The order of operations is a convention used to determine which operations are performed first. In every math exercise that combines more than one operation (addition, subtraction, multiplication, division, etc.), each operation must be performed in a specific order:

1. Parentheses
2. Powers and Roots
3. Multiplication and division (from left to right)
4. Addition and subtraction (from left to right)
• When a type of operation is repeated in an exercise, they must be solved in order from left to right.

examples with solutions for order of arithmetic operations

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

$3+4-1+40=$

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we solve the exercise from left to right since it only has addition and subtraction operations:

$3+4=7$

$7-1=6$

$6+40=46$

$46$

Exercise #3

$-7+5+2+1=$

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we solve the exercise from left to right since it only has addition and subtraction operations:

$-7+5=-2$

$-2+2=0$

$0+1=1$

$1$

Exercise #4

$9+3-1=$

Step-by-Step Solution

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

9+3=11

11-1=10

And this is the solution!

$11$

Exercise #5

Solve:

$9-3+4-2$

Step-by-Step Solution

According to the rules of the order of operations, we will solve the exercise from left to right since it only has addition and subtraction operations:

$9-3=6$

$6+4=10$

$10-2=8$

8

examples with solutions for order of arithmetic operations

Exercise #1

$100+5-100+5$

Step-by-Step Solution

$100+5-100+5=105-100+5=5+5=10$

10

Exercise #2

Solve:

$3-4+2+1$

Step-by-Step Solution

We will use the substitution property to arrange the exercise a bit more comfortably, we will add parentheses to the addition operation:
$(3+2+1)-4=$
We first solve the addition, from left to right:
$3+2=5$

$5+1=6$
And finally, we subtract:

$6-4=2$

2

Exercise #3

$0.18+(1-1)=$

Step-by-Step Solution

According to the order of operations rules, we first solve the expression in parentheses:

$1-1=0$

And we get the expression:

$0.18+0=0.18$

0.18

Exercise #4

Complete the exercise:

$2+3\times6-3\times7+1=$

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we first solve the multiplication exercises.

We place them in parentheses to avoid confusion during the solution:

$2+(3\times6)-(3\times7)+1=$

Now we solve the multiplication exercises:

$2+18-21+1=$

We solve the rest of the exercise from left to right:

$2+18=20$

$20-21=-1$

$-1+1=0$

0

Exercise #5

Complete the exercise:

$4-5\times7+3=$

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we first solve the multiplication exercises.

We place them in parentheses to avoid confusion during the solution:

$4-(5\times7)+3=$

Now we solve the multiplication exercises:

$4-35+3=$

We solve the rest of the exercise from left to right:

$4-35=-31$

$-31+3=-28$

-28

examples with solutions for order of arithmetic operations

Exercise #1

$20-(1+9:9)=$

Step-by-Step Solution

First, we solve the exercise in the parentheses

$(1+9:9)=$

According to the order of operations, we first divide and then add:

$1+1=2$

Now we obtain the exercise:

$20-2=18$

$18$

Exercise #2

$19\times(20-4\times5)=$

Step-by-Step Solution

First, we solve the exercise in the parentheses

$(20-4\times5)=$

According to the order of operations, we first multiply and then subtract:

$20-20=0$

Now we obtain the exercise:

$19\times0=0$

0

Exercise #3

What is the missing number?

$23-12\times(-6)+?\colon7=102$

Step-by-Step Solution

First, we solve the multiplication exercise:

$12\times(-6)=-72$

Now we get:

$23-(-72)+x\colon7=102$

Let's pay attention to the minus signs, remember that a negative times a negative equals a positive.

We multiply them one by one to be able to open the parentheses:

$23+72+x\colon7=102$

We reduce:

$95+x:7=102$

We move the sections:

$x:7=102-95$

$x:7=7$

$\frac{x}{7}=7$

Multiply by 7:

$x=7\times7=49$

49

Exercise #4

$8:2(2+2)=$

Step-by-Step Solution

$2+2=4$
Then we will solve the exercise from left to right

$8:2=4$
$4 × (4)=16$

The answer: $16$

16

Exercise #5

$5-2\times\frac{1}{2}+1=$

Step-by-Step Solution

בשלב הראשון של התרגיל יש לחשב את הכפל.

$2\times\frac{1}{2}=\frac{2}{1}\times\frac{1}{2}=\frac{2}{2}=1$

מכאן ניתן להמשיך לשאר פעולות החיבור והחיסור, מימין לשמאל.

$5-1+1=5$