Percentage Part of a Whole

Learn to find what percentage one number is of another!

1. Finding "What Percentage Is..."

Formula: $\frac{\text{Part}}{\text{Whole}} \times 100\%$

The whole is the denominator, and the part is the numerator.

Example 1: What percentage of 80 is 60?

Since 80 is the whole, the denominator is 80.

Since 60 is part of the whole, the numerator is 60.

$\frac{60}{80} \times 100\%$

= $\frac{6}{8} \times 100\%$ (simplify first)

= $\frac{3}{4} \times 100\%$

= $\frac{3 \times 100}{4}\%$ = $\frac{300}{4}\%$ = 75%

75% of 80 is 60.

Example 2: What percentage of 400 ml is 180 ml?

$\frac{180}{400} \times 100\%$

= $\frac{18}{40} \times 100\%$

= $\frac{9}{20} \times 100\%$

= $\frac{9 \times 100}{20}\%$ = $\frac{900}{20}\%$ = 45%

45% of 400 ml is 180 ml.

2. Remember: Same Units!

⚠️ Important: Make sure both quantities have the same unit before calculating!

Example: Mr Lim bought 2 kg of grapes. His family ate 500 g. What percentage of the grapes did they eat?

Step 1: Convert to same units

2 kg = 2000 g

Step 2: Calculate percentage

$\frac{500}{2000} \times 100\%$

= $\frac{1}{4} \times 100\%$

= 25%

They ate 25% of the grapes.

3. Finding a Quantity from a Percentage

Write the percentage as a fraction over 100, then multiply. For example, 30% of 50 = $\frac{30}{100} \times 50 = 15$

Example: Amy baked 200 cookies. Her friends ate 80% of the cookies. How many cookies did she have left?

Method 1: Find the number eaten, then subtract

80% × 200

= $\frac{80 \times 200}{100}$

= $\frac{16000}{100}$ = 160

Amy's friends ate 160 cookies.

200 − 160 = 40 cookies left

Method 2: Find remaining % first

100% − 80% = 20% left

100% of cookies = 200

10% of cookies = 200 ÷ 10 = 20

20% of cookies = 20 × 2 = 40 cookies

4. Multi-Step Problems

Example: There are 160 students in four Primary 5 classes. The table shows the number in 5A, 5B, and 5C. What percentage of the students are in 5D?

Class	Number of Students
5A	42
5B	38
5C	40
5D	?

Step 1: Find students in 5A, 5B, 5C

42 + 38 + 40 = 120

Step 2: Find students in 5D

160 − 120 = 40

Step 3: Find percentage

$\frac{40}{160} \times 100\% = \frac{1}{4} \times 100\% =$ 25%

Practice Problems

Practice 1: What percentage is...

What percentage of 50 is 15?

ShowHide solution

$\frac{15}{50} \times 100\% = \frac{3}{10} \times 100\% = \frac{300}{10}\% =$ 30%

Practice 2: Unit conversion

A tank holds 5 litres of water. 1500 ml was used. What percentage of the water was used?

ShowHide solution

5 litres = 5000 ml

$\frac{1500}{5000} \times 100\% = \frac{15}{50} \times 100\% = \frac{3}{10} \times 100\% =$ 30%

Practice 3: Finding quantity

There are 400 books in a library. 35% are fiction books. How many fiction books are there?

ShowHide solution

35% × 400 = $\frac{35}{100} \times 400 = \frac{35 \times 400}{100} = \frac{14000}{100} =$ 140 fiction books

Practice 4: Finding remaining

A farmer has 500 chickens. He sold 60% of them. How many chickens does he have left?

ShowHide solution

Method 1: 60% × 500 = 300 sold, 500 − 300 = 200 left

Method 2: 100% − 60% = 40% left, 40% × 500 = 200 chickens

Key Takeaways

What percentage? Use $\frac{\text{Part}}{\text{Whole}} \times 100\%$
Same units: Always convert to same units first!
A percentage of a quantity: Write the percentage over 100 and multiply, e.g. 30% of 50 = $\frac{30}{100} \times 50 = 15$
Finding remaining: Either subtract from the whole OR find the percentage left first (e.g. 100% − 80% = 20%)
The whole goes in the denominator