# Adding and Subtracting Integers Calculator

The Adding and Subtracting Integers Calculator is an online tool that helps users perform arithmetic operations on integers. It is a simple and easy-to-use calculator that can add and subtract positive and negative integers, whole numbers, or decimal numbers. The calculator shows the work for the math and shows you when to change the sign for subtracting negative numbers.

## Concepts

### Integers

Integers are whole numbers that can be positive, negative, or zero. They are represented on a number line, which is a horizontal line that extends infinitely in both directions. Positive integers are located to the right of zero, while negative integers are located to the left of zero.

When adding integers with the same sign, we add their absolute values and keep the sign. For example, 3 + 5 = 8 and -3 + (-5) = -8. When adding integers with different signs, we subtract their absolute values and keep the sign of the larger number. For example, 3 + (-5) = -2.

### Subtraction of Integers

Subtracting an integer is the same as adding its opposite. For example, 3 – 5 is the same as 3 + (-5). When subtracting integers with different signs, we add their absolute values and keep the sign of the larger number. For example, -3 – 5 = -8.

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## Formulae

The formula for adding two integers with different signs is:

``````a + b = a - |b| if a * b < 0
``````

The formula for subtracting two integers with different signs is:

``````a - b = a + |b| if a * b < 0
``````

## Benefits

The Adding and Subtracting Integers Calculator has several benefits:

1. Saves time: The calculator saves time by performing arithmetic operations quickly and accurately.
2. Easy to use: The calculator is easy to use and does not require any special skills or knowledge.
3. Shows work: The calculator shows the work for the math, making it easy to understand how to perform arithmetic operations on integers.
4. Free: The calculator is free to use and does not require any downloads or installations.

## Interesting Facts

1. Adding two negative numbers gives a negative result.
2. Subtracting a negative number from another negative number gives a positive result.
3. Adding two positive numbers gives a positive result.
4. Subtracting a positive number from another positive number gives a positive result.

## Use Cases

The Adding and Subtracting Integers Calculator has several use cases:

1. Education: The calculator can be used by students to learn how to perform arithmetic operations on integers.
2. Business: The calculator can be used by businesses to perform financial calculations involving integers.
3. Personal Finance: The calculator can be used by individuals to manage their personal finances.

## References

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