How do you get the lowest term of 72 over 144?

Answer 1

The lowest term (or simplest form) of this fraction is 1/2.

To simplify any fraction you look to see if there is a number which can be divided into both numbers in the fraction. If there are not (other than 1) then the fraction can not be simplified. If there is, then you look again at the new numbers to see if these can be simplified. This process is repeated until no further simplification is possible.

For this fraction, 72/144; you may notice straight away that 72 is half of 144. Therefore this is going to simplify to 1/2 (both numbers divided by 72). This is because 72 is the highest common factor of both numbers.

Of course, you may not notice this, but as we can see that both numbers are even, they will certainly divide by 2. So 72/144 becomes 36/72. Now there are quite a few numbers, which we might now more easily see, which divide into both of these. 2,3,4,6,9,12,18,36 are all factors (we ignore "1").

However we are always looking for the highest factor we can find so that we can simplify in the least number of steps. But no matter how we proceed, as long as we find a factor of both numbers, and then look to see if we can then find another factor of the new numbers, we will eventually simplify the fraction as far as possible.

Here is an example showing the longest way (by dividing by 2 each time initially):

72/144 - 36/72 - 18/36 - 9/18 - (and then dividing by 3) 3/6 - 1/2.