How to Calculate Percentages: Formula, Worked Examples & Practice

To calculate a percentage, use the formula Percentage = (Part ÷ Total) × 100%. For example, if you answer 45 out of 60 questions correctly, your score is (45 ÷ 60) × 100% = 75%. The same formula works for calculating discounts, taxes, savings interest, price increases, and percentage rises or falls in everyday life.

Definition of Percentage and Its Origin

Percent (%) is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin per centum, which means "per hundred". The concept was first used by Italian merchants in the 15th century to calculate profits and trade taxes between cities.

For example, means 50 out of 100, or half of the whole — written as 50/100 = ½. Percentages are closely related to common and mixed fractions that you have studied before.

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The Formula for Calculating Percentages

The basic formula for calculating a percentage is:

Written out in full: Percentage = (Part ÷ Total) × 100%

Meaning of each symbol in the formula:

• Percentage = the percentage value you want to find (for example: 75%)
• Part = the value being compared (for example: questions answered correctly)
• Total = the total or reference value (for example: total number of questions)

From this formula, we can derive two useful related formulas:

Part = (Percentage ÷ 100) × Total

Total = (Part ÷ Percentage) × 100

💡 Tip: Imagine the percentage formula triangle. Cover the part you want to find, and the triangle will show the operation you need to perform. If two values are side by side → multiply. If one is above the other → divide.

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How to Calculate Percentages: Step-by-Step Examples

Example 1: Calculating a Percentage Score ⭐

Dani scored 45 out of a total of 60 questions. What is Dani's score as a percentage?

Step 1: Identify the known values

• Part = 45 (questions answered correctly)
• Total = 60 (total questions)

Step 2: Substitute into the formula

Percentage = (45 ÷ 60) × 100%

Step 3: Calculate the result

✅ Answer: Dani's score is 75%

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Example 2: Finding the Part from a Percentage ⭐⭐

A shop offers a 25% discount on a shirt priced at Rp200,000. How much is the discount in rupiah?

Step 1: Identify the known values

• Percentage = 25%
• Total = Rp200,000

Step 2: Substitute into the derived formula

Part = (25 ÷ 100) × 200,000

Step 3: Calculate the result

✅ Answer: The discount is Rp50,000. Final price: Rp150,000

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Example 3: Finding the Total from a Percentage ⭐⭐

Sinta has saved Rp60,000, which is 30% of her pocket money for this month. What is Sinta's total pocket money?

Step 1: Identify the known values

• Part = 60,000
• Percentage = 30%

Step 2: Substitute into the formula

Total = (60,000 ÷ 30) × 100

Step 3: Calculate the result

✅ Answer: Sinta's total pocket money is Rp200,000

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Example 4: A Common Mistake — Forgetting to Convert the Percent to a Decimal ⭐

This is the mistake pupils make most often. Many students multiply the percentage by the number straight away without dividing by 100 first.

Question: What is 15% of 80?

Wrong way ❌:

The pupil forgot that 15% must be converted to a decimal first: 15% = 15 ÷ 100 = 0.15

Correct way ✅:

✅ Correct answer: 15% of 80 is 12

💡 Remember: Always convert the percentage to decimal form (divide by 100) before multiplying. A percentage is not the same as a plain whole number.

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Commonly Used Percentage Values

Memorise this table to calculate percentages more quickly without a calculator!

💡 Quick Tip: To calculate 10%, simply shift the decimal point one place to the left. Example: 10% of 350 = 35. Then multiply for other percentages: 20% = 35 × 2 = 70, 5% = 35 ÷ 2 = 17.5.

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How to Calculate Percentage Increase and Decrease

Percentages are also used to measure changes in value — whether something goes up or down. This often appears in problems about salary rises, price changes, or exam scores.

Percentage Increase Formula:

Percentage Decrease Formula:

Increase example: The price of a book rises from Rp40,000 to Rp48,000.

✅ The price of the book has risen by 20%.

Decrease example: Budi's exam score has fallen from 90 to 72.

✅ Budi's score has fallen by 20%.

This concept is closely related to how to calculate ratios, which is often used together with percentages in middle-school maths problems.

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Practice Problems on Calculating Percentages

Work through the following problems to test your understanding!

⭐ Problem 1 (Easy): There are 40 pupils in Budi's class. Of these, 15 pupils wear glasses. What percentage of pupils wear glasses?

⭐⭐ Problem 2 (Medium): The price of a pair of shoes is Rp350,000 and there is a 40% discount. What is the price after the discount?

⭐⭐ Problem 3 (Medium): A tree grows 12 cm in a month, which is 8% of its initial height. What was the tree's initial height?

⭐⭐⭐ Problem 4 (Challenge): In a Maths test, Rina answered 36 out of 45 questions correctly. What is Rina's score as a percentage? Does she pass if the pass mark is 75%?

Answer Key:

1. Percentage = (15 ÷ 40) × 100% = 37.5%. That means nearly 4 in 10 pupils in Budi's class wear glasses.
2. Discount = (40 ÷ 100) × 350,000 = 140,000 → Final price = 350,000 − 140,000 = Rp210,000. Work out the discount first, then subtract it from the original price.
3. Initial height = (12 ÷ 8) × 100 = 150 cm. Use the formula Total = (Part ÷ Percentage) × 100.
4. Percentage = (36 ÷ 45) × 100% = 80% → Pass ✅ because 80% > 75%. Rina's score exceeds the pass mark.

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Summary

1. Percent (%) expresses a number as a part out of 100; the main formula is Percentage = (Part ÷ Total) × 100%.
2. From the main formula we can find: Part = (Percentage ÷ 100) × Total or Total = (Part ÷ Percentage) × 100.
3. Memorise the percent-fraction table: 10% = divide by 10, 25% = divide by 4, 50% = divide by 2 — much quicker than reaching for a calculator.
4. The most common mistake: forgetting to convert the percent to a decimal (divide by 100) before multiplying — 25% is not 25, but 0.25.
5. Percentages are used every day: shopping discounts, exam scores, price rises, taxes. Also master how to calculate ratios to round out your maths skills.

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