Integer Operations Practice — Add, Subtract, Multiply & Divide

Master operations with positive and negative integers using this free practice tool. Choose your difficulty, answer a steady stream of problems, and get instant feedback plus a worked solution — with the sign rules explained every time.

Embed this calculator on your site

Free to use on class pages, blogs and course pages. Copy the code below and paste it into your page:

<iframe src="https://www.effortlessmath.com/math-topics/practice-integer-operations/?em_embed=1" width="100%" height="720" style="border:0;max-width:100%" title="Integer Operations Practice — Add, Subtract, Multiply &amp; Divide by Effortless Math" loading="lazy"></iframe><p><a href="https://www.effortlessmath.com/math-topics/practice-integer-operations/">Integer Operations Practice — Add, Subtract, Multiply &amp; Divide</a> by <a href="https://www.effortlessmath.com/">Effortless Math</a></p>Copy code

How the practice works

1. Pick a difficulty — Easy stays positive, Medium and Hard add negatives.
2. Type your answer (a leading minus is fine) and press Check.
3. Read the feedback and the step-by-step solution, then press Next.

The sign rules

Adding, subtracting, multiplying and dividing signed numbers each follow clear rules. The solution panel restates the relevant rule and the arithmetic so the pattern sticks.

Integer Sign Rules at a Glance

With more than two factors, count the negatives. An even number of negatives gives a positive product, and an odd number gives a negative. For example, (−2) × (−3) × (−1) = −6, because there are three negatives.

Worked Examples and Common Slips

1. −4 − 9. Add the opposite: −4 + (−9). Same signs, so add 4 + 9 = 13 and keep the minus. Answer: −13.
2. −12 + 15. Different signs: 15 − 12 = 3. The 15 is farther from zero and positive. Answer: 3.
3. (−5) × (−3). Same signs, so the product is positive. Answer: 15.
4. −3 − (−10). Add the opposite: −3 + 10 = 7.

The most common slips are using the multiplication rule on addition (thinking −6 + (−4) is positive because it has two negatives), and forgetting to flip the sign of the second number when subtracting. If you get one wrong in the drill, read the worked solution and say the rule out loud before you try the next problem.

Frequently asked questions

What are integer operations?

Integer operations are adding, subtracting, multiplying and dividing integers, which are the positive and negative whole numbers and zero. Each operation has its own sign rule. For example, −9 + 4 = −5, −9 − 4 = −13, −9 × 4 = −36 and −36 ÷ 4 = −9. Students usually master these in grade 7 before moving on to algebra.

How do you do integer operations?

First name the operation, then apply its rule. For adding, compare the signs: same signs add and keep the sign, different signs subtract and keep the sign of the number farther from zero. For subtracting, add the opposite. For multiplying and dividing, same signs give a positive answer. So −10 + 3 = −7 and −10 − 3 = −13.

What are the rules for operations with integers?

There are four main rules. Add with same signs: add and keep the sign, so −15 + (−8) = −23. Add with different signs: subtract and keep the larger absolute value’s sign, so −15 + 8 = −7. Subtract by adding the opposite: 6 − (−11) = 17. Multiply or divide: same signs are positive, different signs negative, so (−32) ÷ 8 = −4.

How does order of operations work with integers?

Use the same order as always, parentheses, exponents, multiplication and division, then addition and subtraction, while applying the sign rules at each step. For −3 + 4 × (−2)², square first: (−2)² = 4. Then 4 × 4 = 16, and −3 + 16 = 13. Watch the parentheses: −2² means −(2²) = −4, but (−2)² = 4.

What are some integer operations practice problems?

Try a mixed set, then check: (−14) + 6 = −8, −5 − 12 = −17, 9 − (−9) = 18, (−3) × (−11) = 33 and (−56) ÷ 7 = −8. If you miss a subtraction problem, rewrite it as adding the opposite and try again. The practice tool above mixes all four operations at the Medium and Hard levels.

What is a good game for practicing integer operations?

A deck of cards makes an easy integer game. Black cards are positive and red cards are negative. Each player draws two cards and adds them, and the higher sum wins the round. A red 7 and a black 3 give −7 + 3 = −4. Change the rule to multiplying for a harder version, so a red 7 and a red 3 give 21.

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Read the full lesson: learn the method step by step.

How to use Integer Operations Practice, Add, Subtract, Multiply & Divide as real practice

Integer Operations Practice, Add, Subtract, Multiply & Divide 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

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 Integer Operations Practice, Add, Subtract, Multiply & Divide 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 Integer Operations Practice, Add, Subtract, Multiply & Divide, 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.