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To Convert a Fraction into a Percentage

To convert a fraction into a percentage; we need to multiply the fraction by 100 and add the percent symbol after the product..

Let us consider how to change a fraction to a percent

(i) 42/100

= 42%

(ii) 73/100

= 73%

(iii) 6/100

= 6%

(iv) 15/100

= 15%

(v) 39/100

= 39%

(vi) 11/100

= 11%

Convert a Fraction into a Percentage Video

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EXPRESSING A FRACTION AS PER CENT

To express a fraction as a per cent, we change the fraction into the equivalent fraction with denominator as 100. Then we express the fraction as a per cent by using the symbol %.

Let us consider some examples.

1. Express $\frac{3}{5}$ as a per cent.

Solution:

$\frac{3}{5}$

= $\frac{3 × 20}{5 × 20}$

(We multiply the numerator and the denominator both by 20 to make the denominator 100.)

= $\frac{60}{100}$

= 60 × $\frac{1}{100}$

= 60%

2. Express 2$\frac{1}{4}$ as per cent

Solution:

2$\frac{1}{4}$

= $\frac{9}{4}$

= $\frac{9 × 25}{4 × 25}$

(We multiply the numerator and the denominator both by 25 to make the denominator 100.)

= $\frac{225}{100}$

= 225 × $\frac{1}{100}$

= 225%

We multiply the numerator and the denominator both by 25.

We can also express a fraction as a per cent simply by multiplying it by 100 and writing % to the right of it.

For example:

(i) Express 3/4 as a percent.

Solution:

¾ × 100

= (3 × 100)/4

= 300/4

= 300/4 ÷ 4/4

[Divide the numerator and denominator by 4]

= 75%.

Answer: 75%

(ii) Express 12/5 as a percent.

Solution:

12/5 × 100

= (12 × 100)/5

= 1200/5

= 1200/5 ÷ 5/5

[Divide the numerator and denominator by 5]

= 240%.

Answer: 240%

(iii) Express 13/6 as a percent.

Solution:

13/6 × 100

= (13 × 100)/6

= 1300/6

= 1300/6 ÷ 2/2

[Divide the numerator and denominator by 2]

= 650/3

= 216 2/3%

Answer: 216 2/3%

(iv) Express 19/4 as a percent.

Solution:

19/4 × 100

= (19 × 100)/4 = 1900/4

= 1900/4 ÷ 4/4

[Divide the numerator and denominator by 4]

= 475%.

Answer: 475%

(v) Express 27/2 as a percent.

Solution:

27/2 × 100

= (27 × 100)/2

= 2700/2

= 2700/2 ÷ 2/2

[Divide the numerator and denominator by 2]

= 1350%.

Answer: 1350%

(vi) Express $\frac{9}{25}$ as a percent.

Solution:

$\frac{9}{25}$

= $\frac{9}{25}$ × 100%

= $\frac{9 × 100}{25}$%

= $\frac{900}{25}$%

= 36%

(vii) Express $\frac{1}{4}$ as a percent.

Solution:

$\frac{1}{4}$

= $\frac{1}{4}$ × 100%

= $\frac{1 × 100}{4}$%

= $\frac{100}{4}$%

= 25%

(viiI) Express 2$\frac{3}{4}$ as a percent.

Solution:

2$\frac{3}{4}$

= $\frac{11}{4}$ × 100%

= $\frac{11 × 100}{4}$%

= $\frac{1100}{4}$%

= 275%

Note: You may think that expressions 235% 275%, 105% etc have no meaning because no one can get more than 100 marks out of 100. It is true but one can earn $ 235, $ 275 or $ 105 per $ 100. If you purchase a watch for $ 100 and sell it for $ 235, you earn 135% profit.