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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.
The document Comparing Quantities Summary Class 7 NCERT Summary Chapter 7 is a part of the Class 7 Course NCERT Textbooks & Solutions for Class 7.
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FAQs on Comparing Quantities Summary Class 7 NCERT Summary Chapter 7

1. What is the concept of comparing quantities in Class 7?
Ans. Comparing quantities in Class 7 involves understanding and analyzing different quantities and determining their relationships. It includes comparing numbers, ratios, percentages, and proportions to make meaningful comparisons and draw conclusions.
2. How can we compare quantities using ratios and proportions in Class 7?
Ans. To compare quantities using ratios and proportions in Class 7, we first need to identify the units and values of the quantities. Then, we can find the ratio between the quantities by dividing one quantity by the other. We can simplify the ratio to its simplest form and compare it with other ratios to determine which quantity is larger or smaller.
3. What are the key steps to solve problems related to comparing quantities in Class 7?
Ans. The key steps to solve problems related to comparing quantities in Class 7 are: 1. Identify the quantities to be compared. 2. Understand the relationship between the quantities (e.g., ratio, percentage, proportion). 3. Apply appropriate mathematical operations to compare the quantities. 4. Simplify the comparison, if necessary, to determine the larger or smaller quantity.
4. How can we compare quantities using percentages in Class 7?
Ans. To compare quantities using percentages in Class 7, we need to convert both quantities into percentages. We can do this by expressing the quantities as a fraction of 100 and then comparing the resulting percentages. The quantity with a higher percentage is larger, while the one with a lower percentage is smaller.
5. Can we compare quantities using different units in Class 7?
Ans. No, we cannot directly compare quantities with different units in Class 7. To compare quantities with different units, we need to convert them into a common unit of measurement. This allows for a meaningful and accurate comparison. Once the quantities are in the same units, we can use the appropriate mathematical operations to compare them.
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