Prove that the product of the two rational numbers 36 and 5/3 is a rational number. Find the product and explain how you know it is a rational number. Explain your reasoning in 2 short sentences.
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To find the product of the two rational numbers \(36\) and \(\frac{5}{3}\), we calculate:
\[ 36 \times \frac{5}{3} = \frac{36 \times 5}{3} = \frac{180}{3} = 60 \]
Since \(60\) can be expressed as a fraction \(\frac{60}{1}\), it is a rational number. A number is rational if it can be expressed as a fraction where both the numerator and the denominator are integers, so the product of two rational numbers is always rational.
Apologies for the confusion in my explanation. Let's clarify the calculation correctly.
To find the product of \(36\) and \(\frac{5}{3}\):
\[ 36 \times \frac{5}{3} = \frac{36 \times 5}{3} = \frac{180}{3} = 60 \]
So, the correct calculation is \(36 \times \frac{5}{3} = 60\).
Now, to explain why \(60\) is a rational number:
A rational number is defined as a number that can be expressed as a fraction where both the numerator and the denominator are integers. Since \(60\) can be expressed as \(\frac{60}{1}\), it meets the definition of a rational number. Hence, the product of the two rational numbers \(36\) and \(\frac{5}{3}\) is also rational.
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