# 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:
$a\times b=b\times a$

And in algebraic expressions:
$X\times numero=numero\times X$

## examples with solutions for the commutative property of multiplication

### Exercise #1

Solve:

$-5+4+1-3$

### 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

$-3$

### Exercise #2

$4:2+2=$

### Step-by-Step Solution

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

$4:2=2$

Now we obtain the exercise:

$2+2=4$

$4$

### Exercise #3

$\frac{1}{4}\times4+2=$

### 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:

$\frac{1\times4}{4}+2=$

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

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

$3$

### Exercise #4

$-2-4+6-1=$

### Step-by-Step Solution

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

$-2-4=-6$

$-6+6=0$

$0-1=-1$

$-1$

### Exercise #5

$12\times13+14=$

### Step-by-Step Solution

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

$12\times13=156$

Now we get the exercise:

$156+14=170$

$170$

## examples with solutions for the commutative property of multiplication

### Exercise #1

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

### 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:

$5\times2\times17=$

Now we solve the exercise from left to right:

$5\times2=10$

$10\times17=170$

170

### Exercise #2

$10-5-2-3=$

### Step-by-Step Solution

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

$10-5=5$

$5-2=3$

$3-3=0$

$0$

### Exercise #3

$4-2+2-4=$

### Step-by-Step Solution

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

$4-2=2$

$2+2=4$

$4-4=0$

$0$

### Exercise #4

$-5+2=$

### 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.

$-3$

### Exercise #5

$11\times3+7=$

### 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:

$11\times3=33$

$33+7=40$

$40$

## examples with solutions for the commutative property of multiplication

### Exercise #1

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

### Step-by-Step Solution

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

Keep in mind that:

$19+21=40$

$34+6=40$

Now, we get a more convenient exercise to solve:

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

90

### Exercise #2

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

### Step-by-Step Solution

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

Keep in mind that:

$4+4=8$

Now we get the exercise:

$74+36+6+8=$

Keep in mind that:

$74+6=80$

$32+8=40$

Now, we get a more comfortable exercise to solve:

$80+40=120$

120

### Exercise #3

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

### 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:

$7+3=10$

$6+4=10$

Now, we obtain a more convenient exercise to solve:

$10+10=20$

20

### Exercise #4

$3-2+10-x=$

### Step-by-Step Solution

We solve the exercise from left to right:

$3-2=1$

$1+10=11$

Now we obtain:

$11-x$

$11-x$

### Exercise #5

Solve:

$2-3+1$

### Step-by-Step Solution

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

$(2+1)-3=$

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

$2+1=3$

$3-3=0$