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Post date: Nov 20, 2011 10:21:32 PM
Multiplication is probably the simplest operation to do with fractions procedurally, but it is one of the hardest ones to make sense of conceptually. Students are used to thinking of multiplication as repeated addition, and for the products of multiplication to be larger than the factors being multiplied. These ideas do not always hold true when multiplying fractions.
One way to help make sense of multiplication with fractions is to replace the multiplication symbol “×” with the word “of”. Thus, 1/2 × 4/9 means 1/2 of 4/9, or 2/9. Notice that in this case the product is actually smaller than the factors being multiplied. That is because we are taking a “part of a part.” There are three cases that can occur when multiplying fractions (or any kind of number, for that matter), excluding cases when one of the factors is 1:
1. The product will be less than both factors when both factors are less than 1.
EXAMPLE: 1/2 × 4/9 = 2/9
2. The product will be between the two factors when one factor is less than 1 and one factor is more than 1.
EXAMPLE: 1 1/2 × 3/4 = 1 1/8
3. The product will be more than both factors when both factors are greater than 1.
EXAMPLE: 1 1/2 × 2 1/3 = 3 1/2
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