**COMPARING AND ORDERING FRACTIONS**
Let's start with ordering fractions first.

I am assuming you know what fractions are, so let's skip that part.

__ORDERING FRACTIONS WITH LIKE DENOMINATORS: __
When ordering fractions with LIKE denominators (the bottom part is the same in both fractions), all you have to do is order the numerators (the top part of the fraction)!

For example:

Let's say we have the fractions, 5/10, 3/10, and 8/10. All the denominators are the same. Now lettuce order them from smallest to largest!

Since the denominators are the same, all we have to do is order them by the numorator. (We do this because the smaller the numerator, the smaller the fraction.)

3/10, 5/10, and 8/10!

Viola! That is how you order fractions with like denominators!

__ORDERING FRACTIONS WITH UNLIKE DENOMINATORS:__
This is where things may get a little tricky.

When ordering fractions with unlike denominators, you have to multiply the fraction by 1. (a number over itself, eg. 1/1, 2/2, 3/3, etc.)

'How is this done?' you may ask.

How about a diagram?

Let's start easy. How about, 4/5 and 7/10?

To start off, what do both of these denominators have in common? Yes, 10. 7/10 already has 10 as it's denominator, so we won't have to change it!

To get from 5 to ten, we multiply by two.

*note we also have to change the numerator because we multiply by 1.

4 2 8

- x- =-

5 2 10

Now we have the fraction, 8/10, that used to be 4/5.

Remember that we had to order fractions?

Now that we have two numbers with the same denominator, we can do exactly what we did before with like denominators!

The answer is 7/10, 8/10

VIOLA! You now know this as well!

__COMPARING FRACTIONS:__
When you compare fractions, you basically compare!

When comparing fractions, you find the difference between them. This is like ordering them to see which one is larger, and which isn't.

So when you have fractions like this: 3/5 and 1/5

You can order them and see which is larger and which is smaller.

1/5 is smaller than 3/5.

VIOLAAAA! You know how to compare now too!

That was my short lesson on Comparing and Ordering Fractions.

*phew.*

Note: Okay, okay, okay. I know this is totally late. My bad.

Mathematically and Scientifically yours,

Nicole :D

Ps. That diagram did not go well as I intended to.