What if we told you that when you subtract integers, you’re not really subtracting—you’re actually adding?
Sounds confusing, right?
But don’t worry, this is just a simple rule that makes integer subtraction easier than you think.
Whether you're just starting to subtract integers, need a refresher on the topic, or are prepping for an exam, this guide is for you.
Read on for clear rules, helpful examples, practice exercises, and answers to your most common questions!
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Before we jump into the rules and examples of subtracting integers, let’s take a moment to define integers:
Integers are whole numbers—which means they don’t have decimals or fractions. They include:
Positive numbers: 1, 2, 3, 4, 5, ..
Negative numbers: … -5, -4, -3, -2, -1
Zero 0
Think of integers like temperatures. Positive numbers are like warm temperatures, such as 50°F or 80°F on a sunny day. Negative numbers represent freezing temperatures, like -10°F or -5°F in the middle of winter. Zero is right in the middle—not hot, not cold—just like the freezing point of water.
Another way to think of them is like money: Positive integers are like having money in your wallet ($10, $20), while negative integers are like owing money or being in debt (-$5, -$20). Zero means you have no money in your wallet or debt.
Integers help us count, measure, and compare things in real life, like scores in games, bank accounts, and temperatures.
You May Also Like: Integers in Real Life
Subtracting integers may seem tricky at first, but there is a simple rule to follow:
When subtracting a number, change the subtraction sign to addition and take the opposite of the second number. In math, this looks like:
a - b = a + (-b)
Let’s see an example!
We’ll subtract -3 from 5:
5 - (-3)
To do so, we change the subtraction sign to addition and take the opposite of -3, which is 3:
5 + 3 = 8
A number line is a great visual tool for understanding integer subtraction.
It helps us see that:
Subtracting a positive number moves us left as we are decreasing in value.
Subtracting a negative number moves us right as we are increasing in value.
For example, let’s use the number line to subtract 2-(-3).
We start at positive 2.
Since we’re subtracting a negative number (-3), we’re moving right.
We move 3 steps to the right from positive 2. This lands us on positive 5.
So, with a little visual help, we’ve confirmed that 2 - (-3) = 5.
Ok, we know the rule, now let’s translate it into steps to follow and explore some examples!
The steps are simple! To subtract integers, we:
Keep the first number the same.
Change the subtraction sign to addition.
Flip the sign of the second number (take its opposite).
Use the rules for adding integers to solve.
Now let’s put these into practice:
Starting off with basic subtraction, let’s subtract 52 from 67:
67 - 52
Keep the first number the same (67), while changing the subscription sign to addition and flipping the second number to its opposite:
= 67 + (-52)
= 15
Ready for a more challenging example?
Let’s try to determine which number we need to add to 120 to get the number 72.
120 + x = 72
To find x, we’ll subtract 120 from 72:
x = 72 - 120
Applying the rules of integer subtraction, we get:
x = 72 + (-120)
x = -48
When practicing integer subtraction, you’ll encounter word problems as well, so let’s solve one!
Word problem: A scuba diver is at -20 feet below sea level. If they descend another 15 feet, what is their new depth?
Let’s express this mathematically:
-20 - 15 = x
= -20 + (-15)
= -35
After descending another 15 feet below sea level, our scuba diver’s new depth is -35 feet below sea level.
It’s time to practice what you’ve learned so far. Try out these exercises to test your skills.
When you’re all done, check your answers at the bottom of the guide.
-27 - (-14)
48 - 73
-95 - 38
In the morning, the temperature in Denver is 65°F. By nighttime, a cold front moves in, causing the temperature to drop 30°F. What is the temperature at night?
Understanding integer subtraction helps us in various real-life situations, especially avoiding mistakes when managing money or tracking temperature changes.
For example, in money and debt, if we owe $10 (represented as -10) and reduce the debt by $5 (-5), it may sound like we’re losing money, but if we apply the rule to subtracting integers:
-10 - (-5) = -10 + 5 = -5
Conclusion: Reducing our $10 debt means that we now owe less.
Similarly, in temperature changes, if it's -2°F and the temperature drops by 5°F, we calculate:
-2 - 5 = -2 + (-5) = -7
As you can see, knowing how to subtract integers gives us clarity—it helps us understand the changes, whether in our budget or temperature, even when they aren’t as intuitive as they seem.
At Mathnasium of Castle Hills, we work with students of all skill levels to help them learn and master topics like operations with integers. Here are some of the questions we often get about subtracting integers:
When we subtract, we are really asking, "How far apart are these numbers on the number line?" Changing subtraction to addition and using the opposite makes the calculation easier and more consistent.
Subtracting a negative is just like reducing a debt—it increases what you have.
Let’s see this in action:
You borrow $5 from a friend, so your balance is -5.
If you return $3 to them, you are reducing your debt by (-3).
To express this, we follow the rules of subtracting integers: -5 - (-3) = -5 + 3 = -2
Since your balance went from -5 to -2, subtracting a negative made your total bigger.
It depends on the integer we are subtracting!
Subtracting a positive integer → Move left
Subtracting a negative integer → Move right
You still follow the add the opposite rule whereby we’re only changing the sign of the second number. For example:
-8 - (-3) = -8 + 3 = -5
Adding integers: If the signs are the same, add and keep the sign. If different, subtract and keep the sign of the larger absolute value.
Subtracting integers: Convert to addition by taking the opposite of the second number, then use addition rules.
With whole numbers, subtraction always results in a smaller number. But with integers, the presence of negative numbers means that subtraction can sometimes increase the value, like in 5 - (-3) = 8.
A helpful way to remember is: "Keep-Change-Change".
Keep the first number
Change subtraction to addition
Change the second number’s sign
Mathnasium of Castle Hills is a math-only learning center for K-12 students in Carrollton, TX.
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 operations with 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 Castle Hills today!
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-27 - (-14) = -27 + (+14) = -27 + 14 = -13
48 - 73 = 48 + (-73) = -25
-95 - 38 = -95 + (-38) = -133
65 - 30 = 65 + (-30) = 35°F
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