HOW TO WRITE RATIO IN SIMPLEST FORM

Express as a ratio in simplest form :

Problem 1 :

3 : 6

Solution :

3 : 6

When we divide by 3, we get

= 3/3 : 6/3

= 1 : 2

So, the simplest form is 1 : 2.

Problem 2 :

3/4 : 1/4

Solution :

3/4 : 1/4

By multiplying both parts by 4, we get

= (3/4) ⋅ 4 : (1/4) ⋅ 4

= 3 : 1

So, the simplest form is 3 : 1.

Problem 3 :

0.5 : 0.2

Solution :

0.5 : 0.2

Multiplying both parts by 10, we get

= 5 : 2

So, the simplest form is 5 : 2.

Problem 4 :

18 : 24

Solution :

18 : 24

When we divide by 6, we get

3 : 4

So, the simplest form is 3 : 4.

Problem 5 :

2 1/2 : 1 1/2

Solution :

2 1/2 : 1 1/2

5/2 : 3/2

By multiplying both parts by 2, we get

= (5/2) ⋅ 2 : (3/2) ⋅ 2

= 5 : 3

So, the simplest form is 5 : 3

Problem 6 :

1.5 : 0.3

Solution :

1.5 : 0.3

Multiplying both parts by 10, we get

15 : 3

When we divide by 3, we get

5 : 1

So, the simplest form is 5 : 1.

Problem 7 :

20 c to $1.20

Solution :

20 c to $1.20

$1.20 = 120 cents

= 20 : 120

When we divide by 20, we get

= 1 ; 6

So, the simplest form is 1 : 6.

Problem 8 :

2 L to 500 ml

Solution :

2 L to 500 ml

1 ml = 0.001 L

500 ml = 500 × 0.001

500 ml = 0.5 L

= 2 : 0.5

Multiplying both parts by 10, we get

20 : 5

When we divide by 5, we get

= 4 : 1

So, the simplest form is 4 : 1.

Problem 9 :

a) The length of the smaller one is 30 cm. The ratio of the smaller to the larger is 1:2. How long is the larger one?

b) The larger flag is 40 cm high. How high is the smaller flag?

Solution :

a) The ratio between the length of smaller to larger flag is 1 : 2

Length of smaller flag = 30 cm, let x the length of larger flag.

1 : 2 = 30 : x

1/2 = 30/x

x = 30(2)

x = 60

So, the length of larger flag is 60 cm.

b) Let x be the length of smaller flag.

x : 40 = 1 : 2

x/40 = 1/2

x = 40/2

x = 20 cm

So, the length of the smaller flag is 20 cm.

Problem 10 :

Two friends buy a lottery ticket. One of them pays $4 towards the ticket while the other one pays $5 towards the ticket. They agree to split any winnings in the same ratio. If they win $8532 how much does each of them get?

Solution :

Ratio between lottery tickets of two friends = 4 : 5

The winning amount = $8532

Decomposing the amount in the ratio of 4 : 5

Amount received by the first friend = 4x

Amount received by the second friend = 5x

4x + 5x = 8532

9x = 8532

x = 8532/9

x = 948

4x = 4(948) ==> 3792

5x = 5(948) ==> 4740

So, both friends will get $3792 and $4740 respectively.

Problem 11 :

The ratio of girls to boys in a school is 6 : 7 and there are 448 boys. How many students are there in the school?

Solution :

Ratio between number of girls to boys is 6 : 7

Number of boys = 448

Let x be the number of girls.

6 : 7 = x : 448

6/7 = x/448

x = (6/7) ⋅ 448

x = 384

Number of girls is 384.

Total number of students = 448 + 384

= 832

So, total number of students is 832.

Problem 12 :

An amount of hay was shared between two farmers who got 420 kg and 700 kg

(i) What was the total amount of hay shared? 

(ii) In what ratio was the hay divided amongst the two farmers? 

Solution :

Amount got by the first farmer = 420 kg

Amount got by the second farmer = 700 kg

i) Total amount they have shared = 420 + 700

= 1120

ii) Ratio between the their sharing

= 420 : 700

= 42 : 70

= 6 : 10

= 3 : 5

So, the required share is 3 : 5.