First of all, you have to find out the greatest common factor between the numerator and the denominator and then divide both the numerator and the denominator by the greatest common factor thus found out and the result will provide you with the fraction reduced to lowest terms.

The way to reduce a fraction into simplest form is to find the greatest common factor between the numerator and denominator. If you have a difficult time doing this you can always start by dividing the numerator and denominator by 2 if both are even numbers. There are other tricks too. If both numbers end in either 5 or 0 you can divide them both by 5. If the numbers, when added are divisible by 3 then the entire number is divisble by three. (18 for example 1+8=9, which is divisible by 3, so 18 is divisible by 3).

Here's a few problems and I'll show you the methods I used above:

4/18, notice that they are both even numbers so you can divide each by 2 to get 2/9. The only number other than 1 that divides into 2 is 2 and 2 does not divide into 9, so the lowest terms is 2/9.

15/80, notice that they end in either 5 or 0 so you can divide each by 5 to get 3/16 and 3 does not divide evenly into 16 so the lowest terms is 3/16.

27/90, note that the digits of 27 add to 9, and 9 is divisible by 3 so 27 is as well. Dividing both by 3 gives you 9/30, and note that 3 divides into both 9 and 30 so lowest terms is 3/10. You might have noticed that 9 divided into 27, if so you could have done that right away.

On problems that don't follow the tricks I mentioned above, you can do a factor tree for each number and see which tree has common numbers in them and divide each by those numbers. Trial and error is also a way to go about tougher problems.

Good luck!