The Commutative Property of Multiplication - Examples, Exercises and Solutions

The commutative property of multiplication tells us that changing the order of factors in an expression doesn't change the answer - even if there are more than two!
Like the commutative property of addition, the commutative property of multiplication helps us simplify basic expressions, algebraic expressions and more.


We can define the commutative property of multiplication as:
a×b=b×a a\times b=b\times a

And in algebraic expressions:
X×numero=numero×XX\times numero=numero\times X

A - The Commutative Property of Multiplication

Practice The Commutative Property of Multiplication

examples with solutions for the commutative property of multiplication

Exercise #1

Solve:

5+4+13 -5+4+1-3

Video Solution

Step-by-Step Solution

According to the order of operations, addition and subtraction are on the same level and, therefore, must be resolved from left to right.

However, in the exercise we can use the substitution property to make solving simpler.

-5+4+1-3

4+1-5-3

5-5-3

0-3

-3

Answer

3 -3

Exercise #2

4:2+2= 4:2+2=

Video Solution

Step-by-Step Solution

According to the order of operations, we first solve the division exercise:

4:2=2 4:2=2

Now we obtain the exercise:

2+2=4 2+2=4

Answer

4 4

Exercise #3

14×4+2= \frac{1}{4}\times4+2=

Video Solution

Step-by-Step Solution

According to the order of operations, we first solve the multiplication exercise:

We add the 4 in the numerator of the fraction:

1×44+2= \frac{1\times4}{4}+2=

We solve the exercise in the numerator of the fraction and obtain:

44+2=1+2=3 \frac{4}{4}+2=1+2=3

Answer

3 3

Exercise #4

24+61= -2-4+6-1=

Video Solution

Step-by-Step Solution

According to the order of operations, we solve the exercise from left to right:

24=6 -2-4=-6

6+6=0 -6+6=0

01=1 0-1=-1

Answer

1 -1

Exercise #5

12×13+14= 12\times13+14=

Video Solution

Step-by-Step Solution

According to the order of operations, we start with the multiplication exercise and then with the addition.

12×13=156 12\times13=156

Now we get the exercise:

156+14=170 156+14=170

Answer

170 170

examples with solutions for the commutative property of multiplication

Exercise #1

5172=? 5\cdot17\cdot2=\text{?}

Video Solution

Step-by-Step Solution

According to the rules of the order of arithmetic operations, in an exercise where there is only one multiplication operation, the order of the numbers can be changed.

We rearrange the exercise to obtain a round number that will help us later in the solution:

5×2×17= 5\times2\times17=

Now we solve the exercise from left to right:

5×2=10 5\times2=10

10×17=170 10\times17=170

Answer

170

Exercise #2

10523= 10-5-2-3=

Video Solution

Step-by-Step Solution

Given that the entire exercise is with subtraction, we solve the exercise from left to right:

105=5 10-5=5

52=3 5-2=3

33=0 3-3=0

Answer

0 0

Exercise #3

42+24= 4-2+2-4=

Video Solution

Step-by-Step Solution

Given that we are referring to addition and subtraction exercises, we solve the exercise from left to right:

42=2 4-2=2

2+2=4 2+2=4

44=0 4-4=0

Answer

0 0

Exercise #4

5+2= -5+2=

Video Solution

Step-by-Step Solution

If we draw a line that starts at negative five and ends at 5

We will go from the point negative five two steps forward (+2) we will arrive at the number negative 3.

Answer

3 -3

Exercise #5

11×3+7= 11\times3+7=

Video Solution

Step-by-Step Solution

In this exercise, it is not possible to use the substitution property, therefore we solve it as is from left to right according to the order of arithmetic operations.

That is, we first solve the multiplication exercise and then we add:

11×3=33 11\times3=33

33+7=40 33+7=40

Answer

40 40

examples with solutions for the commutative property of multiplication

Exercise #1

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

Video Solution

Step-by-Step Solution

To make solving easier, we try to add numbers that give us a round result.

Keep in mind that:

19+21=40 19+21=40

34+6=40 34+6=40

Now, we get a more convenient exercise to solve:

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

Answer

90

Exercise #2

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

Video Solution

Step-by-Step Solution

To make solving easier, we try to add numbers that give us a round result.

Keep in mind that:

4+4=8 4+4=8

Now we get the exercise:

74+36+6+8= 74+36+6+8=

Keep in mind that:

74+6=80 74+6=80

32+8=40 32+8=40

Now, we get a more comfortable exercise to solve:

80+40=120 80+40=120

Answer

120

Exercise #3

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

Video Solution

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 7+3=10

6+4=10 6+4=10

Now, we obtain a more convenient exercise to solve:

10+10=20 10+10=20

Answer

20

Exercise #4

32+10x= 3-2+10-x=

Video Solution

Step-by-Step Solution

We solve the exercise from left to right:

32=1 3-2=1

1+10=11 1+10=11

Now we obtain:

11x 11-x

Answer

11x 11-x

Exercise #5

Solve:

23+1 2-3+1

Video Solution

Step-by-Step Solution

We use the substitution property and add parentheses for the addition operation:

(2+1)3= (2+1)-3=

Now, we solve the exercise according to the order of operations:

2+1=3 2+1=3

33=0 3-3=0

Answer

0

Topics learned in later sections

  1. The commutative property
  2. The Commutative Property of Addition
  3. The Distributive Property
  4. The Distributive Property for Seventh Graders
  5. The Distributive Property of Division
  6. The Distributive Property in the Case of Multiplication
  7. The commutative properties of addition and multiplication, and the distributive property
  8. The Associative Property
  9. The Associative Property of Addition
  10. The Associative Property of Multiplication
  11. Advanced Arithmetic Operations
  12. Subtracting Whole Numbers with Addition in Parentheses
  13. Division of Whole Numbers Within Parentheses Involving Division
  14. Subtracting Whole Numbers with Subtraction in Parentheses
  15. Division of Whole Numbers with Multiplication in Parentheses