Percentage in Grade VI

Hello Friends, in today's math help online session we are going to learn about Percentage. Percentage is a simple way of expressing a number in the ratio form or as a fraction of 100. It is denoted by a symbol %, known as the percentage sign.
For Example 45% is read as forty- five percent, and is equal to 45/100 or 0.45.
It is usually used to represent how large or small a quantity is with respect to the another one. For example, an increase of Rs. 0.15 on a price of Rs. 2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed in percentage form, this is therefore a 6% increase.
What we should keep in mind is that the value of percentage always lies in between zero and one. If the percentage value is greater than 1.00 or 100% then it is not a valid result.
The fundamental concept to remember when performing calculations with percentages is that the percent symbol can be treated as being equivalent to the pure number constant 1 / 100 = 0.01, for example 35% of 300 can be written as(35/100) × 300 = 105 which is our result.
We take another example like if you are having 1250 apples and you want to find the percentage of a single apple, then you will take it as 1/ 1250 x 100% = 0.08%. So if now you have given one apple to your friend then you have reduced 0.08% from the total of 100%. Now what if you gave 100 apples to your friend then the percentage would be 0.08% x 100 = 8%, which is our result.
Let's solve some Examples for better understanding.

1. Solve  50% of 30.
   

30 x 50/ 100 = ½ x 30 = 15.

2. Solve 13 % of 98.
   

13/100 x 98 = 12.74.

3. Solve 60% of all university students are female. There are 2400 female students. How many students are in the university?
   

2400 = 60% x n; n = 2400/ (60/100) = 4000.
We also have increase and decrease in percentage, which is of utmost importance.
Sometimes we say like 10% increase or 10% fall, so this is usually done with initial quantity of the value.
So some examples of percentage change would be -

1. An increase of 100% in a quantity means that the final amount is 200% of the initial amount (100% of initial + 100% of increase = 200% of initial); in other words, the quantity has doubled.
   
2. An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).
   
3. A decrease of 60% means the final amount is 40% of the original (100% − 60% = 40%).
   
4. A decrease of 100% means the final amount is zero (100% − 100% = 0%).
   

So now you would be able to understand what percentage is and how to solve the problems based on the increase and decrease of some quantity. 

In upcoming posts we will discuss about Prime Factorization in Grade VI. Visit our website for information on syllabus for class 12th ICSE