which is bigger two eighths or three sixths?

Answer 1

Generally people have trouble with fractions because they can't relate the number to real life situations. In your case:

You have two pies each of the same size: one is divided into 8 equal slices and the other is divided into 6 equal slices.

You get to choose which pie you'll take a slice from for dessert (you love pie). So which pie will you take that slice?

Clearly the one with 6 equal slices. Why? Because that whole pie is divided into fewer but larger slices than the one with eight pieces. You take the larger slice for dessert.

So now you have all you need to know to answer this question. To wit:

You take one each slice from the two pies. Which is the two slices is the bigger one? The 1/6 slice of course, we've determined earlier that the slices in the pie with six pieces are the bigger slices.

So with one piece from each pie you have 1/6 > 1/8 where > means bigger than. The 1/6 is bigger than the 1/8 slice.

OK, now you draw a second piece from each pie. You add each one to the ones you've already drawn. You now have 1/6 + 1/6 > 1/8 + 1/8. Why? Because if you add that second piece with the one being larger than the other, the two slices of 1/6 pie are still larger than the two pieces of 1/8 pie.

But wait, you're not stopping with just two slices of 1/6 pie. You're adding yet another 1/6 slice to the two you already have. And you're not adding another 1/8 slice. So now you have 1/6 + 1/6 + 1/6 > 1/8 + 1/8.

And you can see that you have three larger pieces on one side and two smaller pieces on the opposite side. So the three 1/6 pieces added up are indeed greater in size than the two 1/8 pieces. ANS.

Math is a great thing because we can do all of the above by following some math rules. They are these. "two eighths" = 1/8 + 1/8 = 2/8 and "three sixths" = 1/6 + 1/6 + 1/6 = 3/6. So we can write 3/6 = 1/2 = 2/4 > 2/8 = 1/4. And there you are. You are getting twice the 1/6 pie (2/4) over the 1/4 of the other pie.

Answer 2

First reduce them. Then it's simple.

two eighths = 2 * 1/8 = 2/8 = 1/4 = 0.25

three sixths = 3 * 1/6 = 3/6 = 1/2 = 0.5

So 3/6 is bigger than 2/8.