
You are using the online sample of the Foundations for Teaching Arithmetic CDROM. Not all linked pages are accessible in this version. For further information about the complete CDROM, click here.  Partition division  Quotition division  Example 1: 1 1/2 ÷ 3 What does 1 1/2 ÷ 3 mean? We can read this example as 1 1/2 divided by 3 and we can think of it as 1 1/2 shared into 3 equal parts. For example, we could be talking about 1 1/2 cakes shared equally among 3 people. In this example, to find each person's share we had to find 1/3 of 1 1/2. Our division problem became a multiplication problem:
In partition division problems we think of sharing between. The divisor is a whole number which represents the number of parts to be shared between. Example 2: 7/10 ÷ 5 = 7/50 Example 3: 6 ÷ 1/3 = 18 What does 6 ÷ 1/3 mean? It does not make much sense to say 6 shared between 1/3. To picture a quotition division problem we ask 'how many?'
We can see that while thinking through this problem we turned a division problem into a multiplication problem. 6 divided by 1/3 became 6 multiplied by 3. 6 ÷ 1/3 = 6 x 3 = 18
Example 4: 1/2 ÷ 1/4 = 2 There are a number of ways we can describe this expression. We can say, 'a half divided by a quarter' or, 'how many quarters in a half?' Would we say, 1/2 shared between 1/4 (of a person)? No! This description does not make any sense to us and certainly does not help us picture the problem. This is best understood as a quotition division problem. Asking 'how many quarters in a half?' helps us to picture this problem. From the square above we can see that the answer is 2. There are 2 quarters in a half. 1/2 ÷ 1/4 = 2 Let's compare to multiplication. If we multiply 1/2 x 4 the answer is 2. 1/2 ÷ 1/4 = 1/2 x 4 = 2
Example 5: 3/8 ÷ 1/6 = 2 1/4 Example 6: 4/3 ÷ 5/7 = 1 13/15
Example 7: 2 2/3 ÷ 1 3/5 = 1 2/3
Using multiplication to check your answer We have seen how multiplication and division are related. We can use the fact that multiplication and division are the inverse of one another to help us check our answers to division problems. Example 8: 4/3 ÷ 5/7 = ? Using multiplication to check our answer
There are a number of ways of explaining why we can turn division problems into multiplication problems. The explanation below relies on our knowing that we can multiply the numerator and denominator of a fraction by the same number without changing its value.
Thus, the general rule for division of fractions is: Find the answers to the following examples:
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