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

Verified step by step guidance

1. Identify the problem as multiplying two fractions: \(-\frac{3}{8}\) and \(-\frac{24}{9}\).
2. Recall the rule for multiplying fractions: multiply the numerators together and multiply the denominators together. So, the product is \(\frac{-3 \times -24}{8 \times 9}\).
3. Calculate the numerator: \(-3 \times -24\) (note that multiplying two negative numbers results in a positive number).
4. Calculate the denominator: \(8 \times 9\).
5. Simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD) to get the fraction in simplest form.

Key Concepts

Multiplication of Fractions

Multiplying fractions involves multiplying the numerators together and the denominators together. For example, (a/b) × (c/d) = (a×c)/(b×d). This rule applies regardless of whether the fractions are positive or negative.

Handling Negative Signs in Multiplication

When multiplying numbers, a negative times a negative results in a positive, while a negative times a positive results in a negative. This rule helps determine the sign of the product when fractions have negative numerators or denominators.

Simplifying Fractions

After multiplying, fractions should be simplified by dividing numerator and denominator by their greatest common divisor (GCD). Simplification makes the fraction easier to interpret and use in further calculations.