The Order of Operations - Examples, Exercises and Solutions

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.

Practice The Order of Operations

Examples with solutions for The Order of Operations

Exercise #1

25+2510= \frac{25+25}{10}=

Video Solution

Step-by-Step Solution

Let's begin by multiplying the numerator:

25+25=50 25+25=50

We obtain the following fraction:

5010 \frac{50}{10}

Finally let's reduce the numerator and denominator by 10 and we are left with the following result:

51=5 \frac{5}{1}=5

Answer

5 5

Exercise #2

0:7+1= 0:7+1=

Video Solution

Step-by-Step Solution

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

0:7=0 0:7=0

0+1=1 0+1=1

Answer

1 1

Exercise #3

12+1+0= 12+1+0=

Video Solution

Step-by-Step Solution

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

12+1=13 12+1=13

13+0=13 13+0=13

Answer

13

Exercise #4

0+0.2+0.6= 0+0.2+0.6=

Video Solution

Step-by-Step Solution

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

0+0.2=0.2 0+0.2=0.2

0.2+0.6=0.8 0.2+0.6=0.8

Answer

0.8

Exercise #5

12+0+12= \frac{1}{2}+0+\frac{1}{2}=

Video Solution

Step-by-Step Solution

According to the order of operations, since the exercise only involves addition operations, we will solve the problem from left to right:

12+0=12 \frac{1}{2}+0=\frac{1}{2}

12+12=11=1 \frac{1}{2}+\frac{1}{2}=\frac{1}{1}=1

Answer

1 1

Exercise #6

90+0.5= 9-0+0.5=

Video Solution

Step-by-Step Solution

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

90=9 9-0=9

9+0.5=9.5 9+0.5=9.5

Answer

9.5

Exercise #7

19+10= 19+1-0=

Video Solution

Step-by-Step Solution

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

19+1=20 19+1=20

200=20 20-0=20

Answer

20 20

Exercise #8

2+0:3= 2+0:3=

Video Solution

Step-by-Step Solution

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

0:3=0 0:3=0

2+0=2 2+0=2

Answer

2 2

Exercise #9

12+3×0= 12+3\times0=

Video Solution

Step-by-Step Solution

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

3×0=0 3\times0=0

12+0=12 12+0=12

Answer

12

Exercise #10

8×(5×1)= 8\times(5\times1)=

Video Solution

Step-by-Step Solution

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

5×1=5 5\times1=5

Now we multiply:

8×5=40 8\times5=40

Answer

40

Exercise #11

7×1+12= 7\times1+\frac{1}{2}=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we first insert the multiplication exercise into parentheses:

(7×1)+12= (7\times1)+\frac{1}{2}=

Let's solve the exercise inside the parentheses:

7×1=7 7\times1=7

And now we get the exercise:

7+12=712 7+\frac{1}{2}=7\frac{1}{2}

Answer

712 7\frac{1}{2}

Exercise #12

63×1= \frac{6}{3}\times1=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we will solve the exercise from left to right, since there are only multiplication and division operations:

63=2 \frac{6}{3}=2

2×1=2 2\times1=2

Answer

2 2

Exercise #13

Solve:

34+2+1 3-4+2+1

Video Solution

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= (3+2+1)-4=
We first solve the addition, from left to right:
3+2=5 3+2=5

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

64=2 6-4=2

Answer

2

Exercise #14

Solve:

93+42 9-3+4-2

Video Solution

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:

93=6 9-3=6

6+4=10 6+4=10

102=8 10-2=8

Answer

8

Exercise #15

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