Comparing quantities means looking at the difference in the given quantities and numbers. It involves finding out whether they are equal or not, or which one is smaller or greater. For example, the height of child A is 160 cm, and that of child B is 80 cm; their heights can be compared by the use of ratio, which will be 160:80 or 2:1. When you compare prices related to an item or buying and selling, you are comparing quantities.
If you want to compare two quantities with different ratios, they must be equivalent ratios. To find an equivalent ratio, it should be written as a fraction, and this fraction must be alike. For example, how will you know that 1:2 and 2:3 are equivalent or not?
Here, you can see that since 3/6 is less than 4/6, 1:2 is greater than 2:3.
Equivalent ratios are said to be in proportion.
Another way to compare the quantities is by finding out the percentage. Take an example of your report card and that of your sibling. With the use of percentage, you can check who performed better.
Percentage = Given quantity x 100/ Total quantity
The percentage is represented by symbol %.
While taking out the percentage, you can use the equivalent fraction as well. For example, you have 8 red beads and 12 blue beads, which has a higher percentage?
Number of red beads = 8
Number of blue beads = 12
Total number of beads = 20
Percentage of red beads = 8×100/20 = 40%
Percentage of blue beads = 12×100/20 = 60%
So, the percentage of blue beads was more.
There are many uses of percentage in day to day life, like:
For example, out of 50 students in your class, 80% of them are going to the picnic. How will you find the exact number of the students going?
Total number of students = 50
Percentage of students going to picnic = 80%
Number of students going to picnic = a
Percentage = given quantity x 100 / total quantity
80 = a x 100 / 50
80 x 50 = 100a
4000 = 100a
4000/100 = a
a = 40
This means out of 50 students in the class, 40 of them are going to the picnic.
While converting decimal to a percentage, first convert decimal into a fraction, 0.2 becomes 2/10. Then multiply it by 100.
What if the question is reversed and you have been asked to convert a percentage to decimal or fraction?
For example: Convert 10% into fraction and decimal.
10% = 10/100, so
Fraction = 1/10
Decimal = 0.1
You can use percentage for calculating prices related to an item or buying and selling. Whenever shopkeepers buy a product, they sell it at a higher price. The buying price of an item is called Cost Price (CP). The selling price of an item is called Selling Price (SP). To check whether the shopkeeper earned the benefit or not, it is found by using profit or loss. Prices related to an item or buying and selling is in terms of Cost Price or Selling Price.
CP < SP, this is profit = SP-CP
CP = SP, neither profit nor loss
CP > SP, this is loss = CP-SP
If CP < SP, then you made a profit = SP – CP.
For example: A toy bought for INR 72 is sold at INR 80. Here, the shopkeeper is getting a profit of INR 8 (SP-CP = 80-72).
For example: A T-shirt bought for INR 120 is sold at INR 100. Here, the shopkeeper is having a loss of INR 20 (CP-SP = 120-100).
In the examples mentioned above, if you want to find the profit or loss as a percentage for the shopkeeper, here is the way:
For the toy, profit was INR 8, so
Profit % = Profit x 100 / CP = 8 x 100 / 72 = 11.11%
For the T-shirt, the loss was INR 20, so
Loss % = Loss x 100 / CP = 20 x 100 / 120 = 16.66%
We use percentage for calculating interest for multiple years. The money that has been borrowed is called the Principal. For keeping the money for some time, the borrower has to pay some extra money to the bank, which is called interest. To find the total sum of money to be paid at the end of the year, the amount of money borrowed and you must add interest. This is called Amount.
Amount = Principal + Interest
For example, if the bank says 10% per annum interest, this means for every INR 100 borrowed, you must pay INR 10 as interest per year.
Comparing quantities is a vital aspect of mathematics, with the most practical application. For any purchase decision, any monetary transaction and any kind of quantitative analysis comparing quantities play a major role. Hence a clear conceptual understanding is not only important for subject-related knowledge, but also a vital life skill.