What are 2 examples of commutative property?

The Commutative Property of Multiplication is one of the four main properties of multiplication. It is named after the ability of factors to commute, or move, in the number sentence without affecting the product.

Commutative Property of Multiplication Definition

Commutative Property of Multiplication says that the order of factors in a multiplication sentence has no effect on the product. The Commutative Property of Multiplication works on integers, fractions, decimals, exponents, and algebraic equations.

The word “commutative” comes from a Latin root meaning “interchangeable”.

Switching the order of the multiplicand (the first factor) and the multiplier (the second factor) does not change the product.

What is 4 × 5? The answer is 20.

What is 5 × 4? The answer is also 20.

The order of the two factors, 4 and 5, did not affect the product, 20.

Commutative Property Of Multiplication Formula

The generic formula for the Commutative Property of Multiplication is:

Any number of factors can be rearranged to yield the same product:

• 1 × 2 × 3 = 3 × 1 × 2 = 6  = 2 × 3 × 1 = 2 × 1 × 3

Often, when demonstrating the commutative property of multiplication, the product is shown in the middle of the multiple arrangements of the equation.

Commutative Property Of Multiplication Examples

Let's see these fancy words in action:

In the first picture we can think of the set of five rubber ducks as the multiplicand, spread across from left to right. Beneath it, vertically, we have the multiplier, 4.

In the second picture we have one set of four rubber ducks arrayed left to right, the multiplicand. Then we have the multiplier, 5, vertically.

Whether we take a set of five rubber duckies and multiply them four times, as on the left, or we take a set of four rubber duckies and multiply them five times, as on the right, we still end up with 20 rubber duckies.

The Commutative Property of Multiplication works on basic multiplication equations and algebraic equations. Here was see how to use commutative property of multiplication various multiplication sentences:

• Integers:

• 6 × 7  = 42 = 7 × 6
• 1,234 * 0 = 0 = 0 * 1,234
• 717 × 11 = 7,887 = 11 × 717

• Exponents:

• 62 × 32  = 324 = 32 × 62
• 23 × 43 = 256 =  43 × 23

• Fractions:

• 34 × 78 = 2132 =  7834
• 910 × 75100 = 75100 × 910 =  6751000 = 2740 (simplified by dividing by 2525)

• Decimals:

• 0.1234 ×  0.987 = 0.1217958 = 0.987 × 0.1234
• 411.52 × 0.3 = 123.456 = 0.3 ×  411.52

• Variables:

• 4x22 = 32 = 24x2

To get our answer 32, we first solved for x.

Definition Of Commutative Property

Commutative property is one of the basic properties of numbers. The word "commute" means "exchange" or "swap over"

Commutative property states that numbers can be added or multiplied in any order.
That is:
Commutative Property of Addition states that changing the order of addends does not change the sum. That is, a + b = b + a.
Commutative Property of Multiplication states that changing the order of factors does not change the product. That is, a x b = b x a

More About Commutative Property

Commutative property holds for both addition and multiplication. 
That is: the operations addition and multiplication are commutative over the set of real numbers. That means, for any two real numbers x and 
y, x + y = y + x and xy = yx.
Subtraction and division are not commutative.

Example of Commutative Property

2 + 3 = 3 + 2. Whether you add 3 to 2 or 2 to 3, you get 5 both ways.
4 x 7 = 7 x 4. Whether you multiply 4 by 7 or 7 by 4, the product is the same, i.e. 28.

Commutative Property in real-life

Counting a combination of different coins reminds you of commutative property.
Suppose you have 20 quarters and 10 dimes.
It doesn't matter whether you add the quarters first and then the dimes OR add the dimes first and then the quarters OR add a quarter and a dime alternately, finally the total is going to be $6.

Video Examples:commutative property

Solved Example onCommutative Property

Rewrite the expression "4 + m + n" using the commutative property.

Solution:

Commutative property means to exchange or swap things. So, the answer is any of the following.
4 + m + n = m + 4 + n OR 
m + n + 4 OR 
n + m + 4 OR
n + 4 + m OR 
4 + n + m

Ques: Is 5 (3x) = (3x) 5 true?

Solution:

Yes it is. Because, just the positions of the terms 5 and 3x have been swapped. So, the equation above is true by the commutative property of multiplication.

Related Worksheet

• Exploring-Commutative-Property-of-Addition-Gr-3
• Exploring-Commutative-Property-of-Multiplication-Gr-3

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