A bucket contains $4\frac{1}{3}$ gallons of water. If Judy adds $4\frac{1}{3}$ gallons more, how many gallons will there be in all? $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ _____ gallons

Full solution

Q. A bucket contains

4\frac{1}{3}

gallons of water. If Judy adds

4\frac{1}{3}

gallons more, how many gallons will there be in all?

\newline

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

\newline

_____ gallons

Identify Amounts: Step $1$ : Identify the total amount of water initially in the bucket and the amount being added. $\newline$ Initial amount in the bucket: $4\frac{1}{3}$ gallons, $\newline$ Amount added by Judy: $4\frac{1}{3}$ gallons, $\newline$ We need to add these two amounts together to find the total.
Convert to Fractions: Step $2$ : Convert mixed numbers to improper fractions for easier addition. $\newline$ $4 \frac{1}{3}$ is equivalent to $\left(4\times3 + 1\right)/3 = \frac{13}{3}$ , $\newline$ So, both the initial amount and the amount added are $\frac{13}{3}$ gallons.
Add Fractions: Step $3$ : Add the two fractions. $\newline$ Total = $\frac{13}{3} + \frac{13}{3} = \frac{26}{3}$ gallons, $\newline$ Convert $\frac{26}{3}$ back to a mixed number: $26 \div 3 = 8$ remainder $2$ , $\newline$ So, $\frac{26}{3} = 8 \frac{2}{3}$ gallons.