To do this problem, you need to change the way the fractions are displayed so that you can simplify them.
The first step is to change them to improper fractions: fractions like 4/3 that represent more than 100% (parts adding to more than one whole).
For example, to change the first fraction in this way, multiply the number in front (2) by the bottom number:
2 * 3 = 6
This means the 2 can also represent 6 / 3. Remember that 1 equals 3/3 so 2 equals 6/3. Now add this to the 1/3 you started with, and you end up with 7/3.
Do the same for the other fraction.
Now that you have both fractions written in this way, you can multiply each by the other's denominator to arrive at their LCD (least common denominator). It won't always be least, but you can always simplify further. In this case, the numbers are small enough that it likely won't matter.
You will end up with a fraction of halves: some number x, over 2, meaning x number of halves.
Your other fraction is 7/3. So the common denominator is the bottom numbers multiplied together: 2 * 3 = 6.
To change 7/3 to a fraction of sixths, you multiply the whole thing by two. This gets the bottom number to be six.
7 * 2 = 14
3 * 2 = 6
So this fraction can also be written as 14/6. Once again, do the same to the other fraction (but multiply by 3, to get the other fraction into sixths also, since it is currently halves).
Now you have two fractions that are both in parts of six. A ratio (x:y) is nothing more than a fraction itself. So if you had for example the ratio
2/5 : 10/5
This ratio could also be written as 1/5 : 5/5, or 1/5 to 1. Both numerators (the top number) are divisible by 2, so you can divide them both by 2 and end up with a simplified version of the same ratio.
Whatever ratio you end up with (14/6 : some other fraction), do the same thing to it. See if any of the numbers share a common factor, and simplify where possible. If it's not possible to simplify further, you're done.
David W.
01/10/16