(upbeat music) - Hello everyone, good morning.

It's so good to be with you this morning.

Well, I just found a postcard for Ms. Post.

So let's see what it says, Ms. Post, I need some help understanding how to compare fractions, especially when there are different numbers.

Will you please explain this to me?

Great question.

I think one of the easiest ways to compare fractions is by using area models.

They help you picture what the fractions represent by letting you compare the shaded areas in the two circles.

Now we use these symbols to compare fractions.

This is greater than, equal to, and less than.

If you ever get greater than and less than mixed up, remember to read from the left to the right, just like you would in a book.

So if the left side of the symbol is the big open part, then you know, that's greater than, and if the left side of the symbol is the smaller closed part, that's less than.

We're going to talk about three types of fractions today, fractions with the same number and the denominators, fractions with the same number in the numerators, and fractions that have completely different numbers in the numerator and the denominator.

Now let's compare area models for fractions that have the same denominator.

We're going to use three-sevenths and five-sevenths.

I have two circles that are both divided into seven parts.

And the denominator represents those numbers of parts.

Now, if we're picturing a big circular cookie cake, then this is how many total slices there are.

Then the numerator is how many of those parts we shade in.

So if we're talking about pizza or cookie cake, you can think of it as how many slices were eaten.

On the first area model, We said that three parts of the whole or three slices were eaten.

So let's shade that in.

On the second area model, we said that five parts of the whole or five slices of the pizza were eaten.

So let's shade that in.

Okay, So we have three out of seven and we have five out of seven.

Now let's compare.

The model shows us that five out of seven is definitely greater than three out of seven.

So here's the trick.

When your denominators are the same, look at the numerator, the larger numerator belongs to the greater fraction.

In this example, since five is greater than three, then we know that five sevenths is greater than three sevenths.

Now let's look at area models to compare fractions with the same numerator, but different denominators.

We're comparing four-fifths and four-ninths.

The first circle is divided into fifths and the second circle is divided into ninths.

And in both circles, we're going to shade four parts of the whole circle.

So let's compare.

This will be four out of five.

That's a lot, and this will be four out of nine.

Not nearly as much is it?

So here's the trick.

When your numerators are the same, look at the denominators.

The smaller denominator belongs to the greater fraction.

And if that seems a little wonky, think of it this way.

If a pizza was only cut into three or four slices, those would be some really big slices.

If a pizza is getting cut into 20 slices, those would be some really, really small slices.

So the smaller, the denominator, the bigger the pieces.

Okay, now let's compare fractions that have different numerators and different denominators.

Which fraction do you think is greater?

Three-fifths or four-sevenths.

I'm going to show you a fun way to solve this problem called the Butterfly Trick.

First, write down both fractions.

We have three-fifths and four-sevenths.

Next draw your butterfly wings like this, so that the two ovals criss-cross.

Then cross-multiply and write down the answers at the top of the butterfly's wings.

Seven times three is 21, 5 times four is 20.

And 21 is greater than 20, which tells us, three-fifths is greater than four-sevenths.

Thank you for the postcard.

I hope today's lesson helped you in comparing fractions and I hope you have a great rest of the day.

Remember, keep a positive mindset, grow every day by reading and asking big questions.

There's nothing you can't do if you put your mind to it, I'll see you soon.

(upbeat music)