Question

1. find the areas of the rectangles with the following side lengths. a. 5 in and $\frac{1}{3}$ in b. 5 in and $\frac{4}{3}$in c. $\frac{5}{2}$ in and $\frac{4}{3}$in d. $\frac{7}{6}$ in and $\frac{6}{7}$in

Explanation:

Step1: Recall area formula for rectangle

The area formula of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width.

Step2: Solve part a

Given $l = 5$ in and $w=\frac{1}{3}$ in. Then $A=5\times\frac{1}{3}=\frac{5}{3}=1\frac{2}{3}$ square - inches.

Step3: Solve part b

Given $l = 5$ in and $w = \frac{4}{3}$ in. Then $A=5\times\frac{4}{3}=\frac{20}{3}=6\frac{2}{3}$ square - inches.

Step4: Solve part c

Given $l=\frac{5}{2}$ in and $w=\frac{4}{3}$ in. Then $A=\frac{5}{2}\times\frac{4}{3}=\frac{5\times4}{2\times3}=\frac{20}{6}=\frac{10}{3}=3\frac{1}{3}$ square - inches.

Step5: Solve part d

Given $l=\frac{7}{6}$ in and $w=\frac{6}{7}$ in. Then $A=\frac{7}{6}\times\frac{6}{7}=1$ square - inch.

Answer:

a. $1\frac{2}{3}$ square - inches
b. $6\frac{2}{3}$ square - inches
c. $3\frac{1}{3}$ square - inches
d. 1 square - inch