Question

1. beach volleyball the dimensions of the playing area and free zone of a beach volleyball court are $78\frac{2}{3}$ feet by $49\frac{1}{6}$ feet. what is the area of a beach volleyball court? source: california beach volleyball association

Explanation:

Step1: Convert mixed numbers to improper fractions

$78\frac{2}{3} = \frac{78\times3 + 2}{3} = \frac{236}{3}$
$49\frac{1}{6} = \frac{49\times6 + 1}{6} = \frac{295}{6}$

Step2: Multiply fractions for area

Area = $\frac{236}{3} \times \frac{295}{6}$
Simplify first: $\frac{236\div2}{3} \times \frac{295}{6\div2} = \frac{118}{3} \times \frac{295}{3} = \frac{118\times295}{9}$

Step3: Calculate numerator and simplify

$118\times295 = (120-2)\times295 = 120\times295 - 2\times295 = 35400 - 590 = 34810$
Area = $\frac{34810}{9} = 3867\frac{7}{9}$

Answer:

The area of the beach volleyball court is $\boldsymbol{3867\frac{7}{9}}$ square feet (or $\boldsymbol{\frac{34810}{9}}$ square feet).