Question: Fractions in Ascending Order

If five numbers are listed in ascending order, the 3rd number is the same as the middle number.

We COULD do that, as long as the numerators are the same.
So, for example, to compare 5/8 and 10/18, we'd need to convert one of the fractions. We might rewrite 5/8 as 10/16, which means we are not comparing 10/16 and 10/18

Since 10/16 has the smaller denominator, we can conclude that 10/16 is the bigger fraction.

As you might imagine, this approach could be quite time consuming.

36 is the biggest denominator, so the least common denominator will be a multiple of 36 (36, 72, 108, etc)

I also see that 5 is a denominator. So, the least common denominator will ALSO be a multiple of 5.

Since 36 is not divisible by 5, I multiplied 36 x 5 to get 180. So, the least common denominator must be a multiple of 180.

Then I checked to see whether 180 is a multiple of the other three denominators (8, 3, and 18).

180 IS a multiple of 3 and 18. BUT, 180 is NOT a multiple of 8.

So, I doubled 180 to get 360, which IS a multiple of 8

So, 360 is the least common multiple of 8, 3, 18, 5 and 36

Phew!!!!