Question

a bucket contains $11\frac{2}{3}$ gallons of water and is $\frac{5}{6}$ full. how many gallons of water would be in a full bucket? write a multiplication and a division equation to represent the situation. write your equations using the \wiris editor\ button

Explanation:

Step1: Define variable for full bucket

Let $x$ = gallons in full bucket.

Step2: Write multiplication equation

$\frac{5}{6}x = 11\frac{2}{3}$

Step3: Convert mixed number to improper fraction

$11\frac{2}{3} = \frac{35}{3}$

Step4: Write division equation

$x = 11\frac{2}{3} \div \frac{5}{6}$

Step5: Solve for $x$ (optional verification)

$x = \frac{35}{3} \times \frac{6}{5} = 14$

Answer:

Multiplication equation: $\boldsymbol{\frac{5}{6}x = 11\frac{2}{3}}$
Division equation: $\boldsymbol{x = 11\frac{2}{3} \div \frac{5}{6}}$
Capacity of full bucket: 14 gallons