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The problem states:

"The product of two rational numbers is \(-\frac{72}{y}\). If one of the numbers is \(\frac{8}{3}\), find the other."

Let's denote the two rational numbers as \( a \) and \( b \). According to the problem:

\[
a \times b = -\frac{72}{y}
\]

Given that one of the numbers is \( a = \frac{8}{3} \), we need to find \( b \).

Substituting \( a = \frac{8}{3} \) into the equation:

\[
\frac{8}{3} \times b = -\frac{72}{y}
\]

To solve for \( b \), we multiply both sides of the equation by the reciprocal of \( \frac{8}{3} \), which is \( \frac{3}{8} \):

\[
b = \left(-\frac{72}{y}\right) \times \frac{3}{8}
\]

Simplifying:

\[
b = -\frac{72 \times 3}{8y} = -\frac{216}{8y} = -\frac{27}{y}
\]

So, the other number \( b \) is \( -\frac{27}{y} \).

Would you like any further details on this solution?

Here are 5 related questions you might be interested in:

1. How can you determine if a given number is rational or irrational?
2. What are some examples of real-life applications where the product of two rational numbers is used?
3. How would the solution change if the given number were negative?
4. How do you simplify the product of two fractions in general?
5. What happens to the product if both rational numbers are negative?

**Tip:** When solving problems involving fractions, always simplify the fractions first to make calculations easier.

The product of two rational numbers is -72/y. If one of the numbers is 8/3, find the other.

Learn how to find the missing rational number when the product of two numbers is given as -72/y and one of the numbers is 8/3. This problem is suitable for students in Grades 7-8 and covers concepts like algebra, rational numbers, and multiplication of fractions.

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