Order of Operations Practice — Free Interactive Drills
Sharpen your order of operations (PEMDAS) with this free practice tool. It serves up an endless stream of problems at your chosen difficulty, checks your answer instantly, and shows the full step-by-step solution — track your streak and aim to get 10 in a row to master the skill.
Quick answer: Order of operations practice means solving expressions in this order: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right (PEMDAS). For example, 3 + 4 × 2² = 3 + 4 × 4 = 3 + 16 = 19. Use the drills below to check each answer and see every step.
How the practice works
- Pick a difficulty — Easy, Medium or Hard.
- Solve the expression and press Check.
- See instant feedback and a step-by-step solution, then press Next for a fresh problem.
Why practice this way
Short, repeated practice with immediate feedback is how skills stick. Your streak and best score are saved on your device, so every visit picks up where you left off. For a change of pace, Equation Guess is a free daily math Wordle that uses the same order-of-operations rules: every guess must be a true equation.
Worked example: one problem, step by step
Evaluate 18 − 2 × (3 + 1)² ÷ 4.
- Parentheses: 3 + 1 = 4, so the expression becomes 18 − 2 × 4² ÷ 4.
- Exponents: 4² = 16, so it becomes 18 − 2 × 16 ÷ 4.
- Multiply and divide, left to right: 2 × 16 = 32, then 32 ÷ 4 = 8. Now it is 18 − 8.
- Add and subtract, left to right: 18 − 8 = 10.
The answer is 10. Writing each step on its own line, as above, makes it easy to spot where a mistake slipped in.
Common order of operations mistakes
- Multiplying before dividing every time. In 8 ÷ 2 × 4, work left to right: 8 ÷ 2 = 4, then 4 × 4 = 16. The answer is not 1.
- Adding before subtracting every time. In 10 − 4 + 3, work left to right: 10 − 4 = 6, then 6 + 3 = 9. The answer is not 3.
- Forgetting the exponent applies first. In 2 × 3², square first: 3² = 9, then 2 × 9 = 18. The answer is not 36.
- Mixing up negatives and exponents. −3² means −(3²) = −9, while (−3)² = 9.
- Skipping work inside parentheses. In 5 × (6 − 2), do 6 − 2 = 4 first, then 5 × 4 = 20.
Frequently asked questions
How do you do order of operations?
Work in this order: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right. For 20 − 3 × (6 − 2), do the parentheses first to get 20 − 3 × 4. Multiply next: 3 × 4 = 12. Then subtract: 20 − 12 = 8. Writing each step on a new line helps you keep track.
Does order of operations go left to right?
Partly. Multiplication and division share one level, and so do addition and subtraction. Within each level you work from left to right. So 24 ÷ 4 × 3 = 6 × 3 = 18, not 2, and 15 − 6 + 2 = 9 + 2 = 11, not 7. Parentheses and exponents still come before both levels.
Why is the order of operations important when solving math problems?
It gives everyone the same answer for the same expression. Without one rule, 5 + 3 × 2 could be read as 16 or as 11. With the order of operations, multiplication comes first, so the answer is always 11. The same rules are built into spreadsheets, calculators and programming languages, so they matter well beyond math class.
Can calculators do order of operations?
Scientific and graphing calculators follow the order of operations when you type the whole expression. Many basic four-function calculators do not; they work out each step as you press it. Type 2 + 3 × 4 on a scientific calculator and you get 14, but a basic calculator may show 20. When in doubt, add parentheses or work in steps.
How do you learn order of operations?
Build up in layers. Start with expressions that mix just two operations, like 8 + 6 ÷ 2 = 11, then add parentheses, and finally exponents. Say the step out loud before you calculate it, and check each answer right away. The drill above gives instant feedback and a full solution, so aim for 10 correct in a row before moving up a level.
What are some order of operations practice problems with answers?
Try these, then check: 6 + 18 ÷ 3² = 6 + 18 ÷ 9 = 6 + 2 = 8. Next, (7 − 2)² × 2 = 25 × 2 = 50. Last, 40 ÷ (5 + 3) − 1 = 40 ÷ 8 − 1 = 4. If an answer was off, find the first step where your work differs from the one shown.
Read the full lesson: learn the method step by step.
How to use Order of Operations Practice, Free Interactive Drills as real practice
Order of Operations Practice, Free Interactive Drills works best when it is used as a short, focused study session rather than a quick click-through activity. The goal is not simply to finish the problems. The goal is to notice which skills feel automatic, which skills still need review, and which mistakes happen when you rush.
Start with a clean piece of scratch paper. For each item, solve each item on paper first, then use the page to check your answer and study the explanation. If you get something wrong, do not immediately move on. Write the correct step, circle the part that caused the mistake, and try one similar item before continuing. That small correction habit is what turns an online practice activity into lasting math improvement.
A three-round study routine
| Round | What to do | Goal |
|---|---|---|
| Round 1 | Work slowly and focus on accuracy. Use notes if the topic is still new. | Understand the method. |
| Round 2 | Repeat missed items or similar problems without looking at the previous answer. | Fix the mistake. |
| Round 3 | Try a short timed set after the skill feels familiar. | Build speed and confidence. |
This routine is simple, but it solves a common problem: students often practice only until an answer looks familiar. Real readiness means you can solve a fresh problem without hints, explain the first step, and check whether the final answer is reasonable.
What to write down while you practice
Keep a tiny mistake log next to the activity. You only need three columns: the topic, the mistake, and the correction. For example, a student might write “fractions,” “forgot common denominator,” and “rewrite both fractions before adding.” A log like that is more useful than a long list of scores because it tells you exactly what to review next.
- If the mistake is a fact or formula, review it before the next round.
- If the mistake is a setup error, copy one worked example and label each step.
- If the mistake is from rushing, slow down and require written work for the next five items.
- If the same mistake appears twice, stop and review that topic before continuing.
When you are ready to move on
You are ready for the next topic when you can get several items correct in a row and explain why the method works. A score by itself is helpful, but it is not the whole story. You should also be able to describe the rule, formula, or pattern that the activity is testing.
For test preparation, come back to Order of Operations Practice, Free Interactive Drills after a day or two and try a fresh round. If the skill still feels easy after a short break, it is much more likely to stay with you during a quiz, unit test, or standardized test. If it feels shaky, that is useful information too: it tells you exactly where to spend your next study session.
Study tips for parents and teachers
When using this page with a student, ask for the reasoning before the answer. Questions such as “What is the first step?”, “Why did you choose that operation?”, and “How can you check it?” help students build mathematical language. That matters because many test questions measure more than calculation; they also measure whether the student can read the problem, choose a method, and explain a result.
Short sessions are usually best. Ten to fifteen minutes of careful practice can be more productive than a long session full of guessing. End by naming one skill that improved and one skill to review next time. That keeps practice positive, specific, and easy to continue.
Your next practice step
After finishing Order of Operations Practice, Free Interactive Drills, choose one next step instead of trying to study everything at once. If the activity felt easy, increase the challenge by working faster, mixing in older topics, or explaining each answer without notes. If it felt difficult, lower the pressure: redo a smaller set, copy one correct example, and focus on accuracy before speed.
A useful rule is to review the same skill three times: once today, once tomorrow, and once later in the week. Spaced review is especially helpful for math because it tells you whether the method truly stuck or only felt familiar right after practice. Use this practice activity as one stop in that review cycle, then return to it when you want to check retention.
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