Question

sue cooks \\(\frac{4}{5}\\) of a 3 - cup box of rice. she wants to know how many cups of rice she cooks. build a model to show \\(\frac{4}{5} \times 3\\).

Explanation:

Step1: Understand the multiplication

We need to calculate $\frac{4}{5} \times 3$, which is equivalent to finding 4/5 of 3.

Step2: Rewrite integer as fraction

Express 3 as a fraction: $3 = \frac{3}{1}$

Step3: Multiply numerators and denominators

Multiply the numerators together and denominators together:
$\frac{4}{5} \times \frac{3}{1} = \frac{4 \times 3}{5 \times 1} = \frac{12}{5}$

Step4: Simplify to mixed number (optional)

Convert the improper fraction to a mixed number:
$\frac{12}{5} = 2\frac{2}{5}$

For the model:

1. Divide the number line from 0 to 3 into 5 equal segments per cup, so 15 total equal parts (since $3 \times 5 = 15$).
2. Each segment represents $\frac{1}{5}$ of a cup.
3. Shade 12 of these segments (since $\frac{12}{5}$ is the product), which will end at the $2\frac{2}{5}$ mark on the number line.

Answer:

Sue cooks $\frac{12}{5}$ or $2\frac{2}{5}$ cups of rice.
For the model: Divide the 0-to-3 number line into 15 equal $\frac{1}{5}$ segments, then shade the first 12 segments to represent $\frac{4}{5} \times 3$.