Question

Prove that the product of two rational numbers 4/3 and 9/2 is a rational number find the product and explain how you know it's a rational or a number

Answer 1

To prove that the product of two rational numbers \( \frac{4}{3} \) and \( \frac{9}{2} \) is a rational number, we start by recalling the definition of rational numbers. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero.

### Step 1: Calculate the product

The product of \( \frac{4}{3} \) and \( \frac{9}{2} \) is calculated as follows:

\[
\frac{4}{3} \times \frac{9}{2} = \frac{4 \times 9}{3 \times 2} = \frac{36}{6}
\]

### Step 2: Simplify the result

Now, we simplify \( \frac{36}{6} \):

\[
\frac{36}{6} = 6
\]

### Step 3: Determine if the result is rational

The number \( 6 \) can be expressed as a fraction \( \frac{6}{1} \), which is in the form of \( \frac{a}{b} \) where \( a \) and \( b \) are integers (with \( b \neq 0 \)). Therefore, \( 6 \) is a rational number.

### Conclusion

Since the product of the two rational numbers \( \frac{4}{3} \) and \( \frac{9}{2} \) is \( 6 \), and \( 6 \) is a rational number, we conclude that the product of any two rational numbers is also a rational number.

Thus, it is proven that the product \( \frac{4}{3} \times \frac{9}{2} = 6 \) is indeed a rational number.