Question 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
Question 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
(i) 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.
(ii) 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
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