EXPRESS THE GIVEN RATIO IN SIMPLEST FORM WORKSHEET

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

Question 3 :

Express as a ratio:

a) 65 g is to 1 kg

b) 87 pence is to $1:00

c) 5 months is to 2 years

d) 60 cents is to $2.40

e) $2 is to 80 cents

f) 200 kg is to 1 tonne

Question 4 :

Joe and Bob share the cost of a video game in the ratio

3 : 7

a) What fraction does each pay?

b) If the game costs $35, how much does each pay?

c) If Joe pays $12, how much does Bob pay?

d) If Bob pays $42, what is the price of the video game?

1)  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.

2) 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

3)  Solution :

If the given quantities are not in same kind

a) 65 g is to 1 kg

1 kg = 1000 grams

= 65 : 1000

= 13 : 200

b) 87 cents is to $1

$1 = 100 cents

= 87 : 100

It cannot be simplified further, so the answer is 

= 87 : 100

c) 5 months is to 2 years

1 year = 12 months

2 years = 2 x 12

= 24 months

= 5 : 24

It cannot be simplified further. So, the answer is 5 : 24.

d) 60 cents is to $2.40

$1 = 100 cents 

$2.40 = 2.40 x 100

= 240 cents

= 60 : 240

= 1 : 4

e) $2 is to 80 cents

$1 = 100 cents

$2 = 200 cents

= 200 : 80

= 200/80

= 10 / 4

= 5/2

= 5 : 2

f) 200 kg is to 1 tonne

1000 kg = 1 tonne

= 200 : 1000

= 200/1000

= 1/5

= 1 : 5

So, the required ratio is 1 : 5.

4) Solution :

a) Total number of parts = 3 + 7

= 10

Joe's share = 3/10

Bob's share = 7/10

b) Cost of game = $35

Joe's share = (3/10) x 35

= $10.5

Bob's share = (7/10) x 35

= $24.5

c) Let x be the value of 1 share

3x = 12

x = 12/4

x = 3

Share by Bob = 7x ==> $21

d) 7x = 42

x = 42/7

x = 6

Total cost = 10x

= 10(6)

= 60

So, the total cost is $60.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.