Question

a. Estimate: \(3850 \div 52\) b. Find the exact answer. c. Is your estimate lower, higher, or the same?

Short answer

Answer: The estimated value of 3850 ÷ 52 is 80, while the exact value is 74 ⅖. The estimate is higher than the actual value.

Step-by-step solution

A. Estimation

To estimate the result of \(3850 \div 52\), try rounding both numbers to the nearest whole number that is a multiple of 10 and then perform the division. In this case, round \(3850\) to \(4000\) and round \(52\) to \(50\). Now, calculate the division for the rounded numbers: \(4000 \div 50 = 80\). So, the estimation for \(3850 \div 52\) is \(80\).

B. Exact Answer

To find the exact answer, perform the actual division: \(3850 \div 52\). Divide the given numbers as follows: \[ \require{cancel} \begin{array}{c|cccc} \multicolumn{2}{r}{73} & \cancelto{5}{7} \\ \cline{2-5} 52 & 3 & 8 & \cancel{5} & 0 \\ \cline{2-3} \multicolumn{2}{r}{\cancel{3}} & 6 \\ \cline{3-3} \multicolumn{3}{r}{} & 2 & 0 \\ \cline{4-4} \multicolumn{4}{r}{2} & 0 \\ \cline{5-5} \multicolumn{5}{r}{0} \\ \end{array} \] Therefore, \(3850 \div 52 = 74 \space with \space remainder \space 2\) or as a mixed number \(74\frac{2}{52}\).

C. Comparison of the Estimate and Exact Answer

The estimate for \(3850 \div 52\) is \(80\), while the exact answer is \(74 \frac{2}{52}\). The estimate is higher than the actual value.