EXPRESS THE FOLLOWING RATIOS IN SIMPLEST FORM

Express the following ratio in simplest form :

Problem 1 :

Solution :

Problem 2 :

34 mm to 1 cm

Solution :

Since the given measurements are in different units, first make their units the same.

10 mm = 1 cm

34 mm = 34/10 cm

=  34/10 : 1

= (34/10×10) : (1×10)

= 34 : 10

HCF(34, 10) is 2.

= (34/2) : (10/2)

Simplest Form = 17 : 5

Problem 3 :

2 m to 125 cm

Solution :

Since the given measurements are in different units, first make their units the same.

1 m = 100 cm

2 m = 200 cm

= 200 : 125

HCF(200, 125) is 25.

= (200/25) : (125/25)

Simplest Form = 8 : 5

Problem 4 :

24 seconds to 1  1/2 min

Solution :

= 24 seconds to 1  1/2 min

Converting mixed fraction into improper fraction.

= 24 seconds to 3/2 min

Now, we need to change their units to be the same.

1 min = 60 sec

3/2 min = 3/2 × 60 = 90 sec

= 24 : 90

HCF(24, 90) is 6.

= (24/6) : (90/6)

Simplest Form  = 4 : 15

Problem 5 :

2 L to 750 ml

Solution :

= 2 L to 750 ml

Now, we need to change their units to be the same.

1 L = 1000 ml

2 L = 2000 ml

= 2000 : 750

HCF(2000, 750) is 250.

= (2000/250) : (750/250)

Simplest Form = 8 : 3

Problem 6 :

1 week to 3 days

Solution :

= 1 week to 3 days

1 week = 7 days

Simplest Form = 7 : 3

Problem 7 :

4 weeks to 1 year

Solution :

= 4 weeks to 1 year

1 year = 52 weeks

= 4 : 52

HCF(4, 48) is 4.

= (4/4) : (52/4)

Simplest Form = 1 : 13

Problem 8 :

250 g to 1 kg

Solution :

= 250 g to 1 kg

1 kg = 1000 g

= 250 : 1000

= (250/250) : (1000/250)

Simplest Form = 1 : 4

Problem 9 :

1.5 kg to 125 g

Solution :

= 1.5 kg to 125 g

1 kg = 1000 g

1.5 kg = 1500 g

= 1500 : 125

= (1500/125) : (125/125)

S.F = 12 : 1

Problem 10 :

3 min to 45 seconds

Solution :

= 3 min to 45 seconds

1 min = 60 sec

3 min = 3 × 60 = 180 sec

= 180 : 45

= (180/45) : (45/45)

S. F = 4 : 1

Problem 11 :

Express in simplest form the ratio of shaded area: unshaded area

	Shaded area : Unshaded area = 5 : 2
	Shaded area : Unshaded area = 4 : 1
	Shaded area : Unshaded area = 2 : 2 = 1 : 1
	Shaded area : Unshaded area = 1 : 8

Problem 12 :

There are 45 males and 60 females in a subway car. The subway car travels 2.5 miles in 5 minutes.

a. Find the ratio of males to females.

b. Find the speed of the subway car.

Solution :

a) 

Number of males = 45

Number of females = 60

Ratio of number of males to females = 45 : 60

3 : 4

b)

Distance covered by the car = 2.5 miles

Time taken = 5 minutes

Ratio betweeen distance covered to time taken = 2.5 : 5

= 0.5 : 1

= 5 : 10

= 1 : 2