Adding and subtracting integers
2026-02-28 09:48 Diff
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Last updated on December 2, 2025

Addition and subtraction of integers are operations that change the value of a number. Integers consist of whole numbers (0, 1, 2, 3, …) and negative numbers. In this topic, we are going to talk about adding and subtracting integers and the rules we need to follow.

What are Integers?

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Adding and subtracting integers involve operations that result in a positive, negative, or zero number. Integers are whole numbers, including positive numbers, negative numbers, and zero. They do not include decimals or fractions. 

  • Positive integers: 1, 2, 3, 4…
     
  • Negative integers: -1, -4, -8…
     
  • Zero: It is neither positive nor negative.

What is Adding and Subtracting Integers?

Getting the hang of adding and subtracting integers really just comes down to watching the signs. When you are subtracting and adding integers, think of it like a battle: if the signs are different, they fight (subtract), and the bigger number decides the sign of the answer. It helps to practice adding and subtracting integers consistently to get a feel for the rhythm, especially if you use the "Keep-Change-Change" trick to convert complex subtraction problems into easier addition problems.


If you're still having trouble with negative numbers, downloading some printable adding and subtracting integers worksheets can be a huge help. Seeing the patterns on paper often helps the concept stick faster than memorizing rules. Once you've worked through a few issues, the logic becomes second nature.

Examples:

  • \(3 + 4 = 7\)
     
  • \(5 + (-2) = 3\)
     
  • \(-6 - 3 = -9\)
     
  • \(7 - (-1) = 8\)

Rules for Adding and Subtracting Integers

Adding and subtracting integers follow specific rules that simplify calculations. Addition and subtraction are inverse operations. We can solve problems by using the following rules:

Integer sign Operation Integer Sign after operation is calculated (+a) - (+b) Subtract + (+a) - (-b) Add + (-a) - (+b) Add - (-a) - (-b) Subtract -

Note: Subtract absolute values. Keep the sign of the larger integer.

Examples:

  • -4 + (-6)
    • Logic: You are combining debt. You owe $4, then you borrow $6 more.
    • Action: Add the numbers (4 + 6 = 10) and keep the negative sign.
    • Answer: -10
  • -8 + 12
    • Logic: The signs are different, so they fight.
    • Action: Subtract the smaller number from the bigger number (12 - 8 = 4).
    • Sign: The 12 is positive, and it’s the bigger number, so it wins.
    • Answer: 4
  • 5 - 9
    • Logic: You have 5, but you spend 9. You are going into debt.
    • Method (Keep-Change-Change):
      • Keep 5
      • Change - to +
      • Change 9 to -9
    • New Problem: 5 + (-9)
    • Answer: -4
  • -3 - (-7)
    • Logic: Taking away debt is the same as gaining money.
    • Method (Keep-Change-Change):
      • Keep -3
      • Change - to +
      • Change -7 to positive 7
    • New Problem: -3 + 7
    • Answer: 4 (Because 7 is bigger than 3, the answer is positive).
  • 15 + (-25)
    • Logic: You have 15 Positives and 25 Negatives.
    • Action: Subtract the values (25 - 15 = 10).
    • Sign: There are way more Negatives (25) than Positives (15), so the Negatives win.
    • Answer: -10

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Addition and Subtraction of Integers on Number Line

A number line is a horizontal straight line where integers are placed in equal intervals. To add and subtract integers on a number line, we use the following steps:
 

Addition of integers on a number line
 

  • If we want to add a positive integer, we move to the right of the number line.
     
  • If we want to add a negative integer, we move to the left of the number line.

Example:

  • 4 + (-6) = -2
    • Start: At positive 4.
    • Move: The negative sign means move Left 6 spaces.
    • Land: You cross zero and land on -2.
       
  • -3 + 5 = 2
    • Start: At negative -3.
    • Move: The positive sign means move Right 5 spaces.
    • Land: You cross zero and land on positive 2.

Subtraction of integers on a number line
 

  • If we want to subtract a positive integer, we move to the left of the number line.
     
  • To subtract a negative integer, we move to the right of the number line.

Example:

  •  -2 - 3 = -5
    • Start: At negative -2.
    • Move: Subtraction moves Left 3 spaces.
    • Land: You end up deeper in the negatives at -5.
       
  • 3 - 7 = -4
    • Start: At positive 3.
    • Move: Move Left 7 spaces.
    • Land: You pass zero and land on -4.

Tips and Tricks for Mastering Addition and Subtraction of Integers

Once understanding the patterns and rules, adding and subtracting integers becomes simple and fun. Here are some quick and effective tips to help you master. 

  • Use Concrete Manipulatives (Two-Color Counters): Start with physical objects before moving to abstract numbers. Use two-color counters (e.g., red for negative, yellow for positive) to demonstrate "Zero Pairs visually." When a student physically pairs a red and yellow chip to make them "disappear" (equal zero), they grasp why -1 + 1 = 0 far better than by memorizing a rule.
     
  • Switch to Vertical Number Lines: Many students struggle with the left/right concept on a standard number line. Try using a vertical one instead (like a thermometer or a building with basements). It is often more intuitive for students to understand that adding and subtracting positive and negative integers involves going "up" (getting warmer/higher) or "down" (getting colder/lower).
     
  • Contextualize with the "Money" Analogy: Money is the ultimate equalizer for math anxiety. Frame every problem in terms of cash and debt. Explain that addition is a transaction (getting money or incurring debt) and subtraction is removing something (forgiving a debt makes you richer). This real-world grounding helps the rules for adding and subtracting integers stick because students instinctively know that eliminating debt is a positive thing.
     
  • Teach "Keep-Change-Change" for Subtraction: Subtraction is the biggest stumbling block. Teach students never to subtract integers directly. Instead, have them immediately rewrite every subtraction problem as an addition problem using Keep-Change-Change (Keep the first number, Change the sign of the second number, Change the operator from minus to plus). This unifies the process so they only need to focus on addition rules.
     
  • Encourage Self-Checking with Tech: Once students have attempted the manual math, allow them to verify their answers using an adding and subtracting integers calculator. This shouldn't replace the work, but rather act as an instant feedback loop. If the calculator gives a different sign than they did, ask them to investigate why their "battle" logic (which number was bigger?) didn't match the result.
     
  • Use Color-Coding for Signs: When writing problems on the board or paper, use distinct colors for positive and negative numbers (e.g., green for positive, red for negative). This visual distinction helps students quickly identify the "teams" in the equation. It reduces simple transcription errors and highlights the "Battle" concept of different signs fighting each other.
     
  • Create a "Rule Cheat Sheet": Have students create a small reference card that summarizes the logic (e.g., "Same Signs = Add/Keep," "Different Signs = Subtract/Winner"). Having the rules for adding and subtracting integers visible reduces cognitive load, allowing them to focus on the calculation rather than panic-searching their memory for the correct rule during a test.

Common Mistakes on Addition and Subtraction of Integers and How to Avoid Them

Addition and subtraction of integers is a basic concept in mathematics and is very important. But learners often make simple mistakes which can be easily rectified. Let us look into some common mistakes and ways to avoid them. 

Real-World Applications on Addition and Subtraction of Integers

Addition and subtraction of integers are used in many real-life situations. Here are a few real-world applications where the addition and subtraction of integers are used:

  • Banking: In bank accounts, transactions involve deposits where we add money to the account and withdrawals where money is subtracted from the account.
     
  • Temperature changes: Meteorologists track temperature changes over time, including a rise (+) in temperature and a decrease (-) in temperature.
     
  • Businesses: Businesses use integers to track profits (+) and losses (-) in financial statements. This is especially useful during accounting and budgeting.
     
  • Speed and distance: To estimate the speed of a vehicle while driving, we add or subtract integers. If you start at a speed of +60 km/hr, then slowing down by 20 means, 60 - 20 = +40km/hr. 
     
  • Game scores: While playing games or matches, the gained points of the player will be added(+), and the lost points will be subtracted (-). 

Download Worksheets

Problem 1

What is 7 + (-4)?

Okay, lets begin

3

Explanation

Start at 7 on the number line and move 4 steps left (since -4 is negative). We will land on 3.

Well explained 👍

Problem 2

Solve -6 + (-8)

Okay, lets begin

-14

Explanation

Both numbers are negative, so add their absolute values: 6 + 8 = 14
Since both numbers are negative, we keep the negative sign. Therefore, the answer is -14.

Well explained 👍

Problem 3

Calculate (-3) - 5.

Okay, lets begin

-8

Explanation

 -3 - 5 is equivalent to -3 + (-5). The result is -8.

Well explained 👍

Problem 4

Solve -10 + (-2).

Okay, lets begin

-12

Explanation

Both numbers are negative, so we will add their absolute values: 10 + 2 = 12.
We will keep the negative sign since both numbers are negative.

Well explained 👍

Problem 5

Find 5 - (-9).

Okay, lets begin

14

Explanation

Subtracting a negative number is the same as adding its positive counterpart: 5 - (-9) = 5 + 9.
Perform addition: 5 + 9 = 14.

Well explained 👍

FAQs on Addition and Subtraction of Integers

1.How can you add two positive integers?

Two positive integers can be added by just adding their values normally.

2.How can a positive integer and a negative integer be added to each other?

To add a negative integer and a positive integer, subtract the smaller absolute value from the larger value. We will keep the sign of the number that has the larger absolute value.

For example, 7 + (-3) = 4.

3.What is the rule for subtracting integers?

The rule for subtracting integers is to change the subtraction to addition and then flip the sign of the second number.

4.What happens when you subtract a positive integer?

When we subtract a positive integer, we move toward the left of the number line.

For example, 4-3 = 1. Here, we move 3 spaces to the left from 4, which is 1.

5.Does the order matter when we add integers?

No, addition follows the commutative property. This means that the order can be changed, and the result will stay the same.