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

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

Well, a teacher in the Teacher House already checked the mail for me and we got a postcard.

So let's see what it says.

"Ms. Post, please explain how fractions that look so different can be the same.

For example, how can 2/3 be the same as 8/12?"

Okay, this is a really good question.

One of the easiest ways to find equivalent fractions is by using area models.

Well, that just means that we can compare the shaded area in one circle to the shaded area in another circle, and if those areas are the same, we know the fractions are equivalent.

Now, I'm not certain you know what equivalent means, so let's talk about that for just a second.

Equivalent fractions are fractions that have different denominators and different numerators, but they're equal when we simplify them.

And simplified just means they're written in the easiest way possible.

Now I want you to be able to picture this.

So let's look at area models.

The two fractions that were mentioned on the postcard were 2/3 and 8/12, so I'm gonna write those on our area models.

Now, if I draw a circle, and we can think of this as a big pizza or a cookie cake, and I slice it into three total parts, that represents the denominator from the first fraction.

Then, if I draw another circle and I slice it into 12 total parts, that represents the denominator from the second fraction.

Now, our numerators are the parts of the whole that we shade in.

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

Now, on the first area model, we said that two parts of that whole, or two slices of the pizza were eaten.

So let's shade those in.

Now, on the second area model, we said that eight parts of the whole, or eight slices of the pizza were eaten, do now let's say those in.

The amount of pizza eaten is the very same.

That means that 2/3 is equal to 8/12.

So equivalent fractions are fractions, they might have different numerators and denominators, but they're really the very same amount.

Now, here's an easy way that you can start to recognize patterns of equivalent fractions.

Start with any fraction, and we'll use 2/3 from the postcard.

Write that fraction down and then multiply that fraction, the numerator and the denominator, by the same numbers, just like this.

So when we do two times two and three times two, we're gonna get a four on top.

Two times two is four, and we're gonna get three times two is six on the bottom.

So that tells us 2/3 is the very same as 4/6.

Let's look at one more.

So I'm gonna write down the fraction that we started with.

And this time, instead of multiplying by twos, let's try multiplying by threes.

So on the top, two times three will give us six as our new numerator, and three times three will give us nine as our new denominator.

And you can use any number you want, you just have to make sure that you multiply the numerator and the denominator by the same number.

So this is how you can see all the possible equivalent fractions for 2/3.

Thank you so much for the postcard.

I hope today's lesson helped you feel more comfortable with how equivalent fractions can look, and also how to find them by multiplying.

Have a great rest of the day.

I would love it if you would spend some time today practicing creating equivalent fractions.

Maybe try it for 1/2.

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

I'll see you soon.

Bye.

(upbeat music)