Questions: Marley makes 3 1/3 cups of smoothies and divides it between containers that hold 5/6 cups. How many containers does she fill?

Marley makes 3 1/3 cups of smoothies and divides it between containers that hold 5/6 cups. How many containers does she fill?
Transcript text: Marley makes $3 \frac{1}{3}$ cups of smoothies and divides it between containers that hold $\frac{5}{6}$ cups. How many containers does she fill?
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Solution

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Solution Steps

To determine how many containers Marley can fill, we need to divide the total amount of smoothies by the capacity of each container. This involves converting the mixed number and fractions into improper fractions, performing the division, and then taking the floor of the result to find the number of completely filled containers.

Step 1: Convert Mixed Number to Improper Fraction

The total amount of smoothies Marley makes is given as \( 3 \frac{1}{3} \). We convert this mixed number to an improper fraction: \[ 3 \frac{1}{3} = \frac{10}{3} \]

Step 2: Define Container Capacity

The capacity of each container is given as \( \frac{5}{6} \) cups.

Step 3: Calculate the Number of Containers Filled

To find the number of containers that can be completely filled, we divide the total amount of smoothies by the capacity of each container: \[ \text{containers\_filled} = \left\lfloor \frac{\frac{10}{3}}{\frac{5}{6}} \right\rfloor \] Calculating the division: \[ \frac{\frac{10}{3}}{\frac{5}{6}} = \frac{10}{3} \times \frac{6}{5} = \frac{60}{15} = 4 \] Thus, the number of containers filled is \( 4 \).

Final Answer

\(\boxed{4}\)

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