Question

a school made $16\frac{1}{3}$ gallons of fruit punch for parents night. parents and teachers drank only $11\frac{11}{12}$ gallons altogether that night. how many gallons of fruit punch did the school have left?
\boxed{1}\frac{\square}{\square} gallons

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \( 16\frac{1}{3} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 16\frac{1}{3} \), we have \( \frac{16\times3 + 1}{3}=\frac{48 + 1}{3}=\frac{49}{3} \).

Next, convert \( 11\frac{11}{12} \) to an improper fraction. Using the same formula, \( \frac{11\times12+11}{12}=\frac{132 + 11}{12}=\frac{143}{12} \).

Step2: Find a common denominator and subtract

The common denominator of 3 and 12 is 12. So we convert \( \frac{49}{3} \) to twelfths: \( \frac{49}{3}=\frac{49\times4}{3\times4}=\frac{196}{12} \).

Now subtract the two fractions: \( \frac{196}{12}-\frac{143}{12}=\frac{196 - 143}{12}=\frac{53}{12} \).

Step3: Convert back to a mixed number

Convert \( \frac{53}{12} \) to a mixed number. Divide 53 by 12: 12×4 = 48, so 53 - 48 = 5. Thus, \( \frac{53}{12}=4\frac{5}{12} \).

Answer:

\( 4\frac{5}{12} \)