## Introduction

- Integers are a set of
**whole**numbers (0, 1, 2, 3, ....) and their**opposites**. For example, 1, -1, 2, -2, 3, -3, and so on. - 0 is an integer. It is also called the origin. 0 does not carry any sign. When any integer is added to 0, the answer is the same number. e.g. $-9+0=-9$
- The integer with a positive sign is greater than 0 and is to the
**right**of 0 on the number line. - The integer with a negative sign is less than 0 and is to the
**left**of 0 on the number line.

- In a vertical number line, numbers above 0 are positive, and numbers below zero are negative.

## Opposites and Additive Inverse

- Two
**integers are opposite**if they have different signs and exactly the same distance from 0, such as $-5and5;3and-3.$ - The opposite of an opposite is a positive, for e.g. $-\left(-3\right)=3$.
- The
**additive inverse**is when a number and its opposite are added resulting in "0". E.g. $\left(-2\right)+\left(+2\right)=0$.

## Adding Integers

- Rule 1: When adding two integers with the same signs, add the numbers and keep the same sign.
- Rule 2: When adding two integers with different signs, subtract the numbers and keep the sign of the greater number.

## Subtracting Integers

**Rule:**When subtracting two integers:

First, change the subtraction sign to the addition.

Next**,** change the sign of the number that is being subtracted.

Last, follow the rules of the addition of integers.

- Follow the order of operations when working with more than two integers.

## Solved Examples

Example 1: What is the opposite of -9?

Solution: The opposite of -9 is 9, as it has exactly the same distance from 0.

Example 2: What is the value of -(-24)?

Solution: The opposite of opposite is positive.

-(-24) = 24

Example 3: Add: $\left(+2\right)+\left(+7\right)$

Solution: Use the rule for adding integers with the same sign.

$\left(+2\right)+\left(+7\right)=9$

Example 4: Add: $\left(-7\right)+\left(+5\right)$

Solution: Use the rule for the addition of integers with different signs.

$\left(-7\right)+\left(+5\right)=-2$

Example 5: Subtract: $\left(-3\right)-\left(-5\right)$

Solution: Use the rule for the subtraction of the integers.

$\left(-3\right)-\left(-5\right)$

$=\left(-3\right)+\left(+5\right)$

$=2$

Example 6: Subtract: $\left(-7\right)-\left(+8\right)$

Solution: Use the rule for the subtraction of the integers.

$\left(-7\right)-\left(+8\right)$

$=\left(-7\right)+\left(-8\right)$

$=-15$

Example 7: Compare: $-3\overline{)?}-10$

Solution: $-3\overline{)}-10$, as -3 is at the right of -10 on a number line.

## Cheat Sheet

- A number without any sign is considered positive (except 0, as 0 is neither positive nor negative).
- The sign indicates the
**direction**.- The number with a positive sign is positioned to the
**right**of 0. - The number with a negative sign is positioned to the
**left**of 0. - When comparing two numbers, the number on the right compared to the other number on the number line, irrespective of its sign, is greater.

- The number with a positive sign is positioned to the
- The opposite of an opposite is a positive, for e.g. $-\left(-3\right)=3$
- When finding the difference in the temperature, consider using a number line.

## Blunder Area

- If a number is written without any sign, it should be assumed to have a positive sign.
- Follow the Order of Operations when working with more than two integers.

- Rishi Jethwa
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