# Associative property - Examples, Exercises and Solutions

## What is the associative property?

The associative property tells us that that we can change the grouping of factors (in multiplication) or addends (in addition) in an expression without changing the end result.

Typically, we use parentheses to associate, since they come first in the order of operations (PEMDAS).

For example:

The expression

$15\times 2\times 9=$

Can be associated as

$\left(15×2\right)×9=15×\left(2×9\right)=270$

## examples with solutions for associative property

### Exercise #1

$6:2+9-4=$

### Step-by-Step Solution

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

$(6:2)+9-4=$

$6:2=3$

Now we place the subtraction exercise in parentheses:

$3+(9-4)=$

$3+5=8$

$8$

### Exercise #2

$3\times5\times4=$

### Step-by-Step Solution

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

But, this can leave us with awkward or complicated numbers to calculate.

Since the entire exercise is a multiplication, you can use the associative property to reorganize the exercise:

3*5*4=

We will start by calculating the second exercise, so we will mark it with parentheses:

3*(5*4)=

3*(20)=

Now, we can easily solve the rest of the exercise:

3*20=60

60

### Exercise #3

$3+2-11=$

### Step-by-Step Solution

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

$3+2=5$

$5-11=-6$

$-6$

### Exercise #4

$4+5+1-3=$

### Step-by-Step Solution

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

$4+5=9$

$9+1=10$

$10-3=7$

7

### Exercise #5

$24:8:3=$

### Step-by-Step Solution

According to the order of operations, we solve the exercise from left to right since the only operation in the exercise is division:

$24:8=3$

$3:3=1$

$1$

## examples with solutions for associative property

### Exercise #1

$-5+2-6:2=$

### Step-by-Step Solution

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

$6:2=3$

Now we get the exercise:

$-5+2-3=$

We solve the exercise from left to right:

$-5+2=-3$

$-3-3=-6$

$-6$

### Exercise #2

$9:3-3=$

### Step-by-Step Solution

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

$9:3=3$

Now we obtain the exercise:

$3-3=0$

$0$

### Exercise #3

$4\times2-5+4=$

### Step-by-Step Solution

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

$4\times2=8$

Now we obtain the exercise:

$8-5+4=$

We solve the exercise from left to right:

$8-5=3$

$3+4=7$

$7$

### Exercise #4

$12\times5\times6=$

### Step-by-Step Solution

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

$12\times5=60$

$60\times6=360$

360

### Exercise #5

$94+12+6=$

### Step-by-Step Solution

According to the rules of the order of operations, you can use the substitution property and organize the exercise in a more convenient way for calculation:

$94+6+12=$

Now, we solve the exercise from left to right:

$94+6=100$

$100+12=112$

112

## examples with solutions for associative property

### Exercise #1

$7+8+12=$

### Step-by-Step Solution

According to the rules of the order of operations, you can use the substitution property and start the exercise from right to left to calculate comfortably:

$8+12=20$

Now we obtain the exercise:

$7+20=27$

27

### Exercise #2

$7\times5\times2=$

### Step-by-Step Solution

According to the rules of the order of operations, you can use the substitution property and start the exercise from right to left to comfortably calculate:

$5\times2=10$

$7\times10=70$

70

### Exercise #3

$-3-2+10=$

### Step-by-Step Solution

First, we place the subtraction exercise in parentheses, and then we add:

$(-3-2)+10=$

$-5+10=$

We use the substitution property to make solving the exercise easier:

$10-5=5$

5

### Exercise #4

$5+2a+4=$

### Step-by-Step Solution

Given that in the exercise there is only one addition operation, the substitution property can be used:

$5+4+2a=$

We solve the exercise from left to right:

$5+4=9$

Now we obtain:

$2a+9$

$2a+9$

### Exercise #5

$2+6-10+30-2=$

### Step-by-Step Solution

We solve the exercise according to the order of operations.

We place the addition and subtraction exercises in parentheses in the following way to make it easier to solve:

$(2+6)-10+(30-2)=$

We solve the exercises in parentheses:

$8-10+28=$

We place the subtraction exercise in parentheses:

$(8-10)+28=$

$-2+28=26$