Percentage

Q: How do you turn a fraction or decimal into a percentage?

Multiply by 100. \tfrac{3}{4} = 0.75 = 75\%.

A percentage is a fraction out of 100. "35%" means 35 out of every 100. Percentages let you compare amounts of different sizes and describe changes such as discounts and growth.

Formulas

Percentage of a quantity

part = \frac{p}{100} \times whole

One quantity as a percentage of another

p % = \frac{part}{whole} \times 100

Percentage change

change % = \frac{new - original}{original} \times 100

Worked examples

Example 1. Find 20% of 350.

$\frac{20}{100} \times 350 = 70$ .

Answer: 70

Example 2. A student scores 45 out of 60. What percentage is that?

$\frac{45}{60} \times 100 = 75$ .

Answer: 75%

Example 3. A shirt costs ₹800. Its price rises by 15%. What is the new price?

Increase = $\frac{15}{100} \times 800 = 120$ .
New price = $800 + 120 = 920$ .

Answer: ₹920

Example 4. A price falls from ₹500 to ₹425. Find the percentage decrease.

Decrease = $500 - 425 = 75$ .
$\frac{75}{500} \times 100 = 15$ .

Answer: 15%

Common mistakes

Dividing the change by the new value. A percentage change is always taken on the original value.
Thinking a 20% rise followed by a 20% fall brings you back. It leaves you at 96% of the start, because the fall is 20% of a bigger number.
Forgetting to multiply by 100 when turning a fraction into a percentage.

Practice questions with answers

1. Convert 50% into a fraction in lowest terms.

A $\frac{1}{2}$
B $\frac{1}{4}$
C $\frac{5}{10}$
D $\frac{2}{5}$

Show answer

Answer: A)

\frac{1}{2}

50% =

\frac{50}{100} = \frac{1}{2}

in lowest terms.

2. A percentage increase or decrease is always worked out on which amount?

AThe original amount
BThe sum of old and new
CThe new amount
DThe change itself

Show answer

Answer: A) The original amount

Percent change = (change ÷ original amount) × 100. We always compare the change with the amount we started from.

3. Increase 500 by 10%.

A550
B495
C1100
D605

Show answer

Answer: A) 550

10% of 500 = 50. New value = 500 + 50 = 550.

4. A milkman in Varanasi sells a mixture that is

\frac{1}{3}

cream by part.
He must print this share as a percentage on the label, rounded to two decimal places.
What percentage of the mixture is cream?

A33.33%
B30%
C3.33%
D66.67%

Show answer

Answer: A) 33.33%

\frac{1}{3} = \frac{1}{3} \times 100

% =

\frac{100}{3}

% = 33.333...%, which rounds to 33.33%.

5. A worker's daily wage was cut by 10%. By what percent must the new wage be raised to get back the original wage?

A9%
B11%
C $11 \frac{1}{9} %$
D10%

Show answer

Answer: C)

11 \frac{1}{9} %

Take ₹100 → ₹90 after the cut. To get back ₹10 on ₹90:

\frac{10}{90} \times 100 = 11 \frac{1}{9} %

. A 10% raise on ₹90 gives only ₹99.

6. The population of a city increased by 10% in the first year and decreased by 10% in the second year, ending at 99000.
What was the population at the start of the first year?

A100000
B200000
C90000
D110000

Show answer

Answer: A) 100000

Factor =

1.10 \times 0.90 = 0.99

. Original

x

0.99 = 99000, so original =

\frac{99000}{0.99} = 100000

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Frequently asked questions

How do you calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. For 20% of 350: $0.20 \times 350 = 70$ .

How do you work out percentage increase?

Find the increase, divide it by the original amount, then multiply by 100.

How do you turn a fraction or decimal into a percentage?

Multiply by 100. $\frac{3}{4} = 0.75 = 75%$ .

How do you find the original price after a discount?

If a price after a 20% discount is ₹640, it is 80% of the original, so the original is $640 \div 0.8 = 800$ .

Percentage

Formulas

Worked examples

Common mistakes

Practice questions with answers

Practice by class

Frequently asked questions

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