Final answer:
To find the equivalent expression with the given denominator q² for the fraction (8/9), one must cross multiply and solve for the numerator, resulting in the equivalent expression of (8q²)/9.
Step-by-step explanation:
To find an equivalent expression with the given denominator (8/9) = (?/q²), you'll need to determine what value should replace the question mark to maintain the equality of the two fractions. This involves cross multiplying to solve for the unknown numerator.
When we cross multiply we get 8 * q² = 9 * the unknown numerator. Let's call the unknown numerator 'n'. Now, we have 8q² = 9n. To find the value of 'n', we divide both sides by 9, resulting in n = (8q²)/9.
The final expression is therefore: (8/9) = ((8q²)/9)/(q²). The equivalent expression with the given denominator q² is (8q²)/9.