what percent of 110 is 71.5

Natashya

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26-12-2024

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Finding what percent one number represents of another is a common mathematical task. This article will walk you through calculating what percentage 71.5 is of 110, step-by-step, and explain the underlying principles. This is useful for various applications, from calculating grades to understanding sales discounts.

Understanding Percentages

Before diving into the calculation, let's refresh the concept of percentages. A percentage is a fraction expressed as a number out of 100. For example, 50% is equivalent to 50/100 or 1/2. We use percentages to represent proportions or parts of a whole.

Calculating the Percentage

To find what percent 71.5 is of 110, we follow these steps:

Step 1: Set up a proportion.

We can represent the problem as a proportion:

71.5 / 110 = x / 100

Where 'x' represents the percentage we want to find.

Step 2: Solve for x.

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

110x = 71.5 * 100

110x = 7150

Step 3: Isolate x.

Divide both sides of the equation by 110:

x = 7150 / 110

x = 65

Therefore, 71.5 is 65% of 110.

Alternative Method: Using Decimal Conversion

Another approach involves converting the fraction to a decimal and then multiplying by 100:

1. Divide: Divide 71.5 by 110: 71.5 / 110 = 0.65
2. Multiply by 100: Multiply the result by 100 to express it as a percentage: 0.65 * 100 = 65%

This method gives us the same result: 65%.

Real-World Applications

Understanding percentage calculations is crucial in many everyday situations:

• Calculating grades: If you scored 71.5 out of 110 points on a test, your percentage score is 65%.
• Determining discounts: A 65% discount on an item originally priced at $110 would mean a reduction of $71.5.
• Analyzing data: Percentages are frequently used to represent data in charts and graphs, making it easier to understand proportions.

Conclusion

Calculating percentages is a valuable skill with widespread applications. As shown, finding what percent 71.5 is of 110 involves a simple proportion or decimal conversion. Both methods lead to the answer: 65%. Mastering percentage calculations enhances your ability to interpret and analyze numerical data effectively.