Find each product or quotient where possible. -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 \(-3\) by \(-24\) to get the new numerator.
3. Multiply the denominators: Multiply \(8\) by \(9\) to get the new denominator.
4. Simplify the fraction: If possible, simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it.
5. Check the sign: Since both original 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.

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). This process makes the fraction easier to understand and work with, ensuring that the values are expressed in the simplest form.

Division of Fractions

Dividing fractions requires multiplying by the reciprocal of the divisor. For instance, to divide -3/8 by -24/9, you would multiply -3/8 by the reciprocal of -24/9, which is 9/-24. This method transforms the division into a multiplication problem, allowing for easier calculation.