The Parent-Teacher Association made $13\frac{5}{6}$ gallons of fruit punch for Parents' Night. Parents and teachers drank only $7\frac{1}{6}$ gallons altogether that night. How many gallons of fruit punch did the Parent-Teacher Association have left? $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ _____ gallons

Full solution

Q. The Parent-Teacher Association made

13\frac{5}{6}

gallons of fruit punch for Parents' Night. Parents and teachers drank only

7\frac{1}{6}

gallons altogether that night. How many gallons of fruit punch did the Parent-Teacher Association have left?

\newline

Write your answer as a fraction or as a whole or mixed number.

\newline

_____ gallons

Identify Total Amounts: Step $1$ : Identify the total amount of fruit punch made and the amount consumed. $\newline$ Total made: $13\frac{5}{6}$ gallons $\newline$ Total consumed: $7\frac{1}{6}$ gallons $\newline$ We need to subtract the amount consumed from the total made to find out how much is left.
Convert to Improper Fractions: Step $2$ : Convert mixed numbers to improper fractions for easier calculation. $\newline$ $13 \frac{5}{6} = (13\times6 + 5)/6 = \frac{83}{6}$ $\newline$ $7 \frac{1}{6} = (7\times6 + 1)/6 = \frac{43}{6}$ $\newline$ Now, subtract the two fractions.
Perform Subtraction: Step $3$ : Perform the subtraction. $\newline$ $\frac{83}{6} - \frac{43}{6} = \frac{83 - 43}{6} = \frac{40}{6}$ $\newline$ Simplify $\frac{40}{6}$ to its lowest terms. $\newline$ $\frac{40}{6} = \frac{20}{3}$ $\newline$ Convert $\frac{20}{3}$ back to a mixed number: $20 \div 3 = 6$ remainder $2$ , so it's $6 \frac{2}{3}$ gallons.