Lillian poured $1\frac{3}{4}$ gallons of water into a bucket. Later, she added $6\frac{3}{4}$ gallons more. How much water is in the bucket now? $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ $\_\_\_\_$ gallons

Full solution

Q. Lillian poured

1\frac{3}{4}

gallons of water into a bucket. Later, she added

6\frac{3}{4}

gallons more. How much water is in the bucket now?

\newline

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

\newline

\_\_\_\_

gallons

Identify initial and additional amounts: Step $1$ : Identify the initial amount of water and the additional amount added. $\newline$ Initial water: $1\frac{3}{4}$ gallons, $\newline$ Additional water: $6\frac{3}{4}$ gallons.
Convert mixed numbers to improper fractions: Step $2$ : Convert mixed numbers to improper fractions for easier addition. $\newline$ $1 \frac{3}{4} = (1\times4 + 3)/4 = \frac{7}{4}$ , $\newline$ $6 \frac{3}{4} = (6\times4 + 3)/4 = \frac{27}{4}$ .
Add improper fractions: Step $3$ : Add the two improper fractions. $\newline$ $\frac{7}{4} + \frac{27}{4} = \frac{7 + 27}{4} = \frac{34}{4}$ .
Simplify the fraction: Step $4$ : Simplify the fraction. $\frac{34}{4} = 8 \frac{1}{2}$ gallons.