## Introduction to adding and subtracting integers

Adding and subtracting integers involve performing mathematical operations with positive and negative whole numbers (integers).

## Table of Contents

Here’s how you can add and subtract integers:

**Adding Integers:**

**Same Sign:**When you’re adding integers with the same sign (both positive or both negative), you can simply add their absolute values (ignoring the signs) and then keep the common sign.- Example 1: (+3) + (+5) = +8
- Example 2: (-2) + (-7) = -9

**Different Signs:**When you’re adding integers with different signs (one positive and one negative), subtract the absolute value of the smaller number from the absolute value of the larger number and use the sign of the number with the larger absolute value.- Example 3: (+4) + (-2) = +2
- Example 4: (-8) + (+6) = -2

**Subtracting Integers:**

Subtracting integers is similar to adding them, but it involves the concept of adding the additive inverse (opposite) of the number you’re subtracting.

**Subtracting a Positive Integer:**Subtract the integer as you normally would.- Example 5: (+7) – 3 = +4

**Subtracting a Negative Integer:**This is equivalent to adding the positive version of that integer.- Example 6: (+5) – (-2) = +7

**Subtracting Integers with Different Signs:**Change the subtraction into addition by changing the sign of the number you’re subtracting, and then follow the rules for adding integers.- Example 7: (-6) – (+3) is equivalent to (-6) + (-3) = -9

Remember that you can also visualize these operations on a number line, where moving to the right is positive, and moving to the left is negative. Adding means moving to the right, and subtracting means moving to the left on the number line. Adding and subtracting integers are used in various aspects of mathematics.

## Adding and subtracting integers Rules

### Adding integers rules

Adding integers involves performing mathematical operations to combine positive and negative whole numbers (integers). Here’s how you can add integers:

**Add Integers with the Same Sign:**When you are adding integers with the same sign (both positive or both negative), you can simply add their absolute values (ignoring the signs) and then keep the common sign.- Example 1: (+3) + (+5) = +8
- Example 2: (-2) + (-7) = -9

**Add Integers with Different Signs:**When you are adding integers with different signs (one positive and one negative), subtract the absolute value of the smaller number from the absolute value of the larger number. The result takes the sign of the number with the larger absolute value.- Example 3: (+4) + (-2) = +2
- Example 4: (-8) + (+6) = -2

**Zero Identity:**Adding zero to any integer doesn’t change the value of that integer.- Example 5: (+7) + 0 = +7
- Example 6: (-3) + 0 = -3

Visualizing these operations on a number line can also be helpful. Moving to the right on the number line represents positive numbers, and moving to the left represents negative numbers. Adding integers means moving either to the right or left on the number line, depending on the signs of the integers you are adding.

### Subtracting integers rules

Subtracting integers involves performing mathematical operations to find the difference between two positive or negative whole numbers (integers). Here’s how you can subtract integers:

**Subtracting a Positive Integer:**When you are subtracting a positive integer from another integer, you can subtract as you normally would in arithmetic.- Example 1: (+7) – 3 = +4
- Example 2: (-10) – 2 = -12

**Subtracting a Negative Integer:**When you are subtracting a negative integer, it’s equivalent to adding the positive version of that integer.- Example 3: (+5) – (-2) = +7
- Example 4: (-8) – (-3) = -5

**Subtracting Integers with Different Signs:**To subtract integers with different signs, you can change the subtraction into addition by changing the sign of the number you’re subtracting (the second number), and then follow the rules for adding integers.- Example 5: (-6) – (+3) is equivalent to (-6) + (-3) = -9
- Example 6: (+4) – (-5) is equivalent to (+4) + (+5) = +9

Remember that you can also visualize these operations on a number line. Moving to the right represents positive numbers, and moving to the left represents negative numbers. Subtracting integers means moving to the left on the number line when subtracting a positive value and moving to the right when subtracting a negative value.

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