Key Points - Comparing Quantities

- Comparing Quantities: We are often required to compare two quantities, in our daily life.
They may be heights, weights, salaries, marks etc. To compare two quantities, their units must be the same.
We are often required to compare two quantities in our daily life. They may be heights, weights, salaries, marks etc.
While comparing heights of two persons with heights150 cm and 75 cm, we write it as the ratio 150: 75 or 2: 1.

- Ratio: A ratio compares two quantities using a particular operation.
- Percentage: Percentage are numerators of fractions with denominator 100. Percent is represent by the symbol % and means hundredth too.
- Two ratios can be compared by converting them to like fractions. If the two fractions are equal, we say the two given ratios are equivalent.
- If two ratios are equivalent then the four quantities are said to be in proportion. For example, the ratios 8: 2 and 16: 4 are equivalent therefore 8, 2, 16 and 4 are in proportion.

-  A way of comparing quantities is percentage. Percentages are numerators of fractions with denominator 100. Per cent means per hundred. For example 82% marks means 82 marks out of hundred.

- Fractions can be converted to percentages and vice-versa.

- Decimals too can be converted to percentages and vice-versa.
For example, 0.25 = 0.25 ×100% = 25%

- Percentages are widely used in our daily life,

(a) We have learnt to find exact number when a certain per cent of the total quantity is given.
(b) When parts of a quantity are given to us as ratios, we have seen how to convert them to percentages.
(c) The increase or decrease in a certain quantity can also be expressed as percentage.
(d) The profit or loss incurred in a certain transaction can be expressed in terms of percentages.
(e) While computing interest on an amount borrowed, the rate of interest is given in terms of per cents. For example, ` 800 borrowed for 3 years at 12% per annum.

- Simple Interest: Principal means the borrowed money.
The extra money paid by borrower for using borrowed money for given time is called interest (I).
The period for which the money is borrowed is called ‘Time Period’ (T).
- Rate of interest is generally given in percent per year.
P × R ×T
Interest (I): 100
Total money paid by the borrower to the lender is called the amount.