimal as integer, write the ratio in the form of a : b as a/b. 

(iii)  Simplify the fraction as much as possible.

(iv)  The simplified form of a/b can be written as a : b.

Example : 

Express the ratio in a simplified form :

0.4 : 0.5

On both parts of the ratio, we have only one digit after the decimal. So, we multiply both parts of the ratio by 10.

=  0.4(10) : 0.5(10)

=  4 : 5

More examples :

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.

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