Adding Subtracting Integers Calculator - Mathematical Calculations & Solutions

Adding & Subtracting Integers Calculator

Step-by-Step Solution:

Please enter valid integers.

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How It Works

1

Enter Integers

Input any positive or negative whole numbers (e.g., -5, 0, 7)

2

Choose Operation

Select addition (+) or subtraction (-) operation

3

Apply Rules

Calculator applies integer arithmetic rules automatically

4

Get Result

View step-by-step solution with detailed explanation

Common Examples

5 + 3 = 8
Both positive integers
Add normally and result is positive
-4 + (-6) = -10
Both negative integers
Add absolute values, keep negative sign
7 + (-3) = 4
Different signs
Subtract smaller from larger, keep larger's sign
8 - 5 = 3
Positive subtraction
Standard subtraction with positive result
3 - 7 = -4
Negative result
Subtracting larger from smaller gives negative
-2 - 5 = -7
Subtracting from negative
Same as -2 + (-5) = -7
Integer Rules: a ± b
Subtraction = Addition of opposite
Same signs: add and keep sign | Different signs: subtract and keep larger's sign

Adding & Subtracting Integers Calculator

±

What

Perform addition and subtraction operations with positive and negative integers.

🎯

Why

Foundation for algebra, number theory, and understanding positive/negative number relationships.

Applications

Temperature changes, financial calculations, elevation differences, and basic algebra.

📊 Integer Rules

Same Signs (Addition)
Rule:Add and keep sign
Example:5 + 3 = 8
(-4) + (-6) = -10
Different Signs
Rule:Subtract, keep larger's sign
Example:7 + (-3) = 4
(-5) + 8 = 3
Subtraction
Rule:Add the opposite
Example:8 - 5 = 8 + (-5)
3 - 7 = 3 + (-7) = -4

Integer Operations Reference Table

Operation TypeRuleExampleResult
Positive + PositiveAdd normally8 + 513
Negative + NegativeAdd absolute values, keep negative(-6) + (-4)-10
Positive + NegativeSubtract smaller from larger9 + (-4)5
Negative + PositiveSubtract smaller from larger(-7) + 3-4
Positive - PositiveSubtract normally10 - 37
Positive - NegativeAdd the opposite6 - (-2)8
Negative - PositiveAdd negative values(-5) - 3-8
Negative - NegativeAdd the opposite(-4) - (-7)3

Frequently Asked Questions

1

What are the fundamental rules for adding integers?

When adding integers with the same sign, add their absolute values and keep the common sign. When adding integers with different signs, subtract the smaller absolute value from the larger and use the sign of the number with the larger absolute value.

2

How do I subtract integers correctly?

Subtraction of integers follows the rule: a - b = a + (-b). This means subtracting a number is the same as adding its opposite. For example, 5 - 3 = 5 + (-3) = 2, and 5 - (-3) = 5 + 3 = 8.

3

What happens when adding positive and negative integers?

When adding a positive and negative integer, find the difference between their absolute values. The result takes the sign of the integer with the larger absolute value. For example: 7 + (-3) = 4 (positive), and (-7) + 3 = -4 (negative).

4

Can integer operations result in zero?

Yes! Zero results occur when: (1) adding opposites like 5 + (-5) = 0, (2) subtracting a number from itself like 7 - 7 = 0, or (3) when the absolute values are equal in addition with different signs.

5

What are practical applications of integer operations?

Integer operations are used in: temperature calculations (above/below freezing), financial transactions (credits/debits), elevation changes (above/below sea level), sports scoring, inventory management, and any scenario involving gains and losses or opposing directions.

6

How do I remember the rules for integer operations?

Use these memory aids: "Same signs, add and keep" for addition with same signs. "Different signs, subtract and keep the larger's sign" for mixed signs. "Subtraction means add the opposite" for all subtraction problems. Practice with a number line visualization.

Quick Reference

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