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Chapter 7: Comparing Quantities

    Introduction

    Meaning of Percentage

    Converting Fractional Numbers to Percentage

    Converting Decimals to Percentage

    Converting Percentages to Fractions or Decimals

    Use Of Percentages

    Charge Given on Borrowed Money or Simple Interest

    Interest for Multiple Years

    Exercise 7.1

    Exercise 7.2

    What Have We Discussed?

    Extra Curriculum Support

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Chapter 7: Comparing Quantities > Converting Fractional Numbers to Percentage

Converting Fractional Numbers to Percentage

Fractional numbers can have different denominator. To compare fractional numbers, we need a common denominator and we have seen that it is more convenient to compare if our denominator is 100.

That is, we are converting the fractions to Percentages. Let us try converting different fractional numbers to Percentages.

Example-1

1. Write 13 as per cent.

Instruction

13

  • To convert 13 into percentage, we can multiply and divide from both sides (the number remains the same).
  • The 100100 fraction denotes the .
  • The 100 is to the numerator giving us the fraction:
  • Upon finding the decimal form we get: 13 is equal to %
  • Hence, the percentage has been found.

Let's have a look pictorially. What is 3/5 as percent.

= 35×100100.

In the last class we saw multiplication of two fractions. 35 and 100100 are represented below. Move one over the other and see how many grids are covered. You will find there are 60 grids covered Out of 100. So it is %.

Instruction

2. Out of 25 children in a class, 15 are girls. What is the percentage of girls?

Solution:

Out of children, there are girls.

Therefore, percentage of girls = 1525 × 100 = .

There are 60% girls in the class.

3.Convert 54 into per cent.

Instruction

54

  • To convert 54 into percentage, we can multiply to the number which denotes the percentage
  • Upon solving, we get the value:
  • Hence 54 is equal to 125%

From these examples, we find that the percentages related to proper fractions are 100 whereas percentages related to improper fractions are 100.

THINK, DISCUSS AND WRITE

(i) Can you eat 50% of a cake?

Can you eat 100% of a cake

Can you eat 150% of a cake?

(ii) Can a price of an item go up by 50%?

Can a price of an item go up by 100%?

Can a price of an item go up by 150%?