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

Verified step by step guidance

1. Identify the operation needed: Since the problem involves two fractions, we need to multiply them.
2. Recall the rule for multiplying fractions: Multiply the numerators together and the denominators together.
3. Write the multiplication of the numerators: \( 12 \times (-4) \).
4. Write the multiplication of the denominators: \( 13 \times 3 \).
5. Combine the results to form the new fraction: \( \frac{12 \times (-4)}{13 \times 3} \).

Key Concepts

Fractions

Fractions represent a part of a whole and are expressed as a ratio of two integers, where the numerator is the top number and the denominator is the bottom number. Understanding how to manipulate fractions, including addition, subtraction, multiplication, and division, is essential for solving problems involving them. In this context, recognizing how to find products and quotients of fractions is crucial.

Multiplication of Fractions

To multiply fractions, you multiply the numerators together and the denominators together. For example, multiplying 12/13 by -4/3 involves calculating (12 * -4) for the numerator and (13 * 3) for the denominator. This process simplifies the multiplication of fractions into a straightforward arithmetic operation, yielding a new fraction as the result.

Division of Fractions

Dividing fractions involves multiplying by the reciprocal of the divisor. For instance, to divide 12/13 by -4/3, you would multiply 12/13 by the reciprocal of -4/3, which is -3/4. This concept is fundamental in fraction operations and allows for the simplification of complex fraction problems into manageable calculations.