## How do you Calculate Percentages?

### 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.

- 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

= \(\frac { 25 }{ 100 } \times 20\)

= 5 matches.

**II method (using percentage):**

### Percentages Problems with Solutions

**1.** Express \(\frac { 7 }{ 20 }\) as a percentage.

**Solution:**

**2.** Express 0.625 as a percentage.

**Solution:** 0.625 = 0.625 × 100% = 62.5%

**3.**

**Solution:**

**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

**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

**7.** Convert each of the following into decimal fraction :

(a) 53%

(b) 0.38%

(c) 4.7%

**Solution:**

**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.

**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%

**Solution:**

**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:**

**13.** The population of India is 113 crore. If it increases by 1.7% every year, Find India’s population after one year.

**Solution:**