How to Add Positive and Negative Integers: A Complete Guide

You and your sister are playing your favorite game. You earn 6 points in one round but lose 4 in the next. Your sister, on the other hand, loses 3 points and then gains 5. Who’s ahead?

To figure that out, you’ll need to add positive and negative numbers, also known as integers. 

In this kid-friendly guide, you’ll learn how to add positive and negative integers using clear steps, avoid common mistakes, practice examples, and read through helpful FAQs along the way. 

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A Quick Refresher: What Are Integers?

Before we explore how to add positive and negative integers, let’s refresh our memory about what integers are. 

Integers are whole numbers that can be:

• Positive (like +1, +5, or +23)

• Negative (like –2, –10, or –87)

• Or zero, which is neutral, not positive or negative

Integers are always whole numbers, which means they don’t include decimals or fractions. They can be positive, negative, or zero, but they’re always complete amounts you can count with, not parts of a number.

To help us visualize integers, we use number lines like this one:

As you can see:

• Zero is right in the middle.

• Numbers get more positive as you move to the right.

• Numbers get more negative as you move to the left.

When we add integers, we imagine ourselves moving along this number line, left or right, depending on the number’s sign.

You May Also Like: Subtracting Positive & Negative Integers

Rules for Adding Integers

Adding integers gets much simpler once you understand a few consistent rules. These rules help you determine what to do based on the signs of the numbers involved. Let’s explore each one and see how they work in real-life examples.

Rule 1: Adding Integers with the Same Sign

When both integers have the same sign, either both positive or both negative, you simply add their absolute values. The sum keeps the shared sign.

For example, if both numbers are positive:

(+4) + (+3) = +7

And when both numbers are negative, you're combining amounts that are already below zero. It’s like walking backward twice—you just end up farther back.

Here’s how it looks on a number line:

Imagine you’re standing at 0.

• You take 5 steps backward, you arrive at –5.

• Then 2 more steps backward and now you’re at –7.

So: (–5) + (–2) = –7

Mathnasium Tip: Think of it like moving in the same direction on the number line. When both numbers point left, the total movement points left, too, and the result stays negative.

Rule 2: Adding Integers with Different Signs

When the integers have different signs—one positive, one negative—you’re actually finding the difference between them. This is where absolute value comes in handy.

The absolute value tells us how far a number is from zero, no matter its sign. Here's the process:

1. Find the absolute values of both numbers.

2. Subtract the smaller absolute value from the larger one.

3. Keep the sign of the number with the greater absolute value.

Let’s walk through an example:

Problem: (+4) + (–2)

• The absolute value of +4 is 4

• The absolute value of –2 is 2

• 4 – 2 = 2

• The larger absolute value was from the positive number, so the answer is +2

Final Answer: (+4) + (–2) = +2

Mathnasium Tip: Picture this on a number line. Start at +4, then move 2 steps to the left (–2). You land on +2. It’s a tug-of-war between two directions, and the stronger pull wins.

Rule 3: Adding Zero

Zero is a special case in math. It's called the identity element for addition because it doesn’t change the other number’s value. When you add zero to any integer, the result stays the same.

–4 + 0 = –4

This is like standing still on a number line: you’re not moving forward or backward.

Adding Positive and Negative Integers Step-by-Step

Now that you know the rules, let’s apply them step-by-step to a typical integer addition problem. This walkthrough will help you understand not just how to solve it, but why each step works.

Problem: (–5) + (+3)

Step 1: Identify the Signs

First, look at the signs of each number. In this case, one number is negative (–5), and the other is positive (+3).

That tells us we’re dealing with integers with different signs.

Step 2: Use Absolute Values

Next, find the absolute value of each number. Remember, absolute value is the distance from zero, so it’s always positive.

• |–5| = 5

• |+3| = 3

Now, you’ll compare these values to figure out the result.

Step 3: Subtract the Absolute Values

Since the signs are different, subtract the smaller absolute value from the larger one:

5 – 3 = 2

We’re almost there! Just one more thing to determine:

Step 4: Decide the Final Sign

Look at the number with the greater absolute value. In this case, it's 5, which came from –5. So, the result takes a negative sign.

Final Answer: (–5) + (+3) = –2

Why This Works

Think about standing at –5 on a number line. If you move 3 steps to the right, you’re heading toward zero. You’ll land on –2. That’s why subtracting the values and using the stronger sign gets you to the right place.

Mathnasium Tip: Use the number line to visualize which way you’re moving and how far. It helps make sense of what’s happening when you add integers with different signs.

Common Mistakes to Avoid

Adding positive and negative integers can seem simple once you understand the rules, but small errors can lead to big confusion, especially if you're rushing or you’re unsure about what each number means. 

Here are some of the most common mistakes students make, along with tips to help you avoid them.

Mistake 1: Confusing Positive and Negative Signs

This might sound obvious, but it’s one of the easiest ways to make a mistake, especially when you're working quickly. 

Students often misread –4 as +4, or assume a number is positive because there’s no sign written in front of it. That tiny detail, the minus sign, completely changes the value and direction of the number.

If you misread –4 as +4, and then try to add it to another number, your answer will be off by 8 points on the number line. That’s a big deal!

Mathnasium Tip: Always pause to read each number carefully. If a number doesn't have a sign in front of it, assume it's positive. Mark negative signs clearly when writing out problems so you don’t lose track of them.

Mistake 2: Forgetting How Absolute Value Works

When adding integers with different signs, you need to subtract the smaller absolute value from the larger one. 

But many students mix up which number has the greater absolute value or forget to apply the correct sign to the final answer.

Example of a mix-up:

If you're solving (–8) + (+5), you should subtract 5 from 8 to get 3, and since 8 is larger and negative, the answer is –3.

But if you subtract the wrong way (like 8 – 5 = 3, then accidentally say it’s +3), you’ve got the right number but the wrong sign.

Mathnasium Tip: Focus on the absolute value - how far each number is from zero. Ignore the signs just for the subtraction, then bring the sign back by looking at which number had the greater absolute value.

Mistake 3: Skipping Visual Tools Like Number Lines

Students stop using number lines too soon, thinking they’ve outgrown them. 

But number lines are powerful tools even for older students! A number line turns invisible math into something you can visualize. They help you see what’s happening when you move forward (add positive) or backward (add negative).

If you’re solving (–3) + (+5), you can start at –3 and move 5 steps right. You’ll land at +2, which helps confirm your answer is correct.

Mathnasium Tip: Draw a quick number line when you’re unsure, especially if the signs are different or you’re working with larger numbers. Visual confirmation can catch mistakes early.

Flash Quiz! Let’s See What You’ve Learned

Ready to practice what you’ve learned? Try our quick quiz to see how well you know how to add positive and negative integers.

When you’re done, check your answers at the bottom of the guide.

1. (+2) + (+6) = ?

2. (–7) + (+5) = ?

3. (–3) + (–4) = ?

4. (+9) + (–3) = ?

5. (–6) + (–2) = ?

6. (–10) + (+4) = ?

7. True or False: Two negative numbers always give a negative sum.

8. You owe $7 and earn $10. What’s your balance?

FAQs About How to Add Positive and Negative Integers

At Mathnasium of Hyde Park, we work with students of all skill levels to help them learn and master topics like how to add positive and negative integers. Here are some of the questions we often get from our students:

1. Do I always need to use a number line?

Not always, but it’s a great tool, especially when you're still learning. 

A number line helps you see what’s happening and makes it easier to understand how adding positive and negative numbers moves you left or right from zero. 

2. Can the answer ever be zero when adding two integers?

Yes! If the numbers are the same but have opposite signs, they cancel each other out.

Example: (+4) + (–4) = 0.

You’re moving forward and backward the same number of steps, so you end up right back at zero.

3. Is adding integers the same as subtracting them?

Not exactly, but they’re closely related. When you add a negative number, it’s like subtracting a positive one. 

For example, (+6) + (–2) is the same as 6 – 2. But when in doubt, stick to the addition rules you've learned and check with a number line.

4. Why do I need to learn this?

Adding positive and negative numbers comes up all the time in games, temperatures, money, and science. Once you understand how integers work, you’ll be ready for algebra and even more advanced math.

Master Adding Positive and Negative Integers at Mathnasium of Hyde Park

Mathnasium of Hyde Park is a math-only learning center for K-12 students in Cincinnati, OH.

Using a proprietary teaching approach called the Mathnasium Method™, our specially trained math tutors offer face-to-face instruction in an engaging and supportive group environment to help students master any math class and topic, including how to add positive and negative integers. 

Students start their Mathnasium journey with a diagnostic assessment that allows us to understand their specific strengths and knowledge gaps. Guided by assessment-based insights, we create personalized learning plans that will put them on the best path toward math mastery. 

Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment and enroll at Mathnasium of Hyde Park today! 

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Psst! Check Your Answers Here

If you’ve given our quick quiz a try, check your answers below.

1. +8

2. –2

3. –7

4. +6

5. –8

6. –6

7. True

8. +3