Commutative Property Practice Problems and Examples

Understanding The Commutative property

Complete explanation with examples

What is the commutative property?

The commutative property is an algebraic principle that allows us to "play" with the position that different elements occupy in multiplication and addition exercises without affecting the final result. Our objective in using the commutative property is to make the resolution of the exercise simpler from the point of view of the calculations.

As we have already said, the commutative property can be applied in the case of addition and multiplication.

In other words:

If we change the place of certain elements in the exercise or equation the result will be the same.

Commutative property of addition:

In addition operations we can change the place of the addends and arrive at the same result.
That is:
$a+b=b+a$
Same as in algebraic expressions:
$X+number=number+X$

Regardless of the order in which we add the terms and no matter how many addends there are, the result will always be the same.

Commutative property of multiplication:

In multiplication operations we can change the place of the terms and arrive at the same result.
That is:
$a\times b=b\times a$
Same as in algebraic expressions:
$X\times number=number\times X$

Regardless of the order in which we multiply the factors and no matter how many there are in the exercise, the product will always be the same.

Note - The commutative property does not act in this way in subtraction and division operations.

Detailed explanation

Practice The Commutative property

Test your knowledge with 13 quizzes

$$ 4:2+2= $$

Examples with solutions for The Commutative property

Step-by-step solutions included

Exercise #1

$5\cdot5\cdot5\cdot2\cdot2\cdot2=?$

Step-by-Step Solution

We use the substitution property and organize the exercise in the following order:

$5\times2\times5\times2\times5\times2=$

We place parentheses in the exercise:

$(5\times2)\times(5\times2)\times(5\times2)=$

We solve from left to right:

$10\times10\times10=$

$(10\times10)\times10=$

$100\times10=1000$

Answer:

1000

Video Solution

Exercise #2

$19+34+21+10+6=\text{?}$

Step-by-Step Solution

In order to simplify our calculations, we try to add numbers that give us a round result.

Keep in mind that:

$19+21=40$

$34+6=40$

Now, we get a more manageable exercise to solve:

$40+40+10=80+10=90$

Answer:

90

Video Solution

Exercise #3

$74+32+6+4+4=\text{?}$

Step-by-Step Solution

In order to simplify the resolution process we try to add numbers that give us a round result.

Keep in mind that:

$4+4=8$

Now we get the exercise:

$74+36+6+8=$

Keep in mind that:

$74+6=80$

$32+8=40$

Now, we get a more manageable exercise to solve:

$80+40=120$

Answer:

120

Video Solution

Exercise #4

$7+4+3+6=\text{?}$

Step-by-Step Solution

To make solving the exercise easier, we try to add numbers that give us a result of 10.

Let's keep in mind that:

$7+3=10$

$6+4=10$

Hence we obtain a more manageable exercise to solve:

$10+10=20$

Answer:

20

Video Solution

Exercise #5

Solve the following exercise:

$8+9+2=\text{ ?}$

Step-by-Step Solution

Since the exercise only involves addition, we will use the commutative property to solve it.

$8+2+9=$

Now let's solve the exercise from left to right:

$8+2=10$

$10+9=19$

Answer:

19

Video Solution

Frequently Asked Questions

Everything you need to know about The Commutative property

What is the commutative property in simple terms?

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The commutative property means you can change the order of numbers in addition and multiplication without changing the answer. For example, 3 + 5 = 5 + 3 and 4 × 6 = 6 × 4.

Does the commutative property work for subtraction and division?

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No, the commutative property does NOT work for subtraction or division. For example, 8 - 3 ≠ 3 - 8 (5 ≠ -5) and 12 ÷ 4 ≠ 4 ÷ 12 (3 ≠ 1/3).

How do you use the commutative property to make math easier?

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Rearrange numbers to group easier calculations together. For instance, in 13.2 + 5.5 + 6.8, you can rearrange to 13.2 + 6.8 + 5.5 to get 20 + 5.5 = 25.5 more easily.

What are some real-world examples of the commutative property?

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Shopping totals work the same regardless of checkout order: milk ($3) + bread ($2) + eggs ($4) = $9, whether you scan milk first or eggs first. The total remains the same.

Can you use commutative property with variables and algebra?

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Yes! In algebra, a + b = b + a and x × 3 = 3 × x. You can rearrange terms with variables just like you do with regular numbers, making equations easier to solve.

What's the difference between commutative and associative properties?

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Commutative property changes the ORDER of numbers (3 + 5 = 5 + 3). Associative property changes the GROUPING with parentheses [(2 + 3) + 4 = 2 + (3 + 4)] but keeps the same order.

How do you teach commutative property to elementary students?

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Use concrete examples like toy collections: 5 red cars + 3 blue cars = 3 blue cars + 5 red cars = 8 total cars. Physical manipulatives help students see that order doesn't change the total.

What grade levels learn about the commutative property?

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Students typically learn commutative property basics in 1st-2nd grade with simple addition, expand to multiplication in 3rd-4th grade, and apply it to algebraic expressions in middle school grades 6-8.

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Topics Learned in Later Sections

The Commutative Property of Addition The Commutative Property of Multiplication The Distributive Property The Distributive Property for Seventh Graders The Distributive Property of Division The Distributive Property in the Case of Multiplication The commutative properties of addition and multiplication, and the distributive property The Associative Property The Associative Property of Addition The Associative Property of Multiplication Advanced Arithmetic Operations Subtracting Whole Numbers with Addition in Parentheses Division of Whole Numbers Within Parentheses Involving Division Subtracting Whole Numbers with Subtraction in Parentheses Division of Whole Numbers with Multiplication in Parentheses

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Commutative Property Practice Problems and Examples

Understanding The Commutative property

What is the commutative property?

Practice The Commutative property

Examples with solutions for The Commutative property

Frequently Asked Questions

What is the commutative property in simple terms?

Does the commutative property work for subtraction and division?

How do you use the commutative property to make math easier?

What are some real-world examples of the commutative property?

Can you use commutative property with variables and algebra?

What's the difference between commutative and associative properties?

How do you teach commutative property to elementary students?

What grade levels learn about the commutative property?

More The Commutative property Questions

The Commutative property

Continue Your Math Journey

Topics Learned in Later Sections

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