Find each product or quotient where possible. See Example 2. -10⁄17 ÷ ( -12⁄5 )

Verified step by step guidance

1. Identify the problem as a division of two fractions: \(\frac{-10}{17} \div \frac{-12}{5}\).
2. Recall that dividing by a fraction is equivalent to multiplying by its reciprocal. So rewrite the expression as \(\frac{-10}{17} \times \frac{5}{-12}\).
3. Multiply the numerators together and the denominators together: numerator = \(-10 \times 5\), denominator = \(17 \times -12\).
4. Simplify the product of the numerators and denominators separately, keeping track of the signs.
5. Reduce the resulting fraction to its simplest form by dividing numerator and denominator by their greatest common divisor (GCD).

Key Concepts

Division of Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. For example, a ÷ b/c is equivalent to a × c/b. This method simplifies division problems by converting them into multiplication.

Multiplication of Fractions

To multiply fractions, multiply the numerators together and the denominators together. For instance, (a/b) × (c/d) = (a×c)/(b×d). This operation is straightforward and essential for solving fraction division problems.

Handling Negative Signs in Fractions

When multiplying or dividing fractions with negative signs, remember that a negative divided by a negative yields a positive result. Keep track of signs carefully to determine the correct sign of the final answer.