How To Add & Subtract Integers Easily

ElevatEd
Math
April 14, 2025

Mastering elementary mathematics starts with understanding how to add and subtract integers. A clear understanding of these rules is vital whether you are an adult refreshing your knowledge or a student working on your mathematics skills. Today we will thoroughly teach you the rules for adding and subtracting integers, including negative numbers, and offer some helpful examples to help highlight these ideas.

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What Are Integers?

Integers are whole numbers that can be zero, positive, or negative. For example, 0, -3, and 5 are all integers. These numbers are utilized in multiple mathematical operations and everyday situations. Now, that you are clear with what integers are let us quickly understand adding and subtracting integers

Rules for Adding Integers

To add integers, check if they have the same signs or different signs, as it will help to understand how tasks are carried out.

Condition	Rule
Same Sign	Add the absolute values and keep a signle sign.
Different Signs	Subtract the smaller absolute value from the biggest number one and take the sign of the larger absolute value.
Adding Positive Integers	When combining two positive whole numbers, add the values.
Adding Negative Integers	When combining two negative whole numbers, add the absolute values and give the result a negative sign.

Adding Two Positive Integers

The addition of an integer is a process of combining two or more integers to get the sum of the given numbers. This fundamental math operation has three potential cases:

When both integers are positive, you add their absolute values and ensure the signs are positive too. The rule is:

Positive + Positive = Positive

For example:

5+3=8+ 7 = 15

10+6=16 10 + 5 = 15

Adding Two Negative Integers

When both negative integers are added, add their absolute values, and keep their sum negative. Remember, when two negative numbers are added together their absolute value is zero.

Negative + Negative = Negative

For example:

−3-(-5)=−8-3 -5=-8

−10+(−2) =-12-10 + (-2) = -12

3. Including a Positive and A negative number

The outcome of combining a positive and a negative number depends on the smaller absolute value. Take the sign of the number with the larger absolute value and subtract the smaller absolute value from it. The rule is:

Positive + Negative = Difference of the absolute values with the sign of the biggest of the absolute values

For example:

7+(−5)=27 + (-5) = 2 (since 7 is larger, the result is positive)

−3 + 5 = 2 - 3 + 5 = 2 (since 5 is greater, the outcome is positive)

Rules of Subtraction of Whole Numbers

For negative values of both numbers, sum and retain the absolute values keeping the negative sign. Two negative numbers added have a total absolute value of zero.

Negative + Negative gives negative

For example:

−3-(-5) =−8-3 -5=-8

−10+(−2) =-12-10 + (-2) = -12

Including a positive and a negative number

The outcome of combining a positive and a negative number would depend on the smaller absolute value. Take the sign of the number with the larger absolute value and subtract the smaller absolute value from it. The rule is:

Positive + Negative = Difference of the absolute values with the sign of the biggest of the absolute values
Example:

7+(−5) =27 + (-5) = 2 (since 7 is larger, the result is positive)

−3 + 5 = 2 - 3 + 5 = 2 (since 5 is greater, the outcome is positive)

+3=−5−8−8+3=−5 (since -8 is larger, the result is negative)

Rules of Subtraction of Whole Numbers

Though subtracting numbers might be difficult, once you grasp the technique it becomes far simpler. The main concept is transforming an addition question into a subtraction one.

Integers Subtracting Two Positive

To subtract two positive numbers, subtract the lower number from the larger one. One should know the pattern is the difference of the numbers with the sign of the larger one positive - positive.

For instance:

8 - 3 = 58 - 3 = 5

10 - 4 = 610 - 4 = 6

2. Two negative numbers subtracted

Subtracting two negative numbers is equivalent to adding the opposite (or the additive inverse) of the second number. According to the rule:

Certainly + certain = Positive + Sure

An illustration of this would be:

−5−(−3) =−5+3=−2-5 - (-3) = -5 + 3 = -2

−7+2=−5 -7 - (-2) = −7+2=−5-7−-2 = −7+2=−5

A negative number minus a positive one

To subtract a negative integer from a negative one, change the subtraction into addition by adding the opposite of the negative number. The rule is:

Negative - Positive means Negative + Positive

Say, for instance,

-6 less -4 equals -4 plus -6 equals -10-4 - 6 = -4 + (-6) = -10

−5-8=−8+(−5) =−13 − 8 - 5 = -8 - 5 = 13

4. Subtracting from a positive integer a negative integer

If you subtract a negative number from a positive number, transform the subtraction into addition by adding the negative of the negative number. The rule runs as follows:

Positive - Negative = Positive + Positive With

By way of illustration:

6−(−2) =6+2=846 - (-2) = 6 + 2 = 8

5−(−4) equals 5+4=95 - (−4) = 5 + 4 = 9.

Children may initially find adding and subtracting integers difficult, particularly when working with negative integers, but once the principles are clear it becomes far easier. Recall the core ideas: Adding their absolute values and maintaining the sign will combine two numbers with the same sign.
Change subtraction to addition and, if needed, negate the second number to subtract integers. For subtracting negative numbers, follow the "Keep, Change, Flip" rule. Practice will let you naturally follow these guidelines and deftly handle operations on integers. Happy math problem-solving!

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