Question

the box that contains the salt lick that the farmer is ordering is $1\frac{1}{4}$ feet by $1\frac{2}{3}$ feet by $\frac{5}{6}$ feet. how many cubes of salt lick fit in the box? \boxed{} cubes

Explanation:

Step1: Convert to improper fractions

$1\frac{1}{4}=\frac{5}{4}$, $1\frac{2}{3}=\frac{5}{3}$, $\frac{5}{6}$ remains

Step2: Find common denominator

Denominators: 4, 3, 6; LCD = 12
Convert each: $\frac{5}{4}=\frac{15}{12}$, $\frac{5}{3}=\frac{20}{12}$, $\frac{5}{6}=\frac{10}{12}$

Step3: Identify cube side length

Side length = $\frac{1}{12}$ ft (unit fraction of LCD)

Step4: Count cubes per dimension

$\frac{15}{12}\div\frac{1}{12}=15$, $\frac{20}{12}\div\frac{1}{12}=20$, $\frac{10}{12}\div\frac{1}{12}=10$

Step5: Calculate total cubes

Multiply the three counts: $15\times20\times10$

Answer:

1500 cubes