Question

1. a rectangular plate has an area of 30 1/16 square inches. if the width of the plate is 4 5/8 inches, what is its length in inches? 30 1/16 ÷ 4 5/8 481/16 ×... for problems 5–8, divide.

Explanation:

Step1: Convert mixed numbers to improper fractions

The area of the rectangle \( A = 30\frac{1}{16} \) square inches. To convert \( 30\frac{1}{16} \) to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 30\frac{1}{16}=\frac{30\times16 + 1}{16}=\frac{480+1}{16}=\frac{481}{16} \).

The width \( w = 4\frac{5}{8} \) inches. Converting \( 4\frac{5}{8} \) to an improper fraction: \( 4\frac{5}{8}=\frac{4\times8 + 5}{8}=\frac{32 + 5}{8}=\frac{37}{8} \).

Step2: Use the formula for the area of a rectangle to find length

The formula for the area of a rectangle is \( A=l\times w \), where \( l \) is the length, \( w \) is the width, and \( A \) is the area. To find the length, we rearrange the formula to \( l=\frac{A}{w} \).

Substituting the values of \( A \) and \( w \) we found: \( l=\frac{\frac{481}{16}}{\frac{37}{8}} \).

When dividing fractions, we multiply by the reciprocal of the divisor: \( l=\frac{481}{16}\times\frac{8}{37} \).

Simplify the fractions: The 8 and 16 have a common factor of 8. So, \( \frac{8}{16}=\frac{1}{2} \). Then we have \( l=\frac{481\times1}{2\times37}=\frac{481}{74} \).

Now, convert \( \frac{481}{74} \) back to a mixed number. Divide 481 by 74: \( 74\times6 = 444 \), and \( 481-444 = 37 \). So, \( \frac{481}{74}=6\frac{37}{74}=6\frac{1}{2} \) (since \( \frac{37}{74}=\frac{1}{2} \)).

Answer:

The length of the rectangular plate is \( 6\frac{1}{2} \) inches.