2-5 Estimate the Percent of a Number

Property

To estimate the percent of a number, round the percent to a nearby benchmark percent that is easy to calculate mentally. Common benchmark percents include $10\% = \frac{1}{10}$, $25\% = \frac{1}{4}$, $50\% = \frac{1}{2}$, and $75\% = \frac{3}{4}$.

Examples

Property

To estimate the percent of a number, you can round both the percent and the number to create a simpler problem. First, round the percent to a nearby benchmark percent (like $10\%$, $25\%$, or $50\%$). Then, round the whole number to a compatible number that is easy to calculate with.

Examples

• To estimate $24\%$ of $81$, round $24\%$ to $25\%$ and $81$ to $80$. The estimate is $25\%$ of $80$, which is $\frac{1}{4} \times 80 = 20$.
• To estimate $48\%$ of $197$, round $48\%$ to $50\%$ and $197$ to $200$. The estimate is $50\%$ of $200$, which is $\frac{1}{2} \times 200 = 100$.

Explanation

This estimation strategy makes calculations much simpler by using numbers that are easier to work with. By rounding the percent to a common benchmark and the whole number to a compatible value, you can often perform the calculation mentally. This method provides a reasonable approximation of the actual answer without needing a calculator. The goal is to choose rounded values that make the multiplication straightforward.

Property

To estimate the percent of a number in real-world scenarios (such as calculating tips, taxes, or discounts), round the percent to a benchmark percent (like $10\%$, $20\%$, $25\%$, or $50\%$) and round the whole number to a compatible number that is easy to compute mentally.

Examples