Introduction

Integers are whole numbers, including both positive and negative numbers, as well as zero. They are used to represent quantities that can be greater or less than zero.

Positive Integers

Positive integers are whole numbers greater than zero. They are denoted by $\mathbb{Z}^+$. Example: $3, 56, 100$

Negative Integers

Negative integers are whole numbers less than zero. They are denoted by $\mathbb{Z}^-$. Example: $-5, -27, -100$

Zero

Zero is considered an integer but is neither positive nor negative. It is denoted by $0$. Example: $0$

Addition of Integers

Adding integers of the same sign: When adding integers with the same sign, add their absolute values and keep the sign. Example: $(-4) + (-7) = -11$

Subtraction of Integers

Subtracting integers is the same as adding the opposite. Change the subtraction sign to addition and change the sign of the integer being subtracted. Example: $5 - (-3) = 5 + 3 = 8$

Common Mistakes

• Forgetting to account for the signs when adding or subtracting integers.
• Confusing positive and negative integers in operations.

Key Points

• Integers include positive numbers, negative numbers, and zero.
• Addition of integers of the same sign involves adding their absolute values and keeping the sign.
• Subtraction of integers is the same as adding the opposite.

Practice Questions

1. Calculate: $(-10) + 15 - (-5)$
2. Evaluate: $-8 - (-12) + 4$