Question

1. there are 7 ½ bottles of orange juice in the restaurants fridge. if each bottle holds 1 5/6 quarts of orange juice, how much orange juice does the restaurant have?

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(7\frac{1}{2}\) to an improper fraction. \(7\frac{1}{2}=\frac{7\times2 + 1}{2}=\frac{15}{2}\). Then, convert \(1\frac{5}{6}\) to an improper fraction: \(1\frac{5}{6}=\frac{1\times6+5}{6}=\frac{11}{6}\).

Step2: Multiply the two fractions

To find the total amount of orange juice, multiply the number of bottles by the amount per bottle. So we calculate \(\frac{15}{2}\times\frac{11}{6}\). Multiply the numerators: \(15\times11 = 165\), and multiply the denominators: \(2\times6=12\). So we have \(\frac{165}{12}\).

Step3: Simplify the fraction

Simplify \(\frac{165}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. \(\frac{165\div3}{12\div3}=\frac{55}{4}\). Convert this back to a mixed number: \(\frac{55}{4}=13\frac{3}{4}\).

Answer:

\(13\frac{3}{4}\) quarts