What is the primary operation for computing products and quotients of positive fractions?

• A. Multiplication and division of fractions, including mixed numbers.
• B. Addition and subtraction of fractions only.
• C. Subtraction of whole numbers.
• D. Power and roots of fractions.

Answer: (A)

To find products and quotients of positive fractions, the operations you use are multiplication and division of fractions (including mixed numbers). When you multiply, you multiply the numerators together and the denominators together. For example, 3/4 × 2/5 equals 6/20, which simplifies to 3/10. When you divide, you multiply by the reciprocal of the divisor. For example, (3/4) ÷ (2/5) is the same as (3/4) × (5/2) = 15/8.

If you have a mixed number, you can convert it to an improper fraction and then apply multiplication or division, or multiply the mixed numbers directly using their fractional parts. This shows why multiplication and division are the tools for these operations.

Addition and subtraction are used for finding sums and differences, not products or quotients. Subtracting whole numbers isn’t about multiplying or dividing fractions, and powers and roots relate to repeated multiplication and inverse operations, not the standard way we compute products and quotients of fractions.