How do you simplify the ratio #\frac { 4} { 5} : \frac { 2} { 3} : 1\frac { 1} { 4}#?
1 Answer
First, rewrite the ratios using a common base (the denominator, if you think of them as fractions). The numerators will show the simpler ratio. Details follow...
Explanation:
Find the least common multiple (LCM) of the three values used as bases in the proportion. In this case, the LCM of 3, 4 and 5 is 60.
Rewrite each ratio using this LCM as the base for each one. To do this, you multiply each numerator by the other two bases. (This really amounts to multiplying top and bottom of each ratio by the values of the other two bases.)
The proportion becomes:
Since all the bases are the same, the ratio can be expressed by using only the top terms:
This is the simplest ratio of whole numbers that is equivalent to the original set of ratios. You will always get the simplest ratio if you correctly found the LCM in the first step.
