Converting percentage as fraction

Converting percentage as fraction

A percentage is a number or ratio expressed as a fraction of 100. Here, let us try to convert different percentage to fraction.

Example 2.5

Write the following percentage into fraction.

(i) 60%

(ii) 125%

(iii) 3/5 %

(iv) 15/10 %

(v) 28 (1/3) %

 Solution

Try these

Convert the following percentage as fractions.

(i) 50%

(ii) 75%

(iii) 250%

(iv) 30 (1/5) %

(v) 7/20 %

(vi) 90%

Solution:  

(i) 50% = 50 / 100 = 5 / 10 = 1/2

(ii) 75% = 75 / 100 = 3 / 4

(iii) 250% = 250 / 100 = 25 / 10 = 5 / 2

(iv) 30 (1/5) % = 30( 1/5 )/100 = (151/5) / 100 = 151 / 500

(v) 7/20 % = (7/20) / 100 = 7 / (20×100) = 7/2000

 (vi) 90% = 90 / 100 = 9 / 10 

Example 2.6

In a survey one out of five people said they preferred a particular brand of soap. Convert it into percentage?

Solution

Fraction = 1/5

Percentage = 1/5 ×100% = 20%

Example 2.7

 75 students from a Government High school appeared for S.S.L.C. examination. 72 of them are declared passed in the examination. Find the percentage of students passed.

Solution

Total number of students = 75

 Number of students declared passed = 72

Percentage = 72/75 ×100%

                  = 24/25 ×100%

                  =24×4%

                  = 96%.

Note

All the parts of the whole when added together gives the whole or 100%. So out of 2 parts if we are given 1 part we can definitely find the other part. That is in the above example, if 96% of the students has passed means, 96 out of 100 has passed and the remaining (100-96)% 4% have failed.

Example 2.8

In a class of 50 students if 28 are girls and 22 are boys then express boys and girls in percentage.

Solution

Let us find the percentage of boys and girls. It is given in the form of table below.

To find the percentage of boys and girls we can also use unitary method or multiply both numerator and denominator by a same number which makes denominator 100.

Example 2.9

There are 560 students in a school. Out of 560 students, 320 are boys. Find the percentage of girls in that school.

Solution

Total number of students = 560

Number of boys = 320

Number of girls = 560 – 320 = 240

Percentage = (240/560) × 100% = (24/56) ×100%

                   = (3/7) ×100% = 300/7 %

                   =42.86%

Think

1. What is the difference between 0.01 and 1%

Solution:  0.01 = 1 / 100 = 1%          0.01 and 1% are the same.

2. In a readymade shop there will be a board showing upto 50% off. Most of the people will realize that everything is half of its original price, Is that true?

Solution:  No. Only some of them are half of its original price.