How do you Calculate Percentages?
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.
‘‘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.
- A fraction may be converted into a percentage by multiplying that fraction by 100%. This does not change its value, since 100% is 1.
- A decimal may be converted into a percentage by multiplying it by 100%.
Uses of Percentages
- Interpreting percentages.
- Converting percentage to ‘How many’.
- Converting ratio to percentage.
- 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
= 5 matches.
II method (using percentage):
Percentages Problems with Solutions
1. Express as a percentage.
2. Express 0.625 as a percentage.
Solution: 0.625 = 0.625 × 100% = 62.5%
4. Out of 50 students in a class, 15 like to play cricket. What is percentage of students who like to play cricket ?
Total students = 50
Students who like to play cricket = 15
So, % age of students who like to play cricket
5. Convert the given decimals to percent:
(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
Solution: We have
7. Convert each of the following into decimal fraction :
8. What percentage of the adjoining figure is shaded and what percentage is unshaded ? Find it.
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.
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,
10. Estimate what region of the following figures is shaded and hence find percentage of that shaded region.
Solution: We have,
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%
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.
13. The population of India is 113 crore. If it increases by 1.7% every year, Find India’s population after one year.