(upbeat music) - Hello everyone, and good morning.

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

Before we get started, let's check the mail.

(mailbox opens and closes) Yay, a postcard from Ms. Post.

Let's see what it says.

Ms. Post, "I need some help understanding how to add fractions.

It gets tricky when the denominators are different."

You are right.

Now remember, fractions are easier when you try to picture an area model.

I always like to think about big pizzas or cookie cakes.

The bottom number, or the denominator, represents how many slices there are in the pizza, so when we're adding fractions with the same denominators, it's like talking about pizza slices that are the same size.

So when we add them, we leave the denominator alone.

We don't even worry about it.

So just write it down and then add the numerators.

Here's a quick example.

Let's say that we were adding 1/4 (pen scratches) plus 2/4.

The denominators are the same, so we don't worry about them.

Add the numerators.

One plus two is three, and we keep our denominator.

So there's a simple example.

Now the reason it gets kind of wonky when the denominators are different is because now we're talking about adding two slices of pizza that were cut very differently.

So this time, let's change the second denominator from our fraction and add 1/4 with 2/5.

Now I'm gonna show you two different ways to do this.

First, the traditional way.

Step one is that you would write the addition problem with your fractions.

1/4 plus 2/5, and you recognize that you have unlike denominators.

Step two is that you need to find the least common denominator between those two fractions.

(paper rustles) So to do that, you write out all the multiples of four, four, eight, 12, 16, 20, and all the multiples of five, five, 10, 15, 20.

And then when you get to one that they have in common, you stop.

And I see that 20 is common to four and five.

Now step three.

Now that we have our least common denominator, we're gonna rewrite our problem.

(paper rustles) I saw that four times five is 20.

So I'm also gonna multiply the numerator times five.

One times five is five.

So 1/4 is the same as 5/20.

Now on my second fraction, five had to be multiplied by four to give me 20.

So that means I multiply the numerator by four also.

Two times four is eight.

Now we're in business.

5/20 and 8/20, I can add together, because the denominator is the same.

(paper rustles) So 5/20 plus 8/20, leave the denominator alone, and add the numerators.

Five plus eight is 13.

Now sometimes you'll have a fourth step.

You need to simplify.

But 13 out of 20, (paper rustles) there's no number that divides into 13 and 20, so it's already simplified and ready to go.

So let's do the same addition problem.

We're gonna add 1/4 and 2/5, but I'm gonna show you how to do it with the butterfly method.

Okay, with the butterfly method, you write your two fractions, 1/4 and 2/5, and then you draw butterfly wings, and they crisscross like this.

And that's to show you how to cross multiply.

So five times one, that's where the five came from, and four times two, that's where the eight came from.

Then you add those top numbers, five plus eight gives you the 13, and then kinda like we did on the first way, but here, you multiply the four times the five, and it gives you the 20, which is that common denominator.

So this is kind of a cool, short way to do the very same work.

Step one, you cross multiply.

Step two, you multiply your denominators.

And then step three, you just add across the top.

It's a fun way, right?

Well, thank you for the postcard.

I hope today's lesson helped you better understand fractions that have different denominators.

Have a great rest of the day.

I would love it if you would spend some time today practicing, adding, and subtracting your fractions.

You can use the butterfly method with subtraction too.

You just subtract instead of add.

Remember, keep a positive mindset, grow every day by reading and asking big questions, and always remember there's nothing you can't do if you put your mind to it.

I'll see you soon.

Bye.

(upbeat music) ♪ It's time to rise and shine ♪