Question

How many groups of 2/3 are in 3/5?

Answer 1

Divide 3/5 by 2/3:

3
---
5 3(3)
------ = ---------- = 9/10 (answer). This is not a very satisfactory answer,
2 5(2) because 9/10 is a fraction. 2/3 is
--- larger than 3/5, so the answer would
3 be zero groups.

Answer 2

To figure this out, divide 3/5 by 2/3. In a similar way, if you were being asked how many groups of 2 were in 6, wouldn't you divide 6 by 2?


`(3)/(5) / (2)/(3)`

When you divide fractions, you can also multiply by the reciprocal of the second fraction:


`(3)/(5) / (2)/(3) = (3)/(5) * (3)/(2)`

Now we can multiply across:


`(3)/(5) * (3)/(2) = (9)/(10)`

There are 9/10 groups of 2/3 in 3/5.