How do you order the following fractions from smallest to largest?: #{18/9, 32/24, 25/20, 33/12}#?
3 Answers
From smallest to largest, they are
Explanation:
The best way to order fractions is to first convert them to decimal fractions. Now
Hence comparing them and ordering them from smallest to largest, they are
Explanation:
If we express these fractions using the same denominator, then we just need to put the numerators in ascending order.
If we first reduce them to simplest terms (but still leave as fractions), then we find that they can all be expressed as multiples of
#18/9 = (2 xx color(red)(cancel(color(black)(9))))/(1 xx color(red)(cancel(color(black)(9)))) = 2/1 = (2 xx 12)/(1 xx 12) = color(blue)(24)/12#
#32/24 = (4 xx color(red)(cancel(color(black)(8))))/(3 xx color(red)(cancel(color(black)(8)))) = 4/3 = (4 xx 4) / (3 xx 4) = color(blue)(16)/12#
#25/20 = (5 xx color(red)(cancel(color(black)(5))))/(4 xx color(red)(cancel(color(black)(5)))) = 5/4 = (5 xx 3)/(4 xx 3) = color(blue)(15)/12#
#33/12 = (11 xx color(red)(cancel(color(black)(3))))/(4 xx color(red)(cancel(color(black)(3)))) = 11/4 = (11 xx 3)/(4 xx 3) = color(blue)(33)/12#
So from smallest to largest, the fractions are:
#color(blue)(15)/12, color(blue)(16)/12, color(blue)(24)/12, color(blue)(33)/12#
In original form:
#25/20, 32/24,18/9,33/12#
Footnote
When reducing a fraction like
One way of finding the GCF of two numbers goes like this:

Divide the larger number by the smaller number to give a quotient and remainder.

If the remainder is
#0# then the smaller number is the GCF. 
Otherwise repeat with the smaller number and the remainder.
So in the case of
#32/24 = 1# with remainder#8#
#24/8 = 3# with remainder#0#
So the GCF of
#32/24 = ((32/8))/((24/8)) = 4/3#
or if you prefer:
#32/24 = (4 xx color(red)(cancel(color(black)(8))))/(3 xx color(red)(cancel(color(black)(8)))) = 4/3#
The ordered set is :
Explanation:
We want to put this set of numbers in ascending order:
First you can notice that all those fractions are improper (their numerators are bigger than denominators), which means that they represent numbers greater than
If you do so you get:
From this you see that the last two numbers are
To order the remaining number you have to either reduce them or expand so that either their numerators or denominators are the same.
In both cases their denominators are multiples of numerators so you can reduce both fractions to get numerators equal to
If two fractions have equal numerators then the one is bigger which has lower denominator. So the ascending order of those numbers is:
If we combine those result we get the final answer: