When you hear the word “subtract,” what do you think of?
Maybe taking a few toys away, spending some of your allowance, or watching points go down in a game. Subtracting usually means you’re getting less of something, right?
But what if the numbers are negative? Can you subtract something from a number that’s already less than zero?
In this guide, we’ll break down how to subtract positive and negative integers, learn some easy-to-remember rules, practice solving problems, and answer the most frequent questions our students have on the topic.
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Before we jump into subtracting positive and negative integers, let’s quickly refresh our memory on what integers are.
Integers are whole numbers. That means they don’t have any decimals or fractions. Integers include:
Positive numbers like 1, 2, 3
Negative numbers like –1, –2, –3
And zero (0)
One of the best ways to picture integers is by using a number line.
Imagine a straight line with zero in the center. The numbers increase as you move to the right; those are your positive integers, and they decrease as you move to the left; those are your negative integers.
So if you’re standing at 0 and someone asks you to move to –4, you would take four steps to the left. If they ask you to go to 5, you'd take five steps to the right of zero.
We’ve just reminded ourselves what integers are and how we can picture them on a number line. Positive numbers move us to the right, and negative numbers move us to the left.
Most students understand positive and negative numbers pretty quickly, but when we start subtracting them, especially when two negative signs show up, it can get a little confusing.
That’s why we use a few simple rules to help make sense of it all.
Think of these rules like a math toolbox. Each one gives you a strategy for figuring out what to do, whether you're subtracting a positive, subtracting a negative, or deciding which sign the answer should have.
Let’s take a closer look at each rule and see how they help us subtract integers with confidence.
One helpful way to think about subtracting integers is by using a number line.
When you subtract a positive number, you move to the left.
What if you’re subtracting a negative number?
That’s where things get interesting.
Subtracting a negative number is the same as adding a positive number.
Why?
Because taking away something negative actually increases the value.
Think of this as returning a debt.
You’ve spent all your allowance, so now you have 0 dollars. You borrow 10 dollars from your friend which means that your balance becomes -10 because you owe that much to your friend.
Say you get 5 dollars from your parents that day, and you decide to start repaying your friend. That is 5 dollars out of your pocket (so, -5) that will reduce your debt. We can write this as:
–10 – (–5) = –10 + 5 = –5
Because we are reducing debt, we are moving right on the number line towards the zero and positive balance.
A great shortcut for subtracting integers is called the “Keep, Change, Change” method.
Let’s look at an example:
–4 – 6 becomes –4 + (–6), which equals –10.
You kept –4, changed the minus to a plus, and changed positive 6 to negative 6.
Then you just add using the rules for adding integers.
Once you’ve rewritten a subtraction problem using Keep, Change, Change, you’ll often need to add integers that have different signs. That’s where comparing magnitudes helps.
The magnitude of a number is how far it is from zero, without worrying about whether it's positive or negative.
For example, the magnitude of –7 is 7. The magnitude of 2 is 2.
Now, let’s look at a problem:
–7 – (–2) = ?
Step 1: Use “Keep, Change, Change.”
Because we have two negatives together in – (–2), this becomes:
–7 – (–2) = –7 + 2 = ?
Step 2: Notice that you’re adding one negative number and one positive number. When the signs are different, you subtract the smaller magnitude from the larger one.
Here, 7 (from –7) is bigger than 2.
So 7 – 2 = 5
Step 3: Use the sign of the number with the greater magnitude.
Since –7 had the greater magnitude (7), and it was negative, the answer is –5.
Final answer: –7 – (–2)= –5
Think of it like this: If you’re $7 in debt (–7) and someone gives you $2 (+2), you’re still in debt, but only $5 now.
So –7 + 2 = –5
The idea of comparing magnitudes helps you decide whether your answer should be positive or negative, and it gives you the tools to solve more complicated problems with confidence.
What happens when we subtract zero? When you subtract zero from any number, nothing changes. That’s because you’re not taking anything away.
For example: 4 – 0 = 4
You start at 4 and don’t move at all, so you stay at 4.
What if we start with a negative number?
–4 – 0 = –4
Same idea! You’re starting at –4 and not changing your position on a number line, so the answer stays –4.
Subtracting zero always leaves the first number the same no matter if it’s positive or negative.
Let’s walk through more subtraction problems together, step by step.
These examples show different types of integer subtraction problems and how to solve each one with confidence.
8 – 5=?
You’re starting at 8 and subtracting a positive number (5), which means you're moving to the left on the number line.
Take 5 steps left from 8, and you land on 3.
Final answer: 8 – 5=3
This is a basic subtraction you’ve probably done before, but it helps remind us how movement on the number line works.
–3 – 4=?
You’re starting at –3, and you’re subtracting a positive number. That means you're moving further left on the number line, deeper into the negatives.
To make this easier, we use a handy method called Keep, Change, Change:
Keep the first number (–3),
Change the subtraction (-) sign to addition (+),
Change the sign of the second number (positive 4 becomes –4).
So, –3 – 4 becomes:
–3 + (–4)
Now we’re just adding two negative numbers.
When the signs are the same, we add the absolute values, in this case: 3 + 4 = 7
Since both numbers are negative, the result is also negative.
Final answer: –3 – 4= –7
Think of it like this: If you're already 3 steps below zero and take 4 more steps down, you're now 7 steps below. You’re just going farther into the negatives.
6 – (–2)=?
Use the “Keep, Change, Change” method:
Keep the first number (6),
Change the subtraction (-) sign to addition (+),
Change the sign of the second number (negative (-2) becomes positive 2).
6 – (–2) becomes 6 + 2
Now you’re just adding two positive numbers: 6 + 2 = 8
Final answer: 6 – (–2)=8
You can picture it like this: If you’re standing at 6 on the number line and you subtract a negative, you’re moving to the right as if someone added more. Taking away something negative increases the total!
–9 – (–3)=?
Use the “Keep, Change, Change” method:
Keep the first number (-9),
Change the subtraction (-) sign to addition (+),
Change the sign of the second number (negative (-3) becomes positive 3).
So, –9 – (–3) becomes –9 + 3
Now, you’re adding two numbers with different signs.
Next, we subtract the smaller absolute value from the larger one: 9 – 3 = 6
Use the sign of the number with the larger absolute value.
Since 9 is bigger and it came from –9, the answer is –6.
Final answer: –9 – (–3)=–6
Think of it like this: You’re 9 floors below ground level in a building (–9). If you go up 3 floors (+3), you’re still underground, but now you're only 6 floors below, so your new position is –6.
Even students who understand the rules sometimes make small mistakes when subtracting integers, and that’s okay.
At Mathnasium, we believe that recognizing and learning from those mistakes is part of the path to truly understanding math.
Let’s go over a few of the most common errors students make and how to fix them.
A lot of students think subtraction always means “take away.” That idea works well when you're dealing with small, positive numbers, but it can lead to confusion when negative numbers enter the picture.
Let’s take a look at this common example:
What is –5 – 3?
Some students might say –2, thinking, “I’m just taking 3 away from –5.” But that’s not how subtraction with negative numbers works.
Here’s where the Keep, Change, Change rule saves the day:
Keep the first number: –5
Change the subtraction sign to addition
Change the second number to its opposite: –3
Now the expression becomes:
–5 + (–3)
This is now an additional problem! So we:
Add the absolute values: 5 + 3 = 8
Keep the negative sign
Correct answer: –5 – 3 = –8
If you forget to change subtraction to addition and flip the sign of the second number, you might head in the wrong direction and get the wrong answer.
The takeaway? Remembering Keep, Change, Change helps you stay on track and builds the confidence to handle any subtraction problem—no matter how tricky it looks!
Another common mistake students make is forgetting that subtracting a negative number actually means adding.
When students see two minus signs—like in 4 – (–2), they sometimes get confused and think they should just subtract the numbers. It’s an easy mistake to make, especially when we’re used to thinking of subtraction as always making numbers smaller.
But here’s the important thing to remember: Subtracting a negative is the same as adding!
Let’s walk through it with this example:
4 – (–2)=?
A lot of students rush and say 4 – 2 = 2.
But this skips a crucial step: the Keep, Change, Change method!
Keep the first number: 4
Change the subtraction sign to addition
Change the negative number to its opposite: 2
When we use this method, 4 – (–2) becomes 4 + 2 = 6
And we get the correct answer: 4 – (–2)= 6
So next time you see a double minus, think of it like turning the problem around—subtracting a negative is really just another way of adding.
Skip that step, and you’ll head the wrong way on the number line and miss the right answer.
Ready to practice what you’ve learned? Try our quick quiz to see how well you know how to subtract positive and negative integers.
When you’re done, check your answers at the bottom of the guide.
7 - 4
- 6 - 2
3 - (-5)
-8 - (-3)
0 - 6
-2 - (-7)
9 - 12
-4 - 5
10 - (-1)
-1 - (-9)
At Mathnasium of Litchfield Park, we work with students of all skill levels to help them learn and master topics like how to subtract positive and negative integers. Here are some of the questions we often get from our students:
Subtracting a negative is like removing a debt, increasing the value. On the number line, it’s a move right.
Compare magnitudes and signs. If the first number is larger and positive, the result is positive, and vice versa.
Use "Keep, Change, Change" to turn subtraction into addition, then apply addition rules.
It shows how subtraction moves left or right, making the process easier to visualize.
Subtraction can be rewritten as addition with the opposite sign, but subtraction moves left, for positive, or right, for negative, on the number line.
Double negatives can be tricky; always rewrite -(-x) as +x to simplify, like -3 - (-4) = -3 + 4 = 1.
Yes, add the result to the number you subtracted. If you get back to the first number, your answer is correct. For example, for 5 - 3 = 2, check: 2 + 3 = 5.
Mathnasium of Litchfield Park & Goodyear is a math-only learning center for K-12 students of all skill levels.
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 subtract positive and negative integers.
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Students begin their Mathnasium journey with a diagnostic assessment that allows us to understand their unique 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 Litchfield Park & Goodyear today!
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If you’ve given our quick quiz a try, check your answers below.
7 - 4 = 3
-6 - 2 = -8
3 - (-5) = 8
-8 - (-3) = -5
0 - 6 = -6
-2 - (-7) = 5
9 - 12 = -3
-4 - 5 = -9
10 - (-1) = 11
-1 - (-9) = 8
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