There are actually ways of determining this without using decimals.
A fraction is basically a fancy way of saying 'divided by'. 8/3 really means '8 divided by 3'. So we can use tricks to make them look very simple.
Anything divided by itself is 1.
Anything multiplied by one is itself.
These two rules are the most important part of this. Using this, we can say that 3/3=1. And 7/7=1. And R/R=1. Anything like this.
Another thing to remember is that it doesn't matter what order you multiply numbers in. 2x3=3x2, 5x8=8x5. This always works with numbers.
When comparing fractions, it helps to have the same number on the bottom. 2/2 is greater than 1/2, 6/13 is less than 11/13. And there are simple ways to put the same number on the bottom.
To multiply two fractions together, you multiply the top numbers, and multiply the bottom numbers. So, 2/3 x 5/4 = 10/12.
Now, everything comes together. To put the same number on the bottom of your two fractions, 8/3 x 7/7 = 56/21 and 16/7 x 3/3 = 48/21. Because 3x7=7x3, you can use this to put the right numbers in place. And because you an multiply anything by one and get the same thing, multiplying by 7/7 or 3/3 is the same. So, 56/21 = 8/3, and 48/21 = 16/7.
This also means that 8/3 is greater than 16/7.
If you really want the decimals, you can use long division. For 8/3, use 3)˜˜8.000. The only thing you need to remember is to put the decimal point in the right spot.
