Find each product or quotient where possible. See Example 2. -3⁄8 ( -24⁄9 )

Verified step by step guidance

1. Identify the operation: This problem involves multiplying two fractions: \(-\frac{3}{8}\) and \(-\frac{24}{9}\).
2. Multiply the numerators: Multiply the top numbers of the fractions: \(-3\) and \(-24\).
3. Multiply the denominators: Multiply the bottom numbers of the fractions: \(8\) and \(9\).
4. Simplify the result: After multiplying, simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
5. Check the sign: Since both fractions are negative, the product will be positive.

Key Concepts

Multiplication of Fractions

To multiply fractions, you multiply the numerators together and the denominators together. For example, when multiplying -3/8 by -24/9, you calculate (-3 * -24) for the numerator and (8 * 9) for the denominator, resulting in a new fraction that can be simplified if necessary.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, if the product of the fractions results in a fraction like 72/72, it can be simplified to 1, as both the numerator and denominator are equal.

Negative Numbers in Multiplication

When multiplying two negative numbers, the result is positive. This is crucial in the given problem, as both -3/8 and -24/9 are negative. Thus, their product will be positive, which is an important aspect to remember when performing operations with negative fractions.