How to Calculate Percentage of a Number

Grade: 7-8 | Topic: Arithmetic

What You Will Learn

After reading this page you will be able to calculate the percentage of any number using a simple formula, determine what percentage one number is of another, and find the original number when only the percentage and result are known. These three skills cover the vast majority of percentage calculations you will encounter in class and in everyday life.

Theory

The percentage formula

A percentage is a number expressed as a fraction of 100. The symbol $\%$ literally means "per hundred." To find $p\%$ of a number $n$, use this formula:

$p\% \text{ of } n = \frac{p}{100} \times n$

Think of it as two quick steps: convert the percentage to a decimal by dividing by 100, then multiply by the number.

For example, to find 40% of 90:

$\frac{40}{100} \times 90 = 0.40 \times 90 = 36$

So 40% of 90 is 36.

Three types of percentage problems

Almost every percentage question fits one of three patterns. The same formula connects all three -- you simply solve for the unknown:

What you need to find	Formula
The part ($p\%$ of $n$)	$\text{Part} = \frac{p}{100} \times n$
The percentage	$p = \frac{\text{Part}}{n} \times 100$
The whole number	$n = \frac{\text{Part} \times 100}{p}$

Once you memorise this relationship you can handle any percentage calculation by identifying which value is missing and rearranging the formula.

Mental math shortcuts

Some common percentages are easy to compute in your head:

• 50% of a number -- divide by 2
• 25% of a number -- divide by 4
• 10% of a number -- divide by 10
• 1% of a number -- divide by 100
• 5% of a number -- find 10% then halve it

You can combine these. For example, 15% = 10% + 5%. To find 15% of 200: $10\%\text{ of }200 = 20$, then $5\%\text{ of }200 = 10$, so $15\%\text{ of }200 = 30$.

Worked Examples

Example 1: Finding a percentage of a number (easy)

Problem: What is 25% of 360?

Step 1: Convert the percentage to a decimal. $25\% = \frac{25}{100} = 0.25$

Step 2: Multiply by the number. $0.25 \times 360 = 90$

Answer: 90

Example 2: Finding what percentage one number is of another (medium)

Problem: A student answered 18 questions correctly out of 24. What percentage did they get right?

Step 1: Identify the part and the whole. Part = 18 (correct answers), Whole = 24 (total questions).

Step 2: Divide the part by the whole. $\frac{18}{24} = 0.75$

Step 3: Multiply by 100 to convert to a percentage. $0.75 \times 100 = 75\%$

Answer: The student scored 75%.

Example 3: Finding the whole when the part and percentage are known (medium)

Problem: 60 is 15% of what number?

Step 1: Write the relationship as an equation. $\frac{15}{100} \times n = 60$

Step 2: Solve for $n$ by dividing both sides by $\frac{15}{100}$ (or equivalently, multiply by $\frac{100}{15}$). $n = \frac{60 \times 100}{15} = \frac{6000}{15} = 400$

Step 3: Verify -- $15\%$ of 400 is $0.15 \times 400 = 60$. Correct.

Answer: The number is 400.

Example 4: Applying percentage to a real-world situation (medium)

Problem: A restaurant bill is $85. You want to leave a 20% tip. How much is the tip, and what is the total you pay?

Step 1: Calculate the tip amount. $\frac{20}{100} \times 85 = 0.20 \times 85 = 17$

Step 2: Add the tip to the bill. $85 + 17 = 102$

Answer: The tip is $17, and the total is $102.

Example 5: Combining two percentage calculations (challenging)

Problem: In a school of 500 students, 52% are girls. Of the girls, 30% play a sport. How many girls play a sport?

Step 1: Find the number of girls. $\frac{52}{100} \times 500 = 0.52 \times 500 = 260$

Step 2: Find 30% of the girls. $\frac{30}{100} \times 260 = 0.30 \times 260 = 78$

Step 3: Verify the overall percentage. Girls who play sport as a percentage of all students: $\frac{78}{500} \times 100 = 15.6\%$. This equals $52\% \times 30\% = 0.52 \times 0.30 = 0.156 = 15.6\%$. Correct.

Answer: 78 girls play a sport.

Common Mistakes

Mistake 1: Forgetting to divide by 100

❌ $30\% \text{ of } 50 = 30 \times 50 = 1500$

✅ $30\% \text{ of } 50 = \frac{30}{100} \times 50 = 0.30 \times 50 = 15$

Why this matters: The percent symbol means "per hundred." If you skip the division, your answer will be 100 times too large. Always convert the percentage to a decimal or fraction first.

Mistake 2: Confusing the part and the whole

❌ "12 is what percentage of 48?" Student writes $\frac{48}{12} \times 100 = 400\%$.

✅ $\frac{12}{48} \times 100 = 25\%$

Why this matters: The part (the smaller piece you are measuring) goes in the numerator and the whole (the total) goes in the denominator. Reversing them flips the answer entirely. Read the problem carefully to identify which value is the part and which is the whole.

Mistake 3: Percentage greater than 100% seems wrong but may be correct

❌ Student gets 120% and assumes they made an error.

✅ A number can absolutely be more than 100% of a smaller number. For example, 60 is 150% of 40 because $\frac{60}{40} \times 100 = 150\%$.

Why this matters: Percentages over 100% are valid and common in real life (a 150% increase, scoring 120% with bonus marks). Do not automatically reject an answer just because it exceeds 100%.

Practice Problems

Try these on your own before checking the answers:

1. What is 45% of 180?
2. 36 is what percentage of 90?
3. 72 is 40% of what number?
4. A jacket costs $120. Sales tax is 8%. What is the total price?
5. A factory produced 800 items. 5% were defective, and 60% of the defective items could be repaired. How many defective items could be repaired?

Click to see answers

1. $0.45 \times 180 = 81$
2. $\frac{36}{90} \times 100 = 40\%$
3. $n = \frac{72 \times 100}{40} = 180$
4. Tax = $0.08 \times 120 = 9.60$. Total = 120 + 9.60 = \129.60$
5. Defective = $0.05 \times 800 = 40$. Repairable = $0.60 \times 40 = 24$

Summary

• To find $p\%$ of a number $n$, compute $\frac{p}{100} \times n$.
• To find what percentage a part is of a whole, use $\frac{\text{Part}}{\text{Whole}} \times 100$.
• To find the whole when you know the part and percentage, use $n = \frac{\text{Part} \times 100}{p}$.
• Use mental math shortcuts (10%, 5%, 1%) to estimate quickly and check your work.

Related Topics

• Percentages — Complete Guide
• How to Calculate Percentage Increase and Decrease
• Percentage Word Problems with Solutions

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