Find each product or quotient where possible. See Example 2. (-4⁄5) / (-3⁄5)

Verified step by step guidance

1. Identify the operation between the two fractions. Here, the problem shows two fractions written side by side: \(-\frac{4}{5}\) and \(-\frac{3}{5}\). This typically means multiplication of the two fractions.
2. Recall the rule for multiplying fractions: multiply the numerators together and multiply the denominators together. So, the product of \(-\frac{4}{5}\) and \(-\frac{3}{5}\) is given by \(\left(-\frac{4}{5}\right) \times \left(-\frac{3}{5}\right) = \frac{(-4) \times (-3)}{5 \times 5}\).
3. Calculate the numerator by multiplying the two numerators: \((-4) \times (-3)\). Remember that multiplying two negative numbers results in a positive number.
4. Calculate the denominator by multiplying the two denominators: \(5 \times 5\).
5. Write the product as a single fraction with the numerator and denominator found in the previous steps. Then, if possible, simplify the fraction by dividing numerator and denominator by their greatest common divisor.

Key Concepts

Multiplication of Fractions

To multiply fractions, multiply the numerators together and the denominators together. For example, multiplying -4/5 by -3/5 involves multiplying -4 by -3 for the numerator and 5 by 5 for the denominator, resulting in a new fraction.

Sign Rules for Multiplication

When multiplying numbers, the product of two negative numbers is positive, while the product of a positive and a negative number is negative. This rule helps determine the sign of the product when multiplying fractions with negative numerators or denominators.

Simplifying Fractions

After multiplying or dividing fractions, simplify the result by dividing numerator and denominator by their greatest common divisor. Simplification makes the fraction easier to interpret and use in further calculations.