How to Apply Integers Addition and Subtraction Rules?

Add integers with the same sign by adding their absolute values and keeping that sign. Subtraction can be rewritten as addition of the opposite.

TL;DR: Integers can feel slippery until you nail two rules. Same signs? Add their sizes and keep the sign, so negative 5 plus negative 3 is negative 8. Different signs? Subtract the smaller size from the larger and keep the sign of the bigger one, so negative 5 plus 3 is negative 2. For subtraction, flip it into adding the opposite, like 5 minus negative 3 becomes 5 plus 3 equals 8. Two rules, every integer problem solved.

Key takeaways:

Same-sign addition: add absolute values, keep the sign. \(-5+(-3)=-8\).
Different-sign addition: subtract absolute values, keep the larger sign. \(-5+3=-2\).
Subtraction = adding the opposite. \(5-(-3)=5+3=8\).
On a number line: positive moves right, negative moves left.
Two negatives make a positive only when multiplying, NOT when adding!

Using the rules of addition and subtraction, two integers can be easily added or subtracted. In this step-by-step guide, you will learn these rules.

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.

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.

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

\(\color{blue}{4}\)
\(\color{blue}{-30}\)
\(\color{blue}{1}\)
\(\color{blue}{-40}\)
\(\color{blue}{14}\)

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 (resource currently unavailable) covers integers alongside fractions, decimals, and proportional reasoning.

Frequently Asked Questions

What are the rules when adding and subtracting integers?

When adding, same signs mean you add the absolute values and keep the sign: −6 + (−4) = −10. Different signs mean you subtract the smaller absolute value from the larger and keep the sign of the larger: −9 + 4 = −5. To subtract, add the opposite: 7 − (−2) becomes 7 + 2 = 9.

What are the rules for adding integers?

There are two cases. If the signs match, add the absolute values and use the shared sign, so 12 + 15 = 27 and −12 + (−15) = −27. If the signs differ, subtract the absolute values and use the sign of the number farther from zero, so −12 + 15 = 3 and 12 + (−15) = −3. Adding 0 leaves any integer unchanged.

How do you apply integer rules to subtraction problems?

Turn every subtraction into addition of the opposite, then use the addition rules. For −8 − 5, rewrite it as −8 + (−5); the signs match, so the answer is −13. For −8 − (−5), rewrite it as −8 + 5; the signs differ, so subtract 8 − 5 = 3 and keep the negative sign of the larger number to get −3.

Is there an integer addition and subtraction rules PDF or worksheet?

Yes. Effortless Math has printable integer worksheets, and the Pre-Algebra for Beginners workbook has a full chapter on integer operations. A good rules sheet fits on one page: same signs add and keep the sign, different signs subtract and keep the larger sign, subtracting means adding the opposite, and a number plus its opposite is 0, as in 6 + (−6) = 0.

Related EffortlessMath Lessons

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

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