Find each product or quotient where possible. $\frac{\frac{7}{6}}{-\frac{2}{3}}$

Verified step by step guidance

1. Identify the problem as a division of two fractions: \(\frac{7}{6} \div \left(-\frac{2}{3}\right)\).
2. Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, rewrite the expression as \(\frac{7}{6} \times \left(-\frac{3}{2}\right)\).
3. Multiply the numerators together and the denominators together: numerator = \(7 \times (-3)\), denominator = \(6 \times 2\).
4. Write the product as a single fraction: \(\frac{7 \times (-3)}{6 \times 2}\).
5. Simplify the fraction by reducing common factors and handling the negative sign appropriately.

Key Concepts

Dividing Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, dividing by 2/3 is the same as multiplying by 3/2.

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together. Simplify the resulting fraction if possible by dividing numerator and denominator by their greatest common divisor.

Simplifying Negative Fractions

A negative fraction can be written with the negative sign in the numerator, denominator, or in front of the fraction. When multiplying or dividing, keep track of the signs: a negative times a positive is negative, and a negative divided by a positive is negative.