EXPRESSING THE RATIO AS PERCENTAGE

Let us consider a : b as the given ratio. To convert the ratio as percentage,

Step 1 :

We have to express the given quantity as ratio.

How to express the ratio as fraction ?

If a : b is the given ratio, then it fraction form will be a / b

Step 2 :

Then convert it into percentage.

How to express the ratio as percentage ?

If a/b is the fraction, then its percentage will be (a/b) x 100%.

Problem 1 :

The ratio of red apples to green apples in a basket is 1 : 2

a) What fractions of the apples in the basket are red?

b) What fractions of the apples in the basket are green?

Solution :

Ratio of red to green apple = 1 : 2

Total = 3

a) Fraction of the apples red in the basket = 1/3

b) Fraction of the apples green in the basket = 2/3

Problem 2 :

The ratio of blue pens to black pens in a box 3 : 5

a) What fractions of the pens are black?

b) What fractions of the pens are blue?

Solution :

Ratio of blue to black pen = 3 : 5

Total = 8

a) Fraction of the black pen = 5/8

b) Fraction of the blue pen = 3/8

Problem 3 :

A farmer keeps cows and pigs on his farm. The ratio of cows to pigs on the farm is 2: 3

a) What percentage of the animals on the farm are cows?

b) What percentage of the animals on the farm are pigs?

Solution :

Ratio of cows to pigs = 2: 3

Total = 5

a) Fraction of the cows on the farm = 2/5

Percentage = (2/5) x 100%

= 40%

b) Fraction of the pigs on the farm = 3/5

Percentage = (3/5) x 100%

= 60%

Problem 4 :

Olivia has blue, pink and orange counters in a bag.

The ratio of blue to pink to orange counters is 4: 5: 2

a) What fractions of the counters are blue?

b) What fractions of the counters are orange?

c) Express the quantities in percentage.

Solution :

Ratio of blue to pink to orange = 4: 5: 2

Total = 11

a) Fraction of the blue = 4/11

b) Fraction of the orange = 2/11

c) Percentage of blue = (4/11) x 100%

= 36.3%

Percentage of orange = (2/11) x 100%

= 18.2%

Percentage of pink = (5/11) x 100%

= 45.4%

Problem 5 :

Chris makes a drink by mixing lemonade and orange juice in the ratio 13: 7

a) What percentage of the drink is lemonade?

b) What percentage of the drink is orange juice?

Solution:

Ratio of lemonade and orange juice = 13: 7

Total = 20

a) The percentage of drink is lemonade

= (13/20) × 100

= 65%

b) The percentage of drink is orange juice

= (7/20) × 100

= 35%

Problem 6 :

Convert the following ratios into percentage

a) 5: 4     b) 3: 5

Solution :

a) 5: 4 = 5/4

Converting the fraction as percentage :

= (5/4) x 100%

= 125 %

b) 3: 5 = 3/5

Converting fraction as percentage :

= (3/5) × 100%

= 60 %

Fraction of the apples red in the basket = 1/3

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