What if we told you that subtracting integers is really just addition in disguise?
Sounds confusing, right?
Actually, it is a simple rule that makes integer subtraction and a portion of middle school math a lot easier.
Whether you are just starting to subtract integers, need a refresher on the topic, or are prepping for an exam, this guide is for you.
Mathnasium tutors will provide you with clear rules, helpful examples, practice exercises, and answers to your most common questions!
Integers are whole numbers that include positive numbers, negative numbers, and zero.
Students typically encounter integer subtraction in 6th or 7th grade.
To subtract integers, change the subtraction sign to addition and take the opposite of the second number: a - b = a + (-b)
On a number line, subtracting a positive moves you left; subtracting a negative moves you right.
Keep-Change-Change: keep the first number, change subtraction to addition, change the sign of the second number.
Integers are whole numbers that include:
Think of integers like temperatures. Positive numbers are warm temperatures, like 50°F or 80°F on a sunny day.
Negative numbers are freezing temperatures, like -10°C or -5°C, in the middle of winter. Zero sits right in the middle, like the freezing point of water.
We can also think of integers using money. Positive integers are like having money in your wallet or bank account ($10, $20), while negative integers are like debt or owing money (-$5, -$20). Zero means you’re even, no money, and no debt.
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To subtract integers, we need to change the subtraction operation sign to addition and take the opposite of the second number.
We can express this through a simple formula:
a - b = a + (-b)
Let's see how this works if we want to subtract -3 from 5:
5 - (-3)
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. Here's what we need to keep in mind:
Subtracting a positive number moves us left; we are decreasing in value.
Subtracting a negative number moves us right; we are increasing in value.
Let's walk through an example together: 2 - (-3).
We start at positive 2. Since we are subtracting a negative number (-3), we move right. Three steps to the right from positive 2 lands us on positive 5.
So, our answer is 2 - (-3) = 2 + 3 = 5
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Let’s go through a few solved examples together!
We’ll subtract 52 from 67:
67 - 52
We keep 67, change the subtraction to addition, and flip 52 to its opposite (-52):
67 + (-52) = 15
Ready for more challenges? Let's find the number we need to add to 120 to get 72.
120 + x = 72
To find x, we subtract 120 from 72:
x = 72 - 120
x = 72 + (-120)
x = -48
You will often find integer subtraction in word problems. Let's work through one of them together.
A scuba diver is at -20 feet below sea level. They descend another 15 feet. What is their new depth? We can express this as:
-20 - 15 = x
x = -20 + (-15)
x = -35
Our diver is now at -35 feet below sea level.
Ready to practice what we’ve covered? Try these problems on your own and 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?
You have $45 in your bank account. You write a check for $70. What is your balance after the check clears?
Here are some of the questions we often get about subtracting integers, with their answers:
With integer subtraction, we are asking, "How far apart are these numbers on the number line?" If we change subtraction to addition and use the opposite, we make the calculation easier and more consistent.
Subtracting a negative works just like reducing a debt. It increases what you have.
Say you owe a friend $5, so your balance is -5. If you return $3, you are reducing your debt by 3:
- 5 - (-3) = -5 + 3 = -2
Your balance went from -5 to -2, so subtracting a negative made your total bigger.
We still follow the same rule, only the sign of the second number changes. In other words, whenever we see two minuses one next to another, we change those to a single plus and use the positive number. For example:
-8 - (-3) = -8 + 3 = -5
In addition, if the signs are the same, you add and keep the sign. If they are different, you subtract and keep the sign of the larger absolute value.
With subtraction, you first convert to addition by taking the opposite of the second number, then follow the same addition rules.
With whole numbers, subtraction always gives you a smaller number. With integers, subtracting a negative can actually increase the value, like in 5 - (-3) = 5 + 3 = 8.
Mathnasium's specially trained tutors guide students through integer operations in a supportive, engaging environment.
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Our specially trained tutors use the Mathnasium Method™, a proprietary teaching approach that combines verbal, visual, mental, tactile, and written techniques to help students understand the math they are working with.
When students get stuck on a concept like subtracting integers, we break it down into manageable steps and teach both the how and the why behind it. Over time, students learn to do the same independently, walking out of our centers with the problem-solving skills and critical thinking tools they can use in math and beyond.
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If you worked through the practice problems, here are the answers:
-27 - (-14) = -27 + 14 = -13
48 - 73 = 48 + (-73) = -25
-95 - 38 = -95 + (-38) = -133
65 - 30 = 65 + (-30) = 35°F (The temperature at night is 35°F.)
45 - 70 = 45 + (-70) = -25 (Your balance is -25$)
How did you do?
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