integer rules cheat sheet

Guri Bee

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21-10-2024

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The Integer Rules Cheat Sheet: Mastering the Basics of Whole Numbers

Integers, those trusty whole numbers, are the building blocks of many mathematical concepts. Whether you're a student tackling algebra or a seasoned programmer, understanding integer rules is crucial.

This cheat sheet will equip you with the fundamental knowledge you need to navigate the world of integers with confidence. We'll explore key concepts like:

• Defining Integers
• Operations with Integers
• Number Line Representation
• Absolute Value

Let's dive in!

What are Integers?

Integers are whole numbers, including positive numbers, negative numbers, and zero. Think of them as a straight line stretching infinitely in both directions, with zero as the central point.

• Positive Integers: 1, 2, 3, 4, 5...
• Negative Integers: -1, -2, -3, -4, -5...
• Zero: 0

Essential Operations with Integers

1. Addition and Subtraction

• Adding Integers with the Same Sign: Add the absolute values and keep the common sign.

  • Example: 5 + 3 = 8 (Both positive, so the result is positive)
  • Example: -2 + (-4) = -6 (Both negative, so the result is negative)

• Adding Integers with Different Signs: Subtract the smaller absolute value from the larger absolute value. The result will have the sign of the number with the larger absolute value.

  • Example: 7 + (-3) = 4 (7 has a larger absolute value than 3, and the result is positive)
  • Example: -8 + 5 = -3 (8 has a larger absolute value than 5, and the result is negative)

• Subtracting Integers: Change the subtraction to addition and change the sign of the second number.

  • Example: 5 - 3 = 5 + (-3) = 2
  • Example: -2 - 4 = -2 + (-4) = -6

2. Multiplication and Division

• Multiplying/Dividing Integers with the Same Sign: The result is always positive.

  • Example: 4 x 2 = 8
  • Example: (-3) x (-5) = 15

• Multiplying/Dividing Integers with Different Signs: The result is always negative.

  • Example: 6 x (-2) = -12
  • Example: (-8) / 2 = -4

The Number Line: Visualizing Integers

The number line is a powerful tool for understanding integer relationships and operations.

• Positive numbers are to the right of zero.
• Negative numbers are to the left of zero.
• Zero is the central point.

To add or subtract integers on a number line:

1. Start at zero.
2. Move right for positive numbers and left for negative numbers.
3. Combine the movements to find the final position.

Absolute Value: The Distance from Zero

The absolute value of an integer is its distance from zero, regardless of direction. It is represented by two vertical bars around the number.

• Example: |5| = 5 (5 is 5 units away from zero)
• Example: |-3| = 3 ( -3 is 3 units away from zero)

Key Takeaways

• Integers are whole numbers, including positive, negative, and zero.
• The rules for addition, subtraction, multiplication, and division with integers depend on the signs of the numbers.
• The number line provides a visual representation of integers and their relationships.
• The absolute value represents the distance of an integer from zero.

Additional Resources

• Khan Academy: https://www.khanacademy.org/math/arithmetic/absolute-value/integers/v/adding-and-subtracting-integers-on-a-number-line
• Math is Fun: https://www.mathsisfun.com/numbers/integers.html

By mastering these basic integer rules, you'll gain a solid foundation for tackling more advanced mathematical concepts and applications in various fields.