Practice Set 7.1
(1) Write the ratio of the first number to the second number in it's simplest form.
i) 36, 88
ii) 72, 18
iii) 91, 65
iv) 85, 102
Solution
(i) 36, 88
Ratio of 36 to 88
=
36
88
=
36 ÷ 4
88 ÷ 4
=
9
22
Ans. 9 : 22
(ii) 72, 18
Ratio of 72 to 18
=
72
18
=
72 ÷ 18
18 ÷ 18
=
4
1
Ans. 4 : 1
(iii) 91, 65
Ratio of 91 to 65
=
91
65
=
91 ÷ 13
65 ÷ 13
=
7
5
Ans. 7 : 5
(iv) 85, 102
Ratio of 85 to 102
=
85
102
=
85 ÷ 17
102 ÷ 17
=
5
6
Ans. 5 : 6
Note:
To find out which number to divide by, just find the GCD of the two numbers and divide both numbers by it.
(2) Write the ratio of the second number to the first number in it's simplest form.
i) 28, 84
ii) 120, 32
iii) 75, 135
iv) 220, 100
Solution
(i) 28, 84
Ratio of second number to the first
∴ Ratio of 84 to 28
=
84
28
=
84 ÷ 28
28 ÷ 28
=
3
1
Ans. 3 : 1
(ii) 120, 32
Ratio of second number to the first
∴ Ratio of 32 to 120
=
32
120
=
32 ÷ 8
120 ÷ 8
=
4
15
Ans. 4 : 15
(iii) 75, 135
Ratio of second number to the first
∴ Ratio of 135 to 75
=
135
75
=
135 ÷ 15
75 ÷ 15
=
9
5
Ans. 9 : 5
(iv) 220, 100
Ratio of second number to the first
∴ Ratio of 100 to 220
=
100
220
=
100 ÷ 20
220 ÷ 20
=
5
11
Ans. 5 : 11
Note:
To find out which number to divide by, just find the GCD of the two numbers and divide both numbers by it.
(3) Find the ratio of the first quantity to the second quantity in it's simplest form.
i) 5 years, 10 months
ii) 750 grams, 1.5 kg
iii) 5 l, 500 ml
iv) 135 minutes, 2 hours
v) 2.1 m, 70 cm
Solution
(i) 5 years, 10 months
1 year = 12 months
∴ 5 years = 12 × 5 = 60 months.
The ratio of 5 years to 10 months means the ratio of 60 months to 10 months.
∴
60 months
10 months
=
60
10
=
60 ÷ 10
10 ÷ 10
=
6
1
= 6 : 1
Ans. 6 : 1 or
6
1
(ii) 750 grams, 1.5 kg
1 kg = 1000 grams.
∴ 1.5 kg = 1.5 × 1000 = 1500 grams.
The ratio of 750 grams to 1.5 kg means the ratio of 750 grams to 1500 grams.
∴
750 g
1500 g
=
750
1500
=
75
150
=
75 ÷ 75
150 ÷ 75
=
1
2
= 1 : 2
Ans. 1 : 2 or
1
2
(iii) 5 l, 500 ml
1 l = 1000 ml
∴ 5 l = 5000 ml
The ratio of 5 l to 500 ml means the ratio of 5000 ml to 500 ml.
∴
5000 ml
500 ml
=
5000
500
=
50
5
=
50 ÷ 5
5 ÷ 5
=
10
1
= 10 : 1
Ans. 10 : 1 or
10
1
(iv) 135 minutes, 2 hours
1 hour = 60 minutes
∴ 2 hours = 60 × 2 = 120 minutes
The ratio of 135 minutes to 2 hours means the ratio of 135 minutes to 120 minutes.
∴
135 min
120 min
=
135
120
=
135 ÷ 15
120 ÷ 15
=
9
8
= 9 : 8
Ans. 9 : 8 or
9
8
(v) 2.1 m, 70 cm
1 m = 100 cm
∴ 2.1 m = 2.1 × 100 = 210 cm
The ratio of 2.1 m to 70 cm means the ratio of 210 cm to 70 cm.
∴
210 cm
70 cm
=
210
70
=
21
7
=
21 ÷ 7
7 ÷ 7
=
3
1
= 3 : 1
Ans. 3 : 1 or
3
1
(4) 320 workers are working in a factory. Out of them, 200 are male workers.
Solve the following questions based on this :
(a) Find the ratio of the number of male workers to the number of female workers.
(b) Find the ratio of the number of male workers to the total number of workers.
(c) Find the ratio of the number of female workers to the total number of workers.
Solution
Total number of workers = 320.
Male workers = 200.
∴ Female workers = 320 − 200 = 120.
(a) Male workers to female workers
The ratio of male workers to female workers
= 200 : 120
=
200
120
=
200 ÷ 40
120 ÷ 40
=
5
3
= 5 : 3
Ans. 5 : 3 or
5
3
(b) Male workers to total workers
Ratio of male workers to total workers
= 200 : 320
=
200
320
=
200 ÷ 40
320 ÷ 40
=
5
8
= 5 : 8
Ans. 5 : 8 or
5
8
(c) Female workers to total workers
Ratio of female workers to total workers
= 120 : 320
=
120
320
=
120 ÷ 40
320 ÷ 40
=
3
8
= 3 : 8
Ans. 3 : 8 or
3
8