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How Commutative Property Relates to Place Value

Instructor: Anna Reinking

Anni taught elementary school for eight years and is currently teaching college. She received her Ed.D. in Curriculum and Instruction.

In this lesson you will briefly review commutative property and place value. Then you will understand how the commutative property and place value are related.

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.

57 Shirt and 32 Pants

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

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