The way to approach this problem is to convert the fractions to a common denominator.
For example, when considering if 2/3 is between 3/7 and 4/8, you would change then to a common denominator.
2/3 is the same as 14/21 (I multiplied by 7 on the top and bottom) and 3/7 is the same as 9/21 (I multiplied by 3 on the top and bottom) so 2/3 is larger than 3/7 because 14/21 is larger than 9/21.
We can next compare 2/3 to 4/8. First 4/8 is the same as 1/2 (divide by 4 on the top and bottom). 2/3 is the same as 4/6 and 1/2 is the same as 3/6, so 2/3 is larger than 4/8. This means 2/3 is NOT between 3/7 and 4/8.
So we'd move on to the next choice (B) and try that...
Hope this helps,
Stephen La Rocque.
There really isn't a formula for this, but some logic. You know that 2/3 is bigger than 1/2 (2/3 of a chocolate bar is bigger than 1/2 of a chocolate bar).
Choice A is not the correct one because 3/7 is a little less than 1/2 and 4/8 is 1/2, so 2/3 can't be between those 2 fractions.
Let's look at choice B: 1/2 and 3/7 - that's really the same choice as choice A, so that's not the correct choice.
Choice C: 6/7 and 9/8 - the first one is just a little under 1 and the second one is just a little over 1 - so it doesn't fit there either.
That leaves choice D: 3/5 and 7/9 - the first one is a bit over 1/2 and the second one is a bit under 1 so the actually is the right choice.
Another way you can do this is by finding a common denominator for each set of choices and 2/3, find the equivalent answers then eliminate some choices.
If you want to show your son what these fractions actually look like you could draw a bunch of identical circles and divide each into different sized pieces, like pies. One circle could be divided into 3 equal pie pieces, another into 7 equal pie pieces, etc. Then you can cut the pieces after marking on each piece what fraction it represents and then you can compare fractions: would 2/3 be bigger or smaller than 3/7, etc.
Hope this helps.