Question

7 in.
2½ in.
number sentence: ​7×2½=5½
area: ​5½

Explanation:

Step1: Convert mixed number to improper fraction

The length is \(7\) (which is \(\frac{7}{1}\)) and the width is \(2\frac{1}{2}\). Convert \(2\frac{1}{2}\) to an improper fraction: \(2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}\).

Step2: Multiply the two fractions

To find the area of a rectangle, we use the formula \(A = l\times w\), where \(l\) is length and \(w\) is width. So we calculate \(7\times\frac{5}{2}\) (since \(7=\frac{7}{1}\), multiplying fractions is \(\frac{7}{1}\times\frac{5}{2}=\frac{7\times5}{1\times2}=\frac{35}{2}\)).

Step3: Convert back to mixed number

\(\frac{35}{2}=17\frac{1}{2}\) (because \(35\div2 = 17\) with a remainder of \(1\)). The original number sentence \(7\times2\frac{1}{2}=5\frac{1}{2}\) is incorrect. The correct calculation is \(7\times2\frac{1}{2}=7\times\frac{5}{2}=\frac{35}{2}=17\frac{1}{2}\).

Answer:

The correct number sentence is \(7\times2\frac{1}{2}=17\frac{1}{2}\) and the area is \(17\frac{1}{2}\) square inches.