10 Order of Operations Practice Problems with Answers
Master PEMDAS and avoid common math mistakes with 10 step-by-step order of operations problems.
Author
Tess Loucka
Published:
May 2026
Key takeaways
- • The order of operations can be simplified to PEMDAS, with each letter representing a specific operation.
- • Multiplication and division are equally important and should be solved as they appear from left to right. The same can be said about addition and subtraction!
- • When solving numerical expressions, always start with what’s in the parentheses.
Math is made up of numerical expressions built of numbers and operations. They can be short and sweet or incredibly long and complex, but no matter their length, the rules for solving expressions are always the same. Once you know the rules, you can solve any expression—with a little practice!
Perhaps the most important of these rules is the order of operations—the particular order in which you must solve expressions. This order is always the same.
The order in which you solve the operations within an expression can be remembered as PEMDAS.
PEMDAS stands for Parentheses, Exponents, Multiplication & Division, Addition & Subtraction.
When solving numerical expressions, you must do so using the order of operations, or PEMDAS! In other words, start with P and end with S.
Keep in mind that if brackets are involved in order of operations problems, treat them like parentheses! If there are parentheses inside the brackets, start with what’s inside the parentheses first, next solve everything else inside the brackets, and then move on to what’s outside the brackets.
Common Order of Operations Mistakes
Following the order of operations is simple once you know PEMDAS, but before you use it, there are a few things to keep in mind.
- Multiplication and division should be treated as equally important.
Although M comes before D in PEMDAS, multiplication and division both have the same level of priority and can be solved as they appear from left to right.
- Addition and Subtraction should be treated as equally important.
Again, although A comes before S in PEMDAS, both operations share the same level of priority and should be solved in order from left to right.
To avoid making these common errors, think of PEMDAS as PEM/DA/S where M and D, and A and S, are interchangeable.
- Don’t simplify parentheses out of order.
When there is more than one pair of parentheses, figuring out where to start can get confusing! Before you solve, map out which pairs of parentheses take priority. Remember, solve from left to right! If there are two pairs of parentheses, the pair closest to the beginning of the expression should be solved first.
Put PEMDAS to the test with the following order of operations problems!
10 Order of Operations Practice Problems
1. 6 x 4 + 12 = ?
Answer:
6 x 4 + 12
24 + 12
36
2. 5 - 2 x 20 ÷ 10 = ?
Answer:
5 – 2 x 20 ÷ 10
5 – 40 ÷ 10
5 – 4
1
3. 37 - (9 + 3) x 8 = ?
Answer:
37 – (9 + 3) x 8
37 – 12 x 8
37 – 96
-59
4. 4 + 2² x 5 ÷ 4 - 10 = ?
Answer:
4 + 2² x 5 ÷ 4 – 10
4 + 4 x 5 ÷ 4 – 10
4 + 20 ÷ 4 – 10
4 + 5 – 10
9 – 10
-1
5. 9 + 8 x 2(12 - 3²) + 1 = ?
Answer:
9 + 8 x 2(12 – 3²) + 1
9 + 8 x 2(12 – 9) + 1
9 + 8 x 2(3) + 1
9 + 8 x 6 + 1
9 + 48 + 1
57 + 1
58
Table of contents
6. (5 + 4²) x (8 ÷ 2) + 12 = ?
Answer:
(5 + 4²) x (8 ÷ 2) + 12
(5 + 16) x (8 ÷ 2) + 12
21 x (8 ÷ 2) + 12
21 x 4 + 12
84 + 12
96
7. 95 - [14 x 2 + (5² + 2)] = ?
Answer:
95 – [14 x 2 + (5² + 2)]
95 – [14 x 2 + (25 + 2)]
95 – [14 x 2 + 27]
95 – [28 + 27]
95 – 55
40
8. (15 + 15) x 2 x [(9 - 4) + 5] = ?
Answer:
(15 + 15) x 2 x [(9 – 4) + 5]
30 x 2 x [(9 – 4) + 5]
30 x 2 x [5 + 5]
30 x 2 x 10
60 x 10
600
9. 14 + (7² - 81 ÷ 9) ÷ 10 + (3 x 2) = ?
Answer:
14 + (7² – 81 ÷ 9) ÷ 10 + (3 x 2)
14 + (49 – 81 ÷ 9) ÷ 10 + (3 x 2)
14 + (49 – 9) ÷ 10 + (3 x 2)
14 + 40 ÷ 10 + (3 x 2)
14 + 4 + (3 x 2)
14 + 4 + 6
18 + 6
24
10. 10 + 7 x 5 - (2 + 3) x [8 x 2 + (12 - 10)] = ?
Answer:
10 + 7 x 5 – (2 + 3) x [8 x 2 + (12 – 10)]
10 + 7 x 5 – 5 x [8 x 2 + (12 – 10)]
10 + 7 x 5 – 5 x [8 x 2 + 2]
10 + 7 x 5 – 5 x [16 + 2]
10 + 7 x 5 – 5 x 18
10 + 35 – 5 x 18
10 + 35 – 90
45 – 90
-45
Want more practice with order of operations problems? Work on more practice problems or play math games using online math practice programs designed to help students master key math skills, including the order of operations.
About the Author
Tess Loucka
Tess Loucka discovered her passion for writing in high school and has not stopped writing since. Combined with her love of numbers, she became a math and English tutor, focusing on middle- and high-school-level topics. Since graduating from Hunter College, her goal has been to use her writing to spread knowledge and the joy of learning to readers of all ages.
About the Author
Amber Watkins
Hello, my name is Miss Amber. I am an Education Specialist with a degree in Early Childhood Education. I have over 12 years of experience teaching and tutoring elementary through college level math. I also create both video and written math content that has helped educate thousands of students online. Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!