Positive Integers
Positive integers are greater than zero. Examples include 1, 4, 12, and 105.
Free Math Guide
Adding Integers Explained
Learn how to add positive and negative integers using simple sign rules, number-line reasoning, and guided practice.
Integers include positive whole numbers, negative whole numbers, and zero. Adding integers becomes much easier once you determine whether the numbers have the same sign or different signs.
What Are Integers?
Integers are positive whole numbers, negative whole numbers, and zero. They do not include fractions or decimals.
Negative Integers
Negative integers are less than zero. Examples include −1, −4, −12, and −105.
Zero
Zero is an integer, but it is neither positive nor negative.
Opposite Integers
Numbers such as 5 and −5 are opposites because they are the same distance from zero.
What Do Positive and Negative Mean?
Positive and negative numbers can represent movement in opposite directions or quantities with opposite meanings.
Temperature
A temperature of 8° is above zero, while −8° is below zero.
Elevation
Positive elevation is above sea level, while negative elevation is below sea level.
Money
A positive amount can represent money you have, while a negative amount can represent money owed.
Movement
Positive movement may represent moving right or forward, while negative movement represents moving left or backward.
How to Add Integers
Before adding, look at the signs of the two integers. The signs tell you which rule to use.
Same Signs
Add the absolute values and keep the common sign.
Different Signs
Subtract the smaller absolute value from the larger absolute value.
Choose the Sign
When the signs are different, use the sign of the number with the larger absolute value.
Opposites Make Zero
A number plus its opposite always equals zero.
Positive + Positive
Add the numbers and keep the answer positive.
Negative + Negative
Add the absolute values and keep the answer negative.
Positive + Negative
Subtract the absolute values and use the sign
of the number farther from zero.
Adding Integers With the Same Sign
When both integers have the same sign, add their absolute values and keep that sign.
Two Positive Integers
6 + 9 = 15
- Both numbers are positive.
- Add 6 and 9.
- The answer stays positive.
Two Negative Integers
−6 + (−9) = −15
- Both numbers are negative.
- Add the absolute values: 6 + 9 = 15.
- Keep the negative sign.
Same-Sign Shortcut
If the signs match, add and keep the sign.
Adding Integers With Different Signs
When one integer is positive and the other is negative, subtract their absolute values. Then use the sign of the number with the larger absolute value.
Positive Has the Larger Absolute Value
12 + (−5) = 7
- The signs are different.
- Subtract: 12 − 5 = 7.
- 12 has the larger absolute value.
- The answer is positive.
Negative Has the Larger Absolute Value
5 + (−12) = −7
- The signs are different.
- Subtract: 12 − 5 = 7.
- −12 has the larger absolute value.
- The answer is negative.
Different-Sign Shortcut
If the signs are different, subtract and keep the sign of the number farther from zero.
Adding Opposite Integers
Opposite integers have the same absolute value but different signs. They cancel each other out.
8 + (−8) = 0
Opposites Always Add to Zero
For any integer a, a + (−a) = 0.
Adding Integers on a Number Line
A number line can help you visualize integer addition. Begin at the first integer, then move according to the sign of the second integer.
−5
−4
−3
−2
−1
0
1
2
3
4
5
Adding a Positive Integer
Move to the right on the number line.
Adding a Negative Integer
Move to the left on the number line.
Move Right
−2 + 5 = 3
Start at −2 and move 5 spaces to the right. You land on 3.
Move Left
3 + (−7) = −4
Start at 3 and move 7 spaces to the left. You land on −4.
How to Check an Integer Addition Answer
Ask whether the sign and size of your answer make sense based on the original numbers.
Check the Signs
Same signs should produce an answer with that same sign.
Compare Absolute Values
With different signs, the answer should have the sign of the number with the larger absolute value.
Estimate the Size
When signs differ, the answer's absolute value should be smaller than the larger original absolute value.
Use a Number Line
Visualize the movement to verify the direction and final location.
Common Integer Addition Mistakes
Adding Every Pair of Numbers
You only add the absolute values when the integers have the same sign. With different signs, subtract the absolute values.
Ignoring the Negative Sign
A negative sign changes both the value of the integer and the rule you may need to use.
Choosing the Sign of the First Number
When signs differ, the answer takes the sign of the integer with the larger absolute value, not automatically the first integer.
Thinking Two Negatives Make a Positive
That rule applies when multiplying or dividing. When adding two negative integers, the answer remains negative.
Confusing Addition With Subtraction
In an expression such as 7 + (−4), the operation is still addition. The second integer happens to be negative.
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