How to Apply Integers Addition and Subtraction Rules?

Addition and subtraction of integers are two operations we perform on integers to increase or decrease their values. Every number shown on a number line that has no fractional part is an integer.

Related Topics

• How to Add and Subtract Integers?
• How to Apply Integers Multiplication and Division Rules?

Step-by-step guide to applying integers addition and subtraction rules

Rules for subtracting integers

The rules for subtracting integers are given below:

• If we subtract \(0\) from any integer, the answer will be the integer itself.
• If we subtract any integer from \(0\), we will find the opposite of the integer.
• Subtraction of integers is done by changing the sign of the subtrahend. After this step, if both numbers are from the same symbol, we add the absolute values and attach the common symbol to it. If both numbers have different symbols, we find the difference between the absolute numbers and put the sign of the bigger number in the result.

Rules for adding integers

Certain rules must be followed to add two or more integers. Integers are complete numbers that do not have fractional parts. This includes positive, zero, and negative integers. The rules for adding integers are as follows:

• The sum of an integer and its inverse is \(0\).
• Adding two positive integers always gives in a positive value that is greater than both integers.
• Adding two negative integers always gives a negative number smaller than the given numbers.
• The addition of a positive number to a negative number is done by finding the difference between the absolute values of both numbers. Then, the sign with the greater number gets attached to the sum.
• Adding integers with \(0\) results in the same number.

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Applying Integers Addition and Subtraction Rules – Example 1:

Using the rules for the addition of integers, find which number should be subtracted from \(15\) to get \(-9\) as the answer.

Solution: 

Suppose \(x\) must be subtracted from \(15\) to \(-9\). Therefore, we can form an equation in terms of \(x\).

\(15-x= -9\)

\(-x = -9 -15\)

\(-x=-24\)

\(x = 24\)

Therefore, \(24\) has to be subtracted from \(15\) to get \(-9\).

Applying Integers Addition and Subtraction Rules – Example 2:

Subtract \(-8\) from \(-13\) using the rules of subtracting integers.

Solution: 

Here we need to subtract two integers with the same sign, \(-13\) and \(-8\).

\(-13- (-8) = -13 + 8\)

\(=-5\)

Exercises for Applying Integers Addition and Subtraction Rules

Perform the following calculations using the addition and subtraction rules.

1. \(\color{blue}{(-5)+9}\)
2. \(\color{blue}{-11-19}\)
3. \(\color{blue}{8 – 10 +(-4) + 7}\)
4. \(\color{blue}{(-16) + (-24)}\)
5. \(\color{blue}{(-3)-(-5)-(-12)}\)

1. \(\color{blue}{4}\)
2. \(\color{blue}{-30}\)
3. \(\color{blue}{1}\)
4. \(\color{blue}{-40}\)
5. \(\color{blue}{14}\)

Recommended EffortlessMath Books

For a complete workbook on integer operations and the rules behind them, the Pre-Algebra for Beginners walks through integer arithmetic with worked examples and plenty of practice. For middle-school mixed-topic practice, the Grade 7 Math for Beginners covers integers alongside fractions, decimals, and proportional reasoning.

Frequently Asked Questions

What are the rules for adding and subtracting integers?

Two main addition rules: same signs add absolute values and keep the sign; different signs subtract absolute values and keep the sign of the bigger one. For subtraction: rewrite as adding the opposite (\(a-b=a+(-b)\)), then use the addition rules. Two rules cover every case.

How do you apply integer rules step by step?

Convert any subtraction to addition of the opposite. Check the signs of the two numbers. Same signs: add absolute values, keep the shared sign. Different signs: subtract the smaller absolute value from the larger, keep the larger’s sign. Sketch a number line if you’re unsure.

What’s the easiest way to add and subtract integers?

Convert subtractions to additions first (add the opposite). Then think of it like a money problem: positives are gains, negatives are losses. \(-5+8\) is like losing 5 and gaining 8 — net gain of 3 (positive). \(-5+3\) is like losing 5 and gaining 3 — net loss of 2 (negative).

When do I use integer addition and subtraction rules?

Constantly — basically every math problem from late elementary onward. Algebra simplification, equation solving, coordinate geometry, sign analysis in calculus, anything with negative quantities (temperature, debt, elevation below sea level). These rules are the foundation for everything that comes after.

Common mistakes when adding and subtracting integers?

Forgetting that subtracting a negative is the same as adding (\(5-(-3)=5+3=8\), NOT 2). Applying same-sign rules when signs are different. Keeping the wrong sign on a different-sign result. Confusing “two negatives make a positive” — that’s a multiplication/division rule, not addition.

How does integer addition compare to subtraction?

Subtraction is just addition of the opposite. \(a-b=a+(-b)\). Once you make this conversion, you only need the addition rules. \(7-3=7+(-3)=4\). \(-5-2=-5+(-2)=-7\). \(8-(-3)=8+3=11\). Convert first, then apply the same-sign/different-sign rule.

Can I add and subtract integers without a calculator?

Absolutely — that’s the whole point of learning the rules. Mental math for integer arithmetic should become automatic with practice. The number line is a backup visualization, but the rules themselves are mental math for any problem with small numbers.

Real-world examples of integer addition and subtraction?

Bank balance after a debit: starting at \$50, withdrawing \$80, new balance is \(50-80=-30\). Temperature change: from 8°F dropping 15° gives \(8-15=-7\)°F. Football yards: lose 5, gain 8 means net \(-5+8=3\) yards gained. Stock change: down 4 points then up 6 gives net \(-4+6=2\) points up.

Worksheet for integer addition and subtraction rules?

EffortlessMath has printable worksheets at multiple difficulty levels covering pure-rule problems and word problems. The Pre-Algebra for Beginners workbook includes a full chapter on integer operations with worked examples and practice sets.

How to teach kids integer addition and subtraction rules?

Use the number line and physical motion first. “Stand on 0. Take 3 steps right (positive 3). Now take 5 steps left (subtract 5). Where are you? At -2.” Then introduce the rules as a shortcut for the number-line work. Always connect back to the physical model when a student gets confused with negatives.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to solve integer addition/subtraction word problems
• How to use input/output tables for integers
• Order of operations (PEMDAS)
• How to solve linear equations
• How to find the slope of a line