Division of Fractions

I was one of the participants in the training at Sampoerna Foundation. I'd like to ask about fractions 2/3 : 5/8 = 2/3 x 8/5. How can I explain to the students the reason why the division symbol becomes multiplication and why the second fraction is inverted.

Tendo, a teacher in Indonesia



There are several variations to this task.

1. 2/3 : 1/3

2. 2/3 : 1/6

3. 2/3 : 1/8

4. 2/3 : 5/8

Students have learnt two meanings of divisions in whole numbers. For example 12 : 4 has been modeled by 12 things shared among 4 persons as well as 12 things put into groups of 4. For the latter, we ask "How many 4s are there in 12?"

We can use this meaning of division to teach 2/3 : 1/3. How many 1/3s are there is 2/3? This is obvious. The answer is 2. For 2/3 : 1/6, students need to be able to see that 2/3 = 4/6. Then the answer to how many 1/6s are there in 2/3 becomes obvious.

For 2/3 : 1/8, students know that 2/3 = 16/24 and 1/8 = 3/24.

It is easier to do 2/3 : 1/6 which is the same as 16/24 : 4/24. There are four 4/24s in 16/24.

In 16/24, there are five 3/24s (which is equal to 15/24) and another 1/3 of it. Thus, 2/3 : 1/8 = 5 and a third.

Can you explain 2/3 : 5/8?