Adding and Subtracting Integers Calculator

Add and subtract positive and negative integers with step-by-step solutions showing sign rules and PEMDAS order.

Add and subtract integers with step-by-step solutions. Supports parentheses and shows sign rules.

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help_outlineHow to Useexpand_more

Working with Integers

This calculator handles addition and subtraction of positive and negative integers. Enter expressions like -10 - (-22) + 33 and see how each step is resolved. Parentheses are fully supported for grouping operations.

Rules for Adding Integers:

  • Same signs: Add absolute values, keep the common sign
  • Different signs: Subtract smaller from larger, keep sign of larger absolute value
  • Example: (-5) + (-8) = -13 (same signs, add, keep negative)
  • Example: 7 + (-4) = 3 (different signs, subtract, positive is larger)

Rules for Subtracting Integers:

  • Key rule: Change subtraction to addition of the opposite
  • a - b = a + (-b) and a - (-b) = a + b
  • Example: 5 - 8 = 5 + (-8) = -3
  • Example: 5 - (-8) = 5 + 8 = 13

Order of Operations (PEMDAS):

Parentheses are evaluated first, from innermost to outermost. Then addition and subtraction are performed left to right. This calculator shows each step clearly.

infoWhat is Adding and Subtracting Integers Calculator?expand_more

Integers are the set of whole numbers including all positive numbers, negative numbers, and zero. They do not include fractions or decimals. Examples include -5, -1, 0, 1, 42, and -1000.

The sign of an integer indicates whether it's positive or negative. Positive integers represent quantities above zero (gains, deposits, increases), while negative integers represent quantities below zero (losses, withdrawals, decreases).

Understanding integer arithmetic is fundamental to algebra and real-world applications like tracking temperature changes, financial transactions, elevation differences, and game scores. The number line helps visualize integers, with zero in the middle, positives extending right, and negatives extending left.

functionsFormulaexpand_more

Adding Integers:

Same signs: Add absolute values, use the common sign

(-a) + (-b) = -(a + b)

(+a) + (+b) = +(a + b)

Different signs: Subtract, use sign of number with larger absolute value

(-a) + (+b) = sign of larger × |larger - smaller|

Subtracting Integers:

Convert subtraction to addition of the opposite:

a - b = a + (-b)

a - (-b) = a + (+b) = a + b

Two negatives in a row become positive: --a = +a

Sign Combinations:

• + + = + (positive plus positive)

• - - = + (double negative becomes positive)

• + - = - (positive minus becomes negative)

• - + = - (negative sign remains)

lightbulbExamplesexpand_more

Example 1: Same Signs (Both Negative)

Calculate: (-5) + (-8)

Both numbers are negative, so add absolute values: 5 + 8 = 13

Keep the negative sign

Result = -13

Example 2: Different Signs

Calculate: 7 + (-12)

Different signs: subtract |12 - 7| = 5

-12 has larger absolute value, so result is negative

Result = -5

Example 3: Subtracting a Negative

Calculate: -10 - (-22)

Convert: -10 - (-22) = -10 + 22

Different signs: |22 - 10| = 12, positive is larger

Result = 12

Example 4: With Parentheses

Calculate: -10 - (-22 + 33)

First solve parentheses: -22 + 33 = 11

Then: -10 - 11 = -10 + (-11) = -21

Result = -21

quizFAQexpand_more
Why does subtracting a negative give a positive result?expand_more
Subtracting a negative is equivalent to adding its positive counterpart. Think of it as 'removing a debt' - if you take away $10 of debt, you effectively gain $10. Mathematically: a - (-b) = a + b. For example, 5 - (-3) = 5 + 3 = 8.
How do I remember the rules for adding integers with different signs?expand_more
Use this approach: (1) Find the difference of the absolute values, (2) Take the sign of the number with the larger absolute value. For 7 + (-12): difference is |12-7| = 5, and -12 has the larger absolute value, so the answer is -5.
What's the difference between -(-5) and -(5)?expand_more
-(-5) means 'the opposite of negative 5' which equals +5 (double negative). -(5) means 'the opposite of positive 5' which equals -5. The double negative rule only applies when you have two negative signs together.
How do parentheses affect integer calculations?expand_more
Parentheses group operations that must be calculated first (PEMDAS order). In -10 - (5 - 12), first calculate inside: 5 - 12 = -7, then: -10 - (-7) = -10 + 7 = -3. Without parentheses, -10 - 5 - 12 = -27.
What is the absolute value and why is it important?expand_more
Absolute value (|n|) is the distance from zero, always positive. |-7| = 7 and |7| = 7. It's essential for integer operations because the rules involve comparing and using absolute values to determine results.