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# Comparing Quantities using Percentage

## Comparing quantities

We compare two or more units, objects, situations, and many more practical things in our daily lives. But, first, we do a comparison to find out which one will be better for us. Comparing quantities is a method by comparing one object to another about a specific unit or standard unit.

The object that we compare must be of the same domain; otherwise, we will not compare. For example, if we need to find which toy is bigger, we need to take two toys. However, if we take one toy and one chocolate, we cannot compare which one is bigger as the toy will be bigger in most cases. So we need a specific domain of objects so that we can compare them.

## Percentage

Percentage deals with the units in terms of 100. Any quantity that will be in terms of hundred can be represented in percentages. We may have percentages greater than 100. For example, a florist has 100 flowers. We have 20 of them. Then the percentage of flowers that we have taken from the florist is 20/100 x 100 = 20 percent.

We can also represent percentages if we have more than 100 quantities. For example, the same florist has 150 flowers. We have taken 50 of them. Then the percentage of flowers we have taken will be equal to:
50 / 150 x 100 = 33.33 percent

## How to find percentage

Percentage formula is given by: Percentage = fractional value / total value x 100

1. We need to find the overall quantities to find the total and fractional value of which we need to find the percentage.
2. For example, if a student has scored 50 out of 100 marks in one subject and 70 out of 100 in another, the fractional marks and total marks will be 120 and 200 marks, respectively.
3. Next, we need to put these in the formula: Percentage = fractional value / total value x 100
4. We will get 120 / 200 x 100 = 60. The percentage of marks the student got is 60.
5. We must not forget to put the % symbol after we find the percent value.
6. Therefore, the final percentage of marks will be 60%.

## Comparing quantities using percentages

We can compare quantities using percentages very easily. Let us study this with the help of an example.
You and your friend visit a granny’s house. Granny gives you 52 flowers and your friend 48 because the four flowers dried somehow. So the total flowers she got were 104.

Let us find the percentage of your flowers = fractional value / total value x 100
= 52 / 104 x 100 = 50%
Now let us calculate the percentage of flowers your friend got,
= 48 / 104 x 100 = 46. 15%
So from this, we can find that you got around 4% more flowers than your friend.

Example: In a test, Hermione secured a 90.38% by getting 47 marks. What is the percentage scored by Harry if he secured 39 marks?
Solution:

Let the total marks be m
Hermione’s percentage = 47 / m x 100 = 90.38
On solving for m, we get total marks = 52
Hence,
Percentage for Harry = 39 / 52 x 100 = 75%
Therefore, the percentage of marks scored by Harry is 75%.

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