Question

a piece of land is $3\\ 2/5$ miles wide. it is $2\\ 3/4$ times as long as it is wide. how long is the piece of land? simplify your answer and write it as a fraction or as a whole or mixed number. \boxed{} miles submit

Explanation:

Step1: Convert mixed numbers to improper fractions

The width is \( 3\frac{2}{5} \) miles. To convert to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 3\frac{2}{5}=\frac{3\times5 + 2}{5}=\frac{15 + 2}{5}=\frac{17}{5} \).

The multiplier for length is \( 2\frac{3}{4} \) times the width. Converting \( 2\frac{3}{4} \) to an improper fraction: \( 2\frac{3}{4}=\frac{2\times4+3}{4}=\frac{8 + 3}{4}=\frac{11}{4} \).

Step2: Multiply the two improper fractions

To find the length, we multiply the width (as an improper fraction) by the multiplier (as an improper fraction). So, length \( L=\frac{17}{5}\times\frac{11}{4} \).

When multiplying fractions, we multiply the numerators together and the denominators together: \( L=\frac{17\times11}{5\times4}=\frac{187}{20} \).

Step3: Convert the improper fraction to a mixed number

To convert \( \frac{187}{20} \) to a mixed number, we divide 187 by 20. \( 20\times9 = 180 \), so the quotient is 9 and the remainder is \( 187-180 = 7 \). So, \( \frac{187}{20}=9\frac{7}{20} \).

Answer:

\( 9\frac{7}{20} \)