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Adding and Subtracting Integers Calculator
To use this tool, enter the integers equation, and click calculate
Addition and Subtraction of Integers
Solve the integer functions containing addition and subtraction with the correct order of operations. This calculator also provides the steps.
What are integers?
Integers are a set of numbers that include all whole numbers, both positive and negative, and zero. Mathematically, the set of integers is represented by the symbol Z. It originates from the German
language.
The set of integers can be represented as:
Z = {…,−3,−2,−1,0,1,2,3,…}
To break it down:
Positive Integers: 1,2,3,…
Negative Integers: −1,−2,−3,…
Zero: 0
Integers do not include fractions, decimals, or numbers with imaginary parts.
Addition and subtraction of integers:
The addition and subtraction of integers follow a set of rules based on the signs of the numbers involved.
Addition:
- If both integers have the same sign, add their absolute values and give the sum the common sign.
Example: −3 + (−5) =−8
and 3 + 5 = 8
.
- If the integers have opposite signs, subtract the smaller absolute value from the larger absolute value. Add the sign of the integer which was originally larger to the result.
Example: −3 + 5 = 2
and 3 + (−5) = −2
.
Subtraction:
- To subtract an integer, you can add its opposite.
Example: 5 − 3 = 5 + (−3) = 2
and −5 − (−3) = −5 + 3 = −2
.
- Then, you can follow the rules of addition.
You can think of subtraction as "adding the opposite
," where the "opposite" of a number is its negation (i.e., the same number with the opposite sign). So when you subtract a number, you are essentially adding its opposite.
Example Table:
Operation | Example | Result |
Positive + Positive | 3+4 | 7 |
Negative + Negative | (−3)+(−4) | (−7) |
Positive + Negative | 3+(−4) | (−1) |
Negative + Positive | (−3)+4 | 1 |
Positive - Positive | 3−4 | (−1) |
Negative - Negative | (−3)−(−4) | 1 |
Positive - Negative | 3−(−4) | 7 |
Negative - Positive | (−3)−4 | (−7) |