Verified Answer :

  • Identify the given fraction as \(\frac{7}{10}\).
  • Set up the equation \(\frac{7}{10} = \frac{x}{100}\) to relate the fraction to a percentage.
  • Solve the equation to find \(x = 70\).
  • Conclude that the required percentage is \(\boxed{70\%}\).

Explanation

  1. Analysis of the Problem

The goal is to express the fraction \(\frac{7}{10}\) of \(800\) as a percentage of \(800\). A percentage is a ratio of a number to \(100\), denoted as \(x\%\) or \(\frac{x}{100}\). We are looking for an unknown value \(\square\) such that \(\frac{7}{10} \times 800 = \frac{\square}{100} \times 800\).

  1. Finding the Missing Percentage Value

To find the missing percentage value, we set the fraction \(\frac{7}{10}\) equal to a ratio with a denominator of \(100\). Let \(x\) be the value we are looking for:
\[\frac{7}{10} = \frac{x}{100}\]
To solve for \(x\), multiply both sides of the equation by \(100\):
\[x = \frac{7}{10} \times 100\]
\[x = \frac{700}{10} = 70\]
Therefore, \(\frac{7}{10}\) is equivalent to \(\frac{70}{100}\), which is \(70\%\).

  1. Verification and Conclusion

We can verify the result by calculating the value of the expressions.
For the fraction: \(\frac{7}{10} \times 800 = 7 \times 80 = 560\).
For the percentage: \(70\% \text{ of } 800 = \frac{70}{100} \times 800 = 0.7 \times 800 = 560\).
Since both calculations result in the same value, \(560\), our conversion is correct. The missing value in the box is \(70\).

Examples

Percentages are used everywhere in daily life to compare values on a scale of 100. For example, if a store offers a discount of \(\frac{1}{4}\) off an item priced at \(\$100\), you can quickly convert this to a percentage: \(\frac{1}{4} = \frac{25}{100} = 25\%\). This helps in quickly calculating savings, tax rates, or interest rates in your head!