Question

use a number line to model each problem. 1. $2 cdot \frac{2}{3}$ 2. $3 cdot \frac{2}{4}$ 3. $2 cdot \frac{2}{5}$ 4. $3 cdot \frac{2}{6}$ 5. $2 cdot \frac{3}{10}$ 6. $2 cdot \frac{4}{5}$

Explanation:

Step1: Multiply integer by numerator

$2 \times \frac{2}{3} = \frac{2 \times 2}{3} = \frac{4}{3}$

Step2: Multiply integer by numerator

$3 \times \frac{2}{4} = \frac{3 \times 2}{4} = \frac{6}{4} = \frac{3}{2}$

Step3: Multiply integer by numerator

$2 \times \frac{2}{5} = \frac{2 \times 2}{5} = \frac{4}{5}$

Step4: Multiply integer by numerator

$3 \times \frac{2}{6} = \frac{3 \times 2}{6} = \frac{6}{6} = 1$

Step5: Multiply integer by numerator

$2 \times \frac{3}{10} = \frac{2 \times 3}{10} = \frac{6}{10} = \frac{3}{5}$

Step6: Multiply integer by numerator

$2 \times \frac{4}{5} = \frac{2 \times 4}{5} = \frac{8}{5}$

Answer:

1. $\frac{4}{3}$
2. $\frac{3}{2}$
3. $\frac{4}{5}$
4. $1$
5. $\frac{3}{5}$
6. $\frac{8}{5}$

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Number Line Modeling Notes (for context):

For each problem, to model on a number line:

1. For $n \times \frac{a}{b}$: Divide the number line into $b$ equal segments between 0 and 1.
2. Locate $\frac{a}{b}$, then jump that length $n$ times from 0 to land on the product.

E.g., for $2 \times \frac{2}{3}$: Mark $\frac{2}{3}$, then jump another $\frac{2}{3}$ to reach $\frac{4}{3}$.