Prove that the product of the two rational numbers rational symbol 36 and 5/3

Question

is a rational number. Find the product and explain how you know it is a rational number. Explain your reasoning in 1–2 sentences.(2 points)

Answer 1

To prove that the product of the rational numbers \( 36 \) and \( \frac{5}{3} \) is a rational number, we can multiply them:

\[ 36 \times \frac{5}{3} = \frac{36 \times 5}{3} = \frac{180}{3} = 60. \]

The result, \( 60 \), is a rational number because it can be expressed as the fraction \( \frac{60}{1} \), where both the numerator and the denominator are integers and the denominator is not zero. Thus, the product of two rational numbers is always a rational number, confirming our result.