## The Commutative Property

The Commutative Property applies to addition as follows:

## 5 + 3  =  0 + 5 + 3  =  0 + 3 + 5  =  3 + 5

Note that 0 (zero) is the neutral element for addition. The operation of plus appears for 5 when 0 is placed in front of it. It does not change the meaning. The commutative property is applied by rearranging the number with its operation. We note that plus for addition is also omitted when 0 is omitted.

## 3   =   0 + 3

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The Commutative Property applies to subtraction as follows:

## 5 – 3  =  0 + 5 – 3  =  0 – 3 + 5  =  – 3 + 5

Note that 0 (zero) is the neutral element for subtraction as well, because addition and subtraction are opposite of each other. The commutative property is applied by rearranging the number with its operation. Therefore, 3 is moved with its minus operation. When 0 is removed, the ‘minus’ becomes a ‘negative’ sign.

## – 3   =   0 – 3

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The Commutative Property applies to multiplication as follows:

## 6 x 2  =  1 x 6 x 2  =  1 x 2 x 6  =  2 x 6

Note that 1 (one) is the neutral element for multiplication. The operation of multiplication appears for 6 when 1 is placed in front of it. It does not change the meaning. The commutative property is applied by rearranging the number with its operation. We note that multiplication sign is also omitted when 1 is omitted.

## 2   =   1 x 2

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The Commutative Property applies to division as follows:

## 6 ÷ 2  =  1 x 6 ÷ 2  =  1 ÷ 2 x 6  =  1/2 x 6

Note that 1 (one) is the neutral element for division as well, because multiplication and division are opposite of each other. The commutative property is applied by rearranging the number with its operation. Therefore, 2 is moved with its division operation. 1 divided by 2 becomes the fraction half.

## 1 ÷ 2   =   1/2 (half)

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• MarkNR  On January 26, 2014 at 12:43 AM

The basic rhythms of math need to be taught early.
Mark

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• vinaire  On January 26, 2014 at 6:36 AM

And those who didn’t get it early, it is never too late to learn it.

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• Chris Thompson  On January 26, 2014 at 10:30 AM

. . . and if not, then learned later.

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• vinaire  On February 9, 2014 at 9:39 AM

I have updated the OP to clarify it to make it closer to what is taught in schools.

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