Find each product or quotient where possible. See Example 2. (12⁄13)/( -4⁄3)

Verified step by step guidance

1. Identify the operation between the two fractions. Here, the expression is \( \frac{12}{13} \times \left(-\frac{4}{3}\right) \), which is a multiplication of two fractions.
2. Recall the rule for multiplying fractions: multiply the numerators together and multiply the denominators together. So, the product is \( \frac{12 \times (-4)}{13 \times 3} \).
3. Calculate the numerator by multiplying 12 and -4, and calculate the denominator by multiplying 13 and 3, but do not simplify yet.
4. Write the resulting fraction from step 3 as \( \frac{12 \times (-4)}{13 \times 3} \) and then simplify the fraction by finding any common factors between numerator and denominator.
5. Express the simplified fraction as the final product of the original multiplication problem.

Key Concepts

Multiplication and Division of Fractions

To multiply fractions, multiply the numerators together and the denominators together. For division, multiply the first fraction by the reciprocal of the second. This process simplifies complex fraction operations into straightforward multiplication.

Reciprocal of a Fraction

The reciprocal of a fraction is obtained by swapping its numerator and denominator. It is essential for division of fractions, as dividing by a fraction is equivalent to multiplying by its reciprocal.

Simplifying Fractions

After performing multiplication or division, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor. Simplification makes the fraction easier to interpret and use in further calculations.