## COMPARING QUANTITITES - ESSENTIAL POINTS

• While comparing heights of two persons with heights 150 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.
• 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.
• Percent is represented by the symbol % and means hundredth too.
• Fractions can be converted to percentages and vice-versa.
• For example, 1/3 = 1/3 x 100% whereas 45% = 45 /100
• Decimals too can be converted to percentages and vice-versa.
• For example, 0.35 = 0.35 x 100% = 35%
• Percentages are widely used in our daily life,
1. To find exact number when a certain per cent of the total quantity is given.
2. When parts of a quantity are given to us as ratios, we can convert them to percentage.
3. Percentage can be used to denote the increase or decrease in a certain quantity.
4. Percentage can be used to denote the profit or loss incurred in a certain transaction.
5. While computing interest on an amount borrowed, the rate of interest is given in terms of per cents. For example, ` 300 borrowed for 2 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. Total money paid by the borrower to the lender is called the amount.
• Interest (I) = (P x R x T)/100