Questions: Which product(s) represent(s) a rational number? Select ALL that apply. 5 × 1/2 3 × 4 √2 × 1/√2 √5/3 × 1/3 √16 × 1/2 π/2 × 2/π

Transcript text: Which product(s) represent(s) a rational number? Select ALL that apply. $5 \times \frac{1}{2}$ $3 \times 4$ $\sqrt{2} \times \frac{1}{\sqrt{2}}$ $\frac{\sqrt{5}}{3} \times \frac{1}{3}$ $\sqrt{16} \times \frac{1}{2}$ $\frac{\pi}{2} \times \frac{2}{\pi}$

Solution

Solution Steps

Step 1: Evaluate $5 \times \frac{1}{2}$

Multiply $5$ by $\frac{1}{2}$: \[ 5 \times \frac{1}{2} = \frac{5}{2} \] $\frac{5}{2}$ is a rational number.

Step 2: Evaluate $3 \times 4$

Multiply $3$ by $4$: \[ 3 \times 4 = 12 \] $12$ is a rational number.

Step 3: Evaluate $\sqrt{2} \times \frac{1}{\sqrt{2}}$

Multiply $\sqrt{2}$ by $\frac{1}{\sqrt{2}}$: \[ \sqrt{2} \times \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{\sqrt{2}} = 1 \] $1$ is a rational number.

Final Answer

The products that represent a rational number are:

$5 \times \frac{1}{2}$
$3 \times 4$
$\sqrt{2} \times \frac{1}{\sqrt{2}}$
$\sqrt{16} \times \frac{1}{2}$
$\frac{\pi}{2} \times \frac{2}{\pi}$

Thus, the final answer is: $\boxed{5 \times \frac{1}{2}, 3 \times 4, \sqrt{2} \times \frac{1}{\sqrt{2}}, \sqrt{16} \times \frac{1}{2}, \frac{\pi}{2} \times \frac{2}{\pi}}$

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