Question

albert purchased a large rectangular field so that he could farm the land. the field measures 22\\(\frac{1}{3}\\) miles long and 21 miles wide. what is the area of his field? the area of the rectangular field is \\(\square\\) (type a whole number, a proper fraction, or a mixed number. simplify your answer.)

Explanation:

Step1: Convert mixed number to improper fraction

The length is \(22\frac{1}{3}\) miles. To convert a mixed number \(a\frac{b}{c}\) to an improper fraction, we use the formula \(\frac{a\times c + b}{c}\). So for \(22\frac{1}{3}\), we have \(a = 22\), \(b = 1\), \(c = 3\). Then \(22\frac{1}{3}=\frac{22\times3 + 1}{3}=\frac{66 + 1}{3}=\frac{67}{3}\).

Step2: Calculate the area of the rectangle

The area \(A\) of a rectangle is given by the formula \(A=\text{length}\times\text{width}\). The length is \(\frac{67}{3}\) miles and the width is \(21\) miles. So we multiply \(\frac{67}{3}\) by \(21\). We can write \(21\) as \(\frac{21}{1}\), then \(\frac{67}{3}\times\frac{21}{1}\). Notice that \(21\) and \(3\) can be simplified. \(21\div3 = 7\), so the expression becomes \(67\times7\).

Step3: Multiply the numbers

\(67\times7 = 469\).

Answer:

\(469\)