How do you Calculate Percentages?

How do you Calculate Percentages?

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Percentage

When we take 100 as the denominator of fractions, the numerators are called percentages. For convenience, the symbol % is used for percent. When we take 100 as the denominator of fractions, the numerators are called percentages. For convenience, the symbol % is used for percent.
Or
‘‘A percentage is simply a ratio in which the second term is arranged to be 100’’. Also percent is an abbreviation of the Latin phrase per centum, meaning per hundred or hundredths.
How do you Calculate Percentages 1
How do you Calculate Percentages 2

  1. A fraction may be converted into a percentage by multiplying that fraction by 100%. This does not change its value, since 100% is 1.
  2. A decimal may be converted into a percentage by multiplying it by 100%.

Uses of Percentages

  1. Interpreting percentages.
  2. Converting percentage to ‘How many’.
  3. Converting ratio to percentage.
  4. Increase or decrease as percent.

Eg: Raju invests 10% of his pocket money in buying toffees means ₹10 out of ₹100 are invested by Raju in buying the toffees.

Eg: A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win ?
Here, the total number of matches played are 20. Out of these 25% are won by the team.

I method (direct):
Out of 100, 25 matches are won by the team. So, out of 20, number of matches won by the team
= \(\frac { 25 }{ 100 } \times 20\)
= 5 matches.

II method (using percentage):
How do you Calculate Percentages 3

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Percentages Problems with Solutions

1. Express \(\frac { 7 }{ 20 }\) as a percentage.
Solution:
How do you Calculate Percentages 4

2. Express 0.625 as a percentage.
Solution: 0.625 = 0.625 × 100% = 62.5%

3.
How do you Calculate Percentages 5
Solution:
How do you Calculate Percentages 6

4. Out of 50 students in a class, 15 like to play cricket. What is percentage of students who like to play cricket ?
Solution:
Total students = 50
Students who like to play cricket = 15
So, % age of students who like to play cricket
How do you Calculate Percentages 7

5. Convert the given decimals to percent:
(a) 0.6
(b) 0.75
(c) 0.08
(d) 0.56
Solution:
We have
(a) 0.6 = (0.6 × 100)% = 60%
(b) 0.75 = (0.75 × 100)% = 75%
(c) 0.08 = (0.08 × 100)% = 8%
(d) 0.56 = (0.56 × 100)% = 56%

6. Convert a percentage into fraction
(i) 45%
(ii) 65%
(iii) 42.5%
Solution: We have
How do you Calculate Percentages 8

7. Convert each of the following into decimal fraction :
(a) 53%
(b) 0.38%
(c) 4.7%
Solution:
How do you Calculate Percentages 9

8. What percentage of the adjoining figure is shaded and what percentage is unshaded ? Find it.
Solution:
First we find the fraction of the figure that is shaded or unshaded. From this fraction we will find the percentage of the shaded and unshaded regions.
How do you Calculate Percentages 10

9. Convert each of the following ratios into a percentage :Convert each of the following ratios into a percentage :
(i) 15 : 45 (ii) 3 : 5
Solution: We have,
How do you Calculate Percentages 11

10. Estimate what region of the following figures is shaded and hence find percentage of that shaded region.
How do you Calculate Percentages 12
Solution: We have,
How do you Calculate Percentages 13

11. Convert given percents to decimal fractions and also to fractions in simplest form :Convert given percents to decimal fractions and also to fractions in simplest form :
(i) 25% (ii) 150% (iii) 20% (iv) 5%
Solution:
How do you Calculate Percentages 14

12. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Solution:
How do you Calculate Percentages 15

13. The population of India is 113 crore. If it increases by 1.7% every year, Find India’s population after one year.
Solution:
How do you Calculate Percentages 16

Maths