Find each product or quotient where possible. -5/2 (-12/25)

Verified step by step guidance

1. Identify the operation: This problem involves multiplying two fractions: \(-\frac{5}{2}\) and \(-\frac{12}{25}\).
2. Multiply the numerators: Multiply the numerators of the fractions together: \(-5 \times -12\).
3. Multiply the denominators: Multiply the denominators of the fractions together: \(2 \times 25\).
4. Simplify the product: Simplify the resulting fraction if possible 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 -5/2 by -12/25, you calculate (-5 * -12) for the numerator and (2 * 25) for the denominator, resulting in a new fraction that can be simplified if necessary.

Division of Fractions

Dividing fractions involves multiplying by the reciprocal of the divisor. For instance, to divide -5/2 by -12/25, you would multiply -5/2 by the reciprocal of -12/25, which is 25/-12. This process also requires multiplying the numerators and denominators to find the resulting fraction.

Simplifying Fractions

Simplifying fractions means reducing them to their lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). After performing multiplication or division, it is essential to check if the resulting fraction can be simplified for clarity and ease of understanding.