So performing the division will answer the question. I can mow 4 lawns with of a tank of gas in my lawnmower is a partitive division problem because I know what of a tank can do, and I want to find what a whole tank can do. When dividing by a fraction, partitive division means that we know the fractional part of a group we have, and we need to find the size of a whole group. How many cookies does each person get? We know the number of groups (3 in this example) and we need to find the size of each group. I have 12 cookies to share equally among 3 people. There are two meanings for division: partitive (or sharing) and quotative (or measuring). The partitive meaning is the most common one we think of when we do whole number division. The conceptual why-for many of us-lies in thinking about fractions as operators, and in thinking about a particular meaning of division. The formalities will invoke the associative property of multiplication, the definition of reciprocal, inverse and the multiplicative identity, et cetera. The formalities leave one feeling cold and empty, for they don’t answer the conceptual why.
Unlike the division by zero stuff from question 1, this question is better tackled with informal notions than with formalities. (And, for the record, I would like to buy that person an adult beverage!)
If anyone on the Internet has had more to say about dividing fractions than I have, I am unaware of who that is. Question 3 You are told to “invert and multiply” to solve division problems with fractions.
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