what is 75 of 240

Natasha willow

2 min read

·

16-01-2025

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Finding a percentage of a number is a common calculation in many areas of life, from calculating discounts to determining the portion of a total. This article will walk you through how to calculate 75% of 240, explaining the process step-by-step. We'll also explore different methods to solve this, empowering you to tackle similar percentage problems with confidence.

Understanding Percentages

Before diving into the calculation, let's refresh our understanding of percentages. A percentage is a fraction or ratio expressed as a number out of 100. For instance, 75% means 75 out of 100, which can also be written as the fraction 75/100 or the decimal 0.75.

Method 1: Converting Percentage to Decimal

This is a straightforward method ideal for quick calculations.

Step 1: Convert the percentage to a decimal.

To do this, divide the percentage by 100. In this case:

75% / 100 = 0.75

Step 2: Multiply the decimal by the number.

Now, multiply the decimal (0.75) by the number you're finding the percentage of (240):

0.75 * 240 = 180

Therefore, 75% of 240 is $\boxed{180}$.

Method 2: Using Fractions

This method utilizes the fractional equivalent of the percentage.

Step 1: Express the percentage as a fraction.

75% can be written as the fraction 75/100. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor (25):

75/100 = 3/4

Step 2: Multiply the fraction by the number.

Multiply the simplified fraction (3/4) by 240:

(3/4) * 240 = 180

Again, we find that 75% of 240 is $\boxed{180}$.

Method 3: Finding 10%, then Scaling Up

This method is particularly useful for mental math and estimations.

Step 1: Calculate 10% of 240.

To find 10%, divide the number by 10:

240 / 10 = 24

Step 2: Multiply to find 70%.

Since 70% is seven times 10%, multiply the result from Step 1 by 7:

24 * 7 = 168

Step 3: Add 5% (half of 10%).

5% is half of 10%, so take half of the result from Step 1:

24 / 2 = 12

Step 4: Add the results for 70% and 5%.

Add the results from Step 2 and Step 3:

168 + 12 = 180

Therefore, 75% of 240 is $\boxed{180}$.

Conclusion

As demonstrated, there are several ways to calculate 75% of 240, all leading to the same answer: 180. Choose the method that you find most comfortable and efficient. Understanding these different approaches will help you confidently tackle various percentage problems in the future. Remember, the core concept involves converting the percentage into a usable form (decimal or fraction) and then performing multiplication.