Certain questions require you to arrange fractions in increasing or decreasing order. How do you usually decide the order? Do you use the “common denominator” method?
What if you are asked to arrange the fractions below in increasing order?
2/7, 2/11, 3/13
It is possible but rather tedious to use the “common denominator” method, isn’t it? For such questions, why not try using the “common numerator” method instead? Below are the same fractions converted into their equivalent counterparts that have 6 as the numerator.
2/7 = 6/21
2/11 = 6/33
3/13 = 6/26
So, what do we do from here? Well, the one with the greatest denominator has the smallest value while the one with the smallest denominator has the greatest value.
You can think about it this way.
Imagine there are 6 (that’s the common numerator) pizzas to be shared. In the first scenario, 33 people shared the 6 pizzas; in the second scenario, 26 people shared the 6 pizzas; and in the third scenario, 21 people shared the 6 pizzas.
Now, if you were sharing the pizzas and feeling rather hungry, which scenario would you prefer? Since the number of pizzas to be shared was the same in all three scenarios (6), you would prefer the one with the smallest number of people in order to gorge on more pizza!
So there you go, sometimes it's easier comparing fractions using the 'common numerator' rather than the 'common denominator' method.