what percent of 120 is 7.8

Natashya

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25-12-2024

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What Percent of 120 is 7.8? A Step-by-Step Guide

Finding what percentage one number represents of another is a common mathematical task. This article will guide you through calculating what percent of 120 is 7.8, explaining the process step-by-step and offering additional context.

Understanding the Problem

The question "What percent of 120 is 7.8?" asks us to find the percentage that 7.8 represents when compared to 120. In other words, we need to determine how many parts out of 100 7.8 represents relative to 120.

Method 1: Using Proportions

One effective way to solve this problem involves setting up a proportion. A proportion is an equation stating that two ratios are equal.

• Set up the proportion: We can represent the problem as a ratio: x/100 = 7.8/120

  Where:

  • x represents the percentage we're trying to find.
  • 7.8 is the part.
  • 120 is the whole.
  • 100 represents the total percentage.

• Cross-multiply: To solve for x, cross-multiply: 120x = 7.8 * 100

• Simplify: This simplifies to 120x = 780

• Solve for x: Divide both sides by 120: x = 780 / 120

• Calculate: This gives us x = 6.5

Therefore, 7.8 is 6.5% of 120.

Method 2: Using a Formula

Alternatively, you can use a more direct formula:

• Formula: (Part / Whole) * 100 = Percentage

• Substitute: (7.8 / 120) * 100 = Percentage

• Calculate: 0.065 * 100 = 6.5

Again, this confirms that 7.8 is 6.5% of 120.

Practical Applications

Understanding percentage calculations is crucial in many real-world situations, including:

• Finance: Calculating interest rates, discounts, and tax percentages.
• Statistics: Analyzing data and interpreting results.
• Everyday Life: Determining sale prices, tips, and proportions in recipes.

Conclusion

By using either the proportion method or the direct formula, we've determined that 7.8 is 6.5% of 120. Mastering these methods will allow you to confidently tackle similar percentage problems in various contexts. Remember that understanding the underlying concepts is key to solving these problems accurately and efficiently.