Percentages are a fundamental concept in mathematics and are widely used in various fields, such as finance, statistics, and everyday calculations. Understanding how to multiply or divide percentages can help you make more informed decisions and perform accurate calculations.

What is Percentage

A percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign, “%”. For example, 50% is equivalent to 50 out of 100, or 0.50 in decimal form. Percentages are used to compare relative sizes and to express ratios, making them a useful tool in various mathematical and practical applications.

How to Multiply Percentages

To multiply two percentages, convert each percentage to its decimal form by dividing by 100, then multiply the decimals. Finally, convert the result back to a percentage by multiplying by 100.

Examples on Multiply Two Percentages

Example: Let’s say you want to multiply 20% by 30%.

Solution:

Convert each percentage to decimal form:

• 20% becomes 0.20
• 30% becomes 0.30

Multiply the decimals:

• 0.20 × 0.30 = 0.06

Convert the result back to a percentage:

• 0.06 × 100 = 6%

So, 20% multiplied by 30% equals 6%.

How to Divide Percentages

To divide two percentages, convert each percentage to its decimal form by dividing by 100, then divide one decimal by the other. Finally, convert the result back to a percentage by multiplying by 100.

Examples on Divide Two Percentages

Example: Let’s say you want to divide 40% by 20%.

Solution:

Convert each percentage to decimal form:

• 40% becomes 0.40
• 20% becomes 0.20

Divide the decimals:

• 0.40 / 0.20 = 2

So, 40% divided by 20% equals 2 (or 200%).

Ways to Multiply or Divide Two Percentages

Follow the steps added below to Multiply or Divide Two Percentages

Step 1: Always convert to decimal form: This is crucial for accurate calculations. Divide the percentage by 100 before performing any multiplication or division.

Step 2: Double-check your conversions: Ensure that your percentages are correctly converted to decimals to avoid any errors in your final result.

Step 3: Use a calculator: For complex percentages or to save time, using a calculator can help you get precise results quickly.

Conclusion

Understanding how to multiply and divide percentages is crucial for accurate calculations in various scenarios. By converting percentages to decimals and following the outlined steps, you can perform these operations confidently and correctly.

Examples on Multiply or Divide Two Percentages

Example 1: Multiply 25% by 40%.

Solution:

Convert to decimal form:

• 25% = 0.25
• 40% = 0.40

Multiply:

• 0.25 × 0.40 = 0.10

Convert back to percentage:

• 0.10 × 100 = 10%

So, 25% multiplied by 40% equals 10%.

Example 2: Divide 60% by 15%.

Solution:

Convert to decimal form:

• 60% = 0.60
• 15% = 0.15

Divide:

• 0.60 / 0.15 = 4

Convert back to percentage:

• 4 × 100 = 400%

So, 60% divided by 15% equals 4 (or 400%).

Practice Problems Related to Multiply or Divide Two Percentages

P1: Multiply 12% by 35%.

P2: Multiply 45% by 60%.

P3: What is 15% of 20%?

P3: Divide 80% by 20%.

P5: Divide 90% by 30%.

P6: Determine the result of 90% divided by 30%.

Read More:

• How to Calculate Percentage
• Maths Trick to Find Percentage

FAQs on Multiply or Divide Two Percentages

Can you multiply two percentages directly?

No, you should first convert the percentages to decimals before multiplying them.

How do you convert a percentage to a decimal?

Divide the percentage by 100. For example, 50% becomes 0.50.

What is the result of dividing a percentage by another percentage?

Convert both percentages to decimals, then divide one decimal by the other. Convert the result back to a percentage by multiplying by 100.

Why is it important to convert percentages to decimals?

Converting percentages to decimals ensures accurate calculations and helps avoid errors.

Are there any shortcuts for multiplying or dividing percentages?

Using a calculator can be a helpful shortcut for quick and accurate results.