A Unified Approach to Multiplying Fractions

What is being overlooked by those that hold this view is the relative difficulty of explaining to students the meanings of addition and multiplication of fractions. Though the words and symbols for addition and multiplication are given many meanings in mathematics, the meaning for addition most used in elementary mathematics textbooks is combining groups. See figure 1. The meanings given for multiplication in elementary school textbooks are more diverse and often seem unrelated. For example, meanings given to multiplication include repeated addition, arrays (area, etc.), comparative size, rates, and Cartesian product. Though they are often treated as distinct meanings, they can easily be interpreted as different manifestations of the repeated-addition meaning of multiplication. Figure 2 offers examples of different meanings given to multiplication according to application.