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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Trisha Fyfe*

Trisha has taught college and K-12 English, reading, writing, and math. She has a master's degree in teaching.

Did you know that you can sometimes move numbers around in math problems, but the answer doesn't change? Let's look at why this happens as we explore the associative property in this lesson.

You are selling cookies at a bake sale to earn money for a new bike. Two of your neighbors come just as you open. You're off to a good start! Sam from next door buys 1 butter cookie and 2 lemon cookies. Mary from down the street buys 4 sugar cookies. How many cookies have you sold so far?

You sold 1 butter cookie and 2 lemon cookies to Sam, so that's 1 + 2. Then you add Sam's cookies to Mary's 4 cookies, to get 1 + 2 + 4. That's 7 cookies total. Pretty good!

Now, let's switch things around. Maybe Sam hates lemons and buys only 1 butter cookie. Mary buys the 2 lemon cookies and 4 sugar cookies. Did the total number of cookies you sold change? Let's find out.

First, Mary. She buys 2 lemon and 4 sugar cookies, 2 + 4. Add those cookies to Sam's 1 cookie, 2 + 4 + 1, and you get 7 cookies, just like before.

Why wasn't the total different in the second example? Because of the **associative property of addition**, which says that even if we change the groupings of the numbers we're adding, the total will always be the same.

Take a look at the associative property in our bake sale example: (1 + 2) + 4 = 1 + (2 + 4). It doesn't matter which grouping (operation inside the parentheses) we complete first. The answer is the same both times.

Notice the parentheses. Have you seen these in math before? In math, we complete the operations (i.e. addition, subtraction, multiplication, or division) inside the parentheses first. Parentheses group together numbers that we need to work with before any other numbers.

The associative property also applies to multiplication. The **associative property of multiplication** says if we change the groupings of the numbers we're multiplying, the total will always be the same. Every time, we promise! Let's take a deeper look.

Try this:

(4 x 5) x 6 = ?

If you got 120, great job! Let's explore the steps.

First, complete the operations inside the parentheses. Remember we always do this step first.

4 x 5 = 20

Next, take a look outside the parentheses. We can see that we need to multiply our answer by 6.

20 x 6 = 120

What if the equation looked like this instead?

4 x (5 x 6) = ?

Did you still get 120? If so, you're on track. Remember the associative property says that we can change, or switch, our groupings around and the answer is always the same. Let's break this one down, too.

Since 5 x 6 is inside the parentheses, we need to complete this operation first.

5 x 6 = 30

Next, we take a look outside the parentheses. We can see that we need to multiply our answer by 4.

30 x 4 = 120

We can see the associative property for this problem here: (4 x 5) x 6 = 4 x (5 x 6). It doesn't matter which grouping (operation within the parentheses) we complete first. The answer is the same both times.

Let's take a few moments to review what we've learned. The **associative property** in math tells us that we can add or multiply numbers using any groupings of these numbers. Specifically, we learned that the **associative property of addition** says that even if we change the groupings of the numbers we're adding, the total will always be the same, and that the **associative property of multiplication** says if we change the groupings of the numbers we're multiplying, the total will always be the same. The associative property itself is just one reason we can get the same answer in completely different math problems, so keep that in mind next time you see problems like the ones we examined in this lesson.

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Math for Kids23 chapters | 325 lessons

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