EXPRESS THE GIVEN RATIO IN SIMPLEST FORM

Example 1 :

Express the following ratio in the simplest form :

(i)  8 : 16

(ii)  35 : 20

(iii)  2/5 : 3/5

(iv)  1   1/2 : 5

(v)  3 : 1  1/2

(vi)  2  1/2 : 1  1/2

(vii)  0.05 : 0.15

(viii)  0.18 : 0.06

Solution :

(i)  8 : 16

When we divide by 8, we get

=  8/8 : 16/8

=  1 : 2

So, the simplest form is 1 : 2.

(ii)  35 : 20

=  35/5 : 20/5

=  7 : 4

So, the simplest form is 7 : 4.

(iii)  2/5 : 3/5

By multiplying both parts by 5, we get

=  (2/5)⋅5 : (3/5) ⋅ 5

=  2 : 3

So, the simplest form is 2 : 3.

(iv)  1   1/2 : 5

Converting 1  1/2 as improper fraction, we get

3/2 : 5

Multiplying both parts by 2, we get

=  (3/2) ⋅ 2 : 5 ⋅ 2

=  3 : 5

So, the simplest form is 3 : 5.

(v)  3 : 1  1/2

Converting the second part 1  1/2 as improper fraction, we get

=  3 : 3/2

Multiplying both parts by 2, we get

=  3 ⋅ 2 : (3/2) ⋅ 2

=  6 : 3

Dividing by 3, we get 

=  2 : 1

So, the simplest form is 2 : 1.

(vi)  2  1/2 : 1  1/2

Changing the mixed numbers as improper fractions, we get

5/2 : 3/2

Multiplying by 2 on both sides, we get

=  5 : 3

So, the simplest form is 5 : 3.

(vii)  0.05 : 0.15

Multiplying both parts by 100, we get

=  5 : 15

Dividing by 5 on both sides, we get

=  1 : 3

So, the simplest form is 1: 3.

(viii)  0.18 : 0.06

Multiplying both parts by 100, we get

=  18 : 6

Dividing both parts by 6, we get

=  3 : 1

So, the simplest form is 3 : 1.

Example 2 :

Express as a ratio in simplest form :

a) the number of circles to squares

(b)  cats to mice

(c)  Teachers to students 

(d)  Trees and flowers

Solution :

(a)  Number of circles  =  3

Number of squares  =  6

Number of circles : Number of squares  =  3 : 6

=  1 : 2

So, circles and squares are in the ratio 1 : 2.

(b)  Number of cats  =  2 and number of mice  =  3

Number of cats : number of mice  =  2 : 3

(c)  Number of teacher  =  1, number of students  =  7

Number of teachers : Number of students  =  1 : 7

(d)  Number of trees  =  3, number of flowers  =  8

Number of teachers : Number of students  =  3 : 8

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.