Rewrite this fraction problem as a percent problem.
Find $\frac{7}{10}$ of 700.
Find □ % of 700.
We are given the problem to calculate \(\frac{7}{10}\) of \(700\). Our objective is to rewrite this as an equivalent percent problem in the form "Find \(\_\_\_\) % of \(700\)". Recall that a percent is a ratio where the second term is 100, so a value expressed as a fraction \(\frac{a}{b}\) can be converted to a percentage by multiplying it by \(100\%\), which is \(\frac{a}{b} \times 100\% = \frac{a \times 100}{b} \%\).
To convert the fraction \(\frac{7}{10}\) into a percentage, we follow the standard conversion method: \[\frac{7}{10} \times 100\% = \frac{700}{10}\% = 70\%.\] This means that \(\frac{7}{10}\) is equivalent to \(70\%\). Therefore, calculating \(\frac{7}{10}\) of \(700\) is mathematically identical to calculating \(70\%\) of \(700\).
We can verify our result by calculating both values:
\(\frac{7}{10} \times 700 = 7 \times 70 = 490\)
\(70\% \times 700 = \frac{70}{100} \times 700 = 70 \times 7 = 490\)
Since both calculations yield \(490\), our conversion is correct. Thus, the original problem "Find \(\frac{7}{10}\) of \(700\)" is equivalent to "Find \(70\%\) of \(700\)". The value to fill in the blank is \(\boxed{70}\).
Percentages are commonly used in daily life for tasks like calculating discounts during sales. For instance, if a store offers a 30% discount on an item costing \$700, knowing that 30% is equivalent to the fraction 3/10 helps you quickly calculate the savings as \$700 \times 0.3 = \$210, leaving the final price as \$490. Understanding the equivalence between fractions and percentages allows for faster mental math and more efficient resource management in financial situations.