Question
Rational & Irrational Numbers Unit test:
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.
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.
Answers
Answer
36 \times \frac{5}{3} does not equal \frac{36 \times 5}{3}
Answer
Prove that the product of the two rational numbers 36−−√ and 53 is a rational number. Find the product and explain how you know it is a rational number. Explain your reasoning in 1–2 sentences.
Answered by
GPT-4o mini
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.
\[
36 \times \frac{5}{3} = \frac{36 \times 5}{3} = \frac{180}{3} = 60
\]
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.
Answered by
GPT-4o mini
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.
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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