My Ambivalence Towards Equivalent, Less Than, and Greater Than Fractions

Equivalent fractions have always been a mixed bag of emotions for me.  On one hand I get excited and think it is so obvious which fractions are equal, less than, and greater than one another.  However, on the other hand I get terrified when I really start to look and compare because there is a lot of obscurity in fractions. There is usually a point where I start to panic and draw pictures to try and compare differences visually.

Here is a great, fast cheat to see if two fractions are equivalent: a/b = c/d if and only if ad = bc

For example 1/2 = 5/10 because 1 x 10 = 10 and 2 x 5 = 10

I love being able to do this because I know that no matter what fractions are thrown at me, I will be able to quickly and easily tell if they are equivalent.

Ok, great, I think we can tackle fractions that are equal... how about fractions that are less than or greater than one another?

I have found that the easiest way to determine which fraction is larger or smaller is to do a little leg work.  I think if you do some calculations up front, you can easily compare the fractions in the end.  The trick is to turn the fractions into like fractions.  This is done by making them share a common denominator.

You have to multiply the top and bottom of each fraction by the denominator of the other fraction.  Like this:
1/2 and 3/9 would become 1 x 9 over 2 x 9 = 9/18 and 3 x 2 over 9 x 2 = 6/18
Now that we have a common denominator we can compare the fractions 9/18 and 6/18.  9/18 is slightly larger than 6/18.

TONS of free fraction worksheets covering all kinds of processes.