what percent of 72 is 27

2 min read 22-12-2024

Finding what percent one number represents of another is a common mathematical task. This article will guide you through calculating what percentage 27 is of 72, step-by-step, and explain the underlying concepts. We'll also explore different methods for solving this type of problem.

Understanding Percentages

A percentage is a fraction or ratio expressed as a number out of 100. For example, 50% means 50 out of 100, or 50/100, which simplifies to 1/2. Percentages are used to express proportions and comparisons.

Method 1: Using a Proportion

This method is a classic approach to solving percentage problems. We set up a proportion:

Part/Whole = Percentage/100

In our case:

Part: 27
Whole: 72
Percentage: This is what we need to find (let's call it 'x')

Therefore, our proportion is:

27/72 = x/100

To solve for 'x', we cross-multiply:

27 * 100 = 72 * x

2700 = 72x

Now, divide both sides by 72:

x = 2700 / 72

x = 37.5

Therefore, 27 is 37.5% of 72.

Method 2: Using Decimal Conversion

This method involves converting the fraction to a decimal and then multiplying by 100 to get the percentage.

Form a fraction: Represent the problem as a fraction: 27/72
Divide: Divide the numerator (27) by the denominator (72): 27 ÷ 72 = 0.375
Multiply by 100: Multiply the decimal by 100 to convert it to a percentage: 0.375 * 100 = 37.5%

Again, we find that 27 is 37.5% of 72.

Method 3: Using a Calculator

Most calculators have a percentage function. Simply enter 27 ÷ 72 * 100 to get the answer directly: 37.5%

Practical Applications

Understanding percentages is crucial in many real-world scenarios, including:

Calculating discounts: Determining the sale price after a percentage discount.
Analyzing data: Representing proportions in charts and graphs.
Financial calculations: Calculating interest rates, taxes, and profits.
Grading: Determining a percentage score on a test.

Conclusion

We've explored three different methods to determine that 27 is 37.5% of 72. Whether you prefer using proportions, decimal conversion, or a calculator, the key is understanding the underlying concept of percentages and how to apply the appropriate formula or method. Mastering percentage calculations is a valuable skill applicable across various fields.