Comparing Quantities Summary Class 7 NCERT Summary Chapter 7

Introduction

• In our daily life, there are many occasions when we compare two quantities such as comparing height, weight etc.
• To compare two quantities, the units must be the same.

Ratios

• A ratio compares two quantities using a particular operation.
• The ratio of two quantities of the same kind and in the same units is fraction that shows how many times the one quantity is of the other.
• The ratio of two quantities a and b (b ≠ 0) is a ÷ b or a/b and is denoted by a:b.
• Two ratios can be compared by converting them into like fractions. If the two fractions are equal, we say that the two given ratios are equivalent.
• If the two ratios are equal then the involved four quantities are said to be in proportion.
• Four numbers a, b, c, d are said to be in proportion if a:b=c:d and we write, a:bc:d.

Percentage – another way of comparing quantities

• Per cent is derived from Latin word ‘per centum’ meaning ‘per hundred’.
• Percentages are numerators of fractions with denominator 100.
• Per cent is represented by the symbol % and means hundredths too. That is 1% means 1 out of hundred or one hundredth. It can be written as: 1% = 1/100 = 0.01.

Conversion

• To convert a fraction into percent, multiply the fraction by 100 and write % sign.
• To convert percent into decimals, drop the sign of percent and shift the decimal point two places to the left.
• To convert a decimal into percent, shift the decimal point two places to the right side and write % sign.

Use of Percentages

• When parts of a quantity are given to us as ratios, we need to convert those to percentages.
• The percent of increase tells what per cent the amount of increase, of the original number.
• Percent of increase = Amount of increase/Original number × 100 
• There are times when we need to know the increase or decrease in a certain quantity as percentage.
• Percent of decrease = Amount of decrease/Original number × 100.

Buying and Selling

• The buying price of any item is known as its cost price (CP).
• The price at which an item is sold is known as its selling price (SP).
• If CP <SP, then a profit is made and profit = SP-CP . If CP = SP, there is no profit or loss.
• If CP > SP, then a loss is made and Loss = CP-SP.
• Profit percent = Profit/CP × 100 
• Loss percent = Loss/SP × 100

Simple Interest

• The money you borrow is known as sum borrowed or principal.
• For keeping the money for some time the borrower has to pay some extra money to the bank which is known as Interest.
• The period for which the money is borrowed is called 'Time Period' (T).
• Total money paid by the borrower to the lender is called the amount.
• Amount = Principal + Interest
• Rate of interest is generally given in percent per year.
• Simple Interest (S.I.): P×R×T/100.
• Percentage to Fractions: Drop the percent sign and divide the number by 100.
• Percentage to Decimals: First convert the given percentage into fraction with denominator as 100 and then put the fraction into decimal form.