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# NCERT Solutions for Class 7 Maths Chapter 8 – Comparing Quantities

NCERT Solutions for Class 7 Maths Chapter 8 is about the comparison of quantities. In this chapter, there are a total of 3 exercises and 21 questions. The Chapter ratios and percentages and their practical use. In this chapter, you will also study ‘simple interest’.

NCERT Solutions for Class 7 Chapter 8 ‘Comparing Quantities’ is based on the latest syllabus approved by CBSE. At Instasolv, we provide the most reliable study material for Class 7 Maths. Solutions of NCERT Class 7 Maths Book are provided chapter-wise that help you in understanding the concepts better and score high marks in the exams.

Chapter 8 ‘Comparing Quantities’, of CBSE NCERT Class 7 Maths Book covers ratios, percentages and simple interest. These are simple concepts that are very frequently used in our daily life. For the Maths subject in Class 7, we explain the important elements and summarise each part and subpart of the Chapter. We follow the same sequence as in the book so that it becomes easy to understand and use as a reference.

## NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities: Summary

1.  Introduction – Comparison is used every day in our life. The words taller, shorter, bigger, smaller, faster, slower are all used for comparison. If a teacher has to line up students based on their height, she is comparing the height of all the students.
2. Equivalent Ratios – Ratios can also be compared to check whether they are equal or not. The steps to be followed are:
• Convert the ratios to fractions. Example 1:4 is converted to 1/4, 2:3 is converted to 2/3
• Then use multipliers or dividers to convert the fractions into like fractions. Example 1/4 = 3/12 and 2/3 = 8/12
• Now compare 3/12 and 8/12. They are not equal.

3. Percentage – Another Way of Comparing Quantities:–

In the exams, percentages can also be compared to know who scored higher or lower.

1. Meaning of Percentage

Percentage means a hundredth. Percent is derived from the Latin word ‘per centum’ meaning ‘per hundred’.

Fractions can be represented as percentages. A percentage is the numerator of a fraction whose denominator is 100.

If you get 95 out of 100 marks, as a fraction it can be denoted as 95/100 and the percentage becomes 95.

If the marks are not 100 but rather 50 and the score out of 50 is 48, then the fraction is 48/50. Convert this into a fraction where the denominator is 100 by multiplying the numerator and denominator by 2. So 48/50 can also be written as 96/100. In other words, 48 out of 50 can also be represented as 96 percent.

1. Converting Fractional Numbers into Percentage

This has also been explained in the above example. To convert into a percentage the denominator of the fraction must be 100. Use multipliers or divisors to the denominator of the fraction to get 100 as the denominator. The value of the numerator then becomes the percentage.

1. Converting Decimals into Percentage

Use the same principle. Arrive at a fraction where the denominator is 100 and the value of the numerator will be the percentage.

Example: 0.9 can be written as a fraction as 9/10. Multiply the numerator and denominator by 10 we get 9/10 = 90/100. So 0.9 as a percentage is 90.

1. Converting Percentages to Fractions or Decimals

Keep following the same principle and you will always get it right. A percentage is the numerator of a fraction whose denominator is a hundred.

Ex. 62% as a fraction is 62/100 and as a decimal is 0.62

1. Fun With Estimation

We often estimate in many situations in our daily life. Suppose you are planning your birthday party and you invite 40 friends. Your mother asks you to estimate what percentage of your friends may not come. Suppose you feel five percent of your friends may not come. How many friends would your mother prepare the cake for?

5% written as a fraction is 5/100. In your case, the whole is 40 so let us first multiply the numerator and denominator by 2.

5/100 = 10/200

Now let us divide the numerator and denominator by 5

10/200 = 2/40

The number of friends your mother expects to not come is 2, so she will prepare the cake for 40 – 2 = 38 friends.

1. Use of Percentages

1. Interpreting Percentages

Use the same principle. Write the percentage as a fraction applying the principle that the percentage is a fraction with denominator a hundred. So 22% as a fraction can be written as 22/100.

1. Converting Percentages to “How Many”

We have already done one example of this above in “Fun with Estimation”. For better understanding let us take one more example.

A survey shows that 40% of people who buy tickets to a movie also buy popcorn. If 1000 people bought movie tickets for the coming Sunday how many of them would buy popcorn.

We have to find 40% of 1000.

40% as a fraction can be written as 40/100

Multiply the denominator and numerator by 10

40/100 = 400/1000

The answer is 400. Out of 1000 people who bought movie tickets, 400 would buy popcorn.

1. Ratios to Percents

Remember we have been using one principle right through. Let us apply the same again.

Example: A ratio of 2:5 can be written as a fraction. 2:5 = 2/5.

Now multiply the numerator and denominator by 20.

2/5 = 40/100

In other words, 2:5 is equal to 40 percent.

1. Increase or Decrease as a percent

Suppose you want to compare the percentage. For example, in the previous class test, you scored 40 out of 50 and this time you scored 47 out of 50. By what percentage did your score increase?

Let us first solve this by the principle we have been using.

40/50 = 80/100 if the numerator and denominator are both multiplied by 2.

So in the previous test, you scored 80 percent.

47/50 = 94/100 if the numerator and denominator are both multiplied by 2.

So in this test, you scored 94 percent

The increase is 94 minus 80 equal to 14 percent.

Alternatively, we can do this by applying the following method

The percentage increase is equal to the amount of change divided by the original amount or base, the result multiplied by 100.

In the above example, the amount of change is 47 – 40 = 7

The original amount or base is 50.

By this method, the percentage increase is (7/50) x 100 = 14

Instasolv suggests that you do not try to learn by rote. If there is a doubt apply the same principle explained through this chapter to cross-check your answer and you will never go wrong.

1. Prices Related to an Item or Buying and Selling

Let us use some standard notations

Cost Price can be represented as CP

Selling Price can be represented as SP

Profit is made when SP is greater than CP

Loss occurs when SP is less than CP

Break-even or no Profit no Loss situation is when SP is equal to CP

5.1 Profit or Loss as a Percentage

The important thing to note here is that the base is the cost price over which there would be profit or loss.

Suppose CP = 50 and SP = 60.

Profit is SP – CP = 60 – 50 = 10

Representing as a percent where the base or CP is 50.

10/50 = 20/100 if we multiply the numerator and denominator by 2.

So the percentage of profit is 20.

1. Charge Given on Borrowed Money or Simple Interest

Let us consider a situation where a loan is taken from a bank or money is borrowed from the bank.

The sum borrowed from the bank is called Principal which we will write as P.

The amount charged by the bank for lending money for a given period is called Interest which we will write as I.

The rate of interest is usually for one year. So we will denote Rate percent per annum as R.

Interest for one year on a rate percent per annum can be calculated as

I = (P x R)/100

The total amount that has to be repaid to the bank is Principle plus Interest. This we will write as A.

A = P + I

Let us take an example

Suppose money borrowed P = 10000

Rate of interest per annum R = 12%

Then the interest charged for one year, I = (10000 x 12)/100 = 1200

The amount to be paid to close the loan after one year would be A = 10000 + 1200 = 11200.

1. Interest for Multiple Years

If we do not change the Principal then the interest calculated is called Simple Interest. For understanding better, if the interest is paid every year then the principal will not change but if the interest is added to the principal at the end of every year the principal will go up. That will be called compound interest which you will study in future classes.

In the case of Simple Interest, if the number of years for which interest has to be paid is denoted as T, then the total interest would be (PxRxT)/100

In the same example taken above if T = 5 years the total interest would be 1200 x 5 = 6000.

By simple interest method, the amount to be paid to close the loan after five years would be A = 10000 + 6000 = 16000.

Study Tips for NCERT Class 7 Maths  Chapter 8: Comparing Quantities

Every student aims to get a high score in the exams. Instasolv recommends that you read chapter 8 Comparing Quantities of CBSE NCERT Solutions for Class 7 Maths. Instasolv has provided a simple explanation and summary of each part. Use this summary as a ready reference. It will also help in improving your conceptual clarity.

1. If any concept is still not understood, ask the experts on the Instasolv app which does not charge any student for this support.
2. Do all the exercises, solved examples and self-practice questions on your own before you cross-check from the NCERT Solutions for Class 7 Maths or ask the experts on the Instasolv app.

Subject matter experts of Instasolv never recommend learning by rote. In this chapter, there is one principle that has been used to explain several parts. Practice Class 7 Maths Chapter 8 extra questions as well and you would be able to answer any question on these concepts easily.

Remember, the examples at the end where interest is calculated, if there is a currency mentioned in the question like rupees or dollars, then the same should be mentioned in the answer as well.

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