# How Commutative Property Relates to Place Value

## Commutative Property

Every morning we wake up and put on clothes to get ready for the day. When people get dressed in the morning, there are some items that must be put on before other items. For example, you have to put on your socks before you put on your shoes. But, then there are other pieces of clothing you can put on in any order. For example, it doesn't matter if you put on your shirt before your pants or your pants before your shirt. Why are we talking about getting dressed? Because it can help you understand the **commutative property**.

It doesn't matter which we put on first, our shirt or our pants because the end result is the same; we are dressed and ready for our day. That is exactly like the commutative property, which states that it does not matter which number goes first in the equation where you're doing addition or multiplication because the end result is the same.

But, why does it work with only multiplication and addition? It is because in addition and multiplication we are increasing numbers. It does not work with subtraction and division because we are making the numbers smaller, so it is important to have the numbers in those equations in a specific order.

## Place Value

**Place value** is important when talking about commutative property. When we look at the number 45, we see two digits. We see the digit 4 and we see the digit 5. Each of these separate digits is in a specific spot or place in the number; this gives the digits a place value. For example, in the number 45 the digit 4 is in the tens place (giving it the value of forty) and the 5 is in the ones place (giving it the value of 5).

## Commutative Property and Place Value

Do you have a favorite shirt you like when to wear or a pair of pants that are your favorite? I do. It may sound funny, but I love to wear my green shirt with a big 57 on the front. My favorite pair of pants are jeans with the number 32 going down the legs.

And guess what? My clothes are going to help us understand how the commutative property and place value relate. Remember, it doesn't matter which goes on first, my shirt or my pants - when I put on my green 57 shirt and my blue 32 jeans, I always have a sum of 89 and a product of 1,824. Let's see how.

57 + 32 = 32 + 57

When adding these together, using place values, we can see that the order does not matter because the answer is the same either way.

- Adding the 10s place: 50 + 30 = 80 or 30 + 50 = 80
- Adding the 1s place: 7 + 2 = 9 or 2 + 7 = 9
- Adding the 10s to the 1s: 80 + 9 = 89

Commutative property works with addition and multiplication because multiplication is repeated addition.

57 x 32 = 32 x 57

- Step One: Multiply the two numbers in the TENS place: 50 x 30 (or 30 x 50) = 1500
- Step Two: Multiply the two numbers in the ONES place: 7 x 2 (or 2 x 7) = 14
- Step Three: Multiply the first tens by the second ones: 50 x 2 = 100
- Step Four: Multiply the second tens by the first ones: 30 x 7 = 210
- Step Five: Add the products together: 1500 + 14 + 100 + 210 = 1,824

## Lesson Summary

Place value and commutative property are important to remember when understanding and solving addition and multiplication equations. The order of the numbers in the equation does not matter, as related to the commutative property, because the sum or product is the same. This is directly related to the place value of the digits within the numbers, which do not change.

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## Visual Examples of the Commutative Property

In this creative activity, students will be using visual representations to create fun examples of the commutative property. Students will be creating at least three representations to demonstrate the property, using visual examples. For example, students might choose to show the multiplication of 23 by 14. Students can choose images to represent the numbers, such as 23 apples and 14 oranges. They should include the steps for solving the problem using the commutative property and the result, which can be creative in nature. For example, multiplying apples by oranges might produce 322 cool new fruits that have an apple shape, but are divided into sections like an orange. Students can get creative with their examples!

### Directions

In this activity, you will be creating some fun examples to teach others about the commutative property. You should create three examples using visual representations on a poster. For each example, you should include the steps needed to solve the math using the commutative property. For example, you could consider multiplying tigers and lions to produce ligers, or apples with oranges to create a weird new fruit. All of your examples should show clear steps in applying the commutative property from the lesson. To make sure your example poster has everything you need, check out the criteria for success below.

### Criteria for Success

- Poster includes three examples of the commutative property
- Each example includes the steps needed to solve it using the commutative property
- Poster is colorful and attractive

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Back*How Commutative Property Relates to Place Value*

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