(upbeat music) Good morning, my magnificent magical mathematicians.

I'm so excited to be with you this morning.

We're going to have so much fun today, learning more about math and growing our brains.

This morning, we're going to talk about some math tricks that we need to remember when it comes to multiplication.

Let me pull the first trick out of my hat.

Math amagical.

(magical chime) Oh, the associative property of multiplication.

That sounds really smart, doesn't it?

It sure does, but it's not complicated at all.

The associative property of multiplication simply says that the way we group numbers and a multiplication problem doesn't change the product.

Remember, the product is the answer we get when we multiply those numbers.

So that means that you can do the multiplication in any order you want.

Okay.

This is always easier to understand when we can picture it.

And for this concept, I've picked cupcakes as a way to show you how this works.

But I need cupcakes.

All right, here comes the magic snap.

Are you ready?

One, two, three.

Perfect.

This is exactly what we needed.

Okay, look at these two packages of cupcakes.

Each package looks like an array with three rows and four columns.

To figure out how many we have in total, we can multiply three rows times four columns.

Times two packages.

That would be three times four times two.

Now three times four is 12 and 12 times two is 24.

In that problem, we decided to multiply our numbers in the order three, four, two.

But here's something to think about.

Would it have mattered if we changed the order to four, three, two?

No.

The associative property of multiplication tells us that we will get the same answer.

And our cupcakes?

Well, they show us it's true.

Look at the package.

When I turn it, now we see four rows and three columns, but it doesn't change the number of cupcakes inside, does it?

Of course not.

If I turn the cupcake package the other direction, the array or the arrangement that they're in, changes from having three rows and four columns to four rows and three columns, but it doesn't change how many cupcakes there are.

Now, let's multiply again.

This time we'll multiply the rows by the columns by the number of packages to see how many cupcakes we have total.

Four rows times three columns times two packages.

Four times three is 12 and 12 times two equals 24.

Great job.

Now remember, any time you're multiplying three or more numbers, the associative property says that the order of the numbers does not matter.

You'll always arrive at the same answer.

Okay, here comes our second trick.

Are you ready?

Math amagical.

(magical chime) Oh, this one is called the distributive property of multiplication.

Now, when you hear distributive, think about the root word there, which is distribute.

And that just means to give out.

The distributive property in math tells us that when we multiply a value by a sum, we can multiply the value by each number in that sum and then add those numbers together.

Here's an example: four times the sum, three plus eight.

So let's say that the number four is being multiplied by that sum, three plus eight, the four gets multiplied by both of those numbers inside.

So I'm going to distribute or pass out the four to both the three and the eight.

Four times three plus four times eight, four times three equals 12 and four times eight is 32.

When we add those together, 12 plus 32, we get 44.

Okay, one more thing.

Here's how you can use this to help you with harder multiplication problems.

If there is a math fact with a big number that you don't know or can't remember, you can use the distributive property to figure it out.

Here's an example.

Five times 17.

Now I don't know about you, but I only have my multiplication facts memorized through the 12's.

I do not have the seventeens memorized, so I'm going to pull one more math trick out of my hat.

The magic hat tells me, (magical chime) Oh, it says, Rewrite 17 as ten plus seven.

We can do that.

So instead of five times 17, we'll do five times the sum ten plus seven.

That's five times ten plus five times seven.

That gives us 50 plus 35 equals 85.

Okay, magical mathematician.

That's all of our time for today.

Great job growing your brain with me.

I hope you have a great day and I'll see you next time on.

Rise and Shine.