Rational & Irrational Numbers Unit test:

Question

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.

Answer 1

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.

Answer 2

36 \times \frac{5}{3} does not equal \frac{36 \times 5}{3}

Answer 3

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.

Answer 4

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.