A recipe uses cups of flour. Think of the 9 cups as being divided into 3 equal parts, then taking 2 of those parts. What does the product represent?
- It represents 2 cups, because you take 2 cups from 9 cups.
- It represents 6 cups, because you divide 9 cups into 3 equal parts (3 cups each) and take 2 parts. (correct answer)
- It represents 13.5 cups, because multiplying always makes the amount larger.
- It represents 9 ÷ 2 cups, because you swap the fraction and divide.
Explanation: Fraction multiplication has a concrete meaning, representing taking a part of a whole amount. When multiplying a fraction like 2/3 by a whole number such as 9 cups, you start by partitioning the 9 cups into 3 equal parts, since the denominator is 3. The numerator 2 then tells you to take 2 of those equal parts. In this recipe context, the product represents the amount of flour used, which is 6 cups. A common misconception is that multiplying by a fraction always increases the value, but here it results in less than 9 since 2/3 is less than 1. Models like this help explain fraction multiplication by visually showing division into equal parts and selection of some parts. Overall, such interpretations build understanding of fractions as operators on quantities.