Directed Numbers

Directed Numbers

Directed numbers are a way to represent integers with a direction or sign.

Key Concepts:

• Positive numbers: Numbers greater than zero, represented by a plus sign (+) or no sign at all. Examples: +5, 3
• Negative numbers: Numbers less than zero, represented by a minus sign (-). Examples: -2, -10
• Zero: The number that is neither positive nor negative, represented by 0

Operations with Directed Numbers:

• Addition:
  • Same signs: Add the numbers and keep the sign. Example: (+3) + (+2) = +5
  • Different signs: Subtract the smaller number from the larger number and keep the sign of the larger number. Example: (+3) + (-2) = +1
• Subtraction:
  • Same signs: Subtract the smaller number from the larger number and keep the sign. Example: (+5) - (+2) = +3
  • Different signs: Add the numbers and keep the sign of the first number. Example: (+3) - (-2) = +5
• Multiplication:
  • Same signs: Multiply the numbers and keep the sign. Example: (+2) × (+3) = +6
  • Different signs: Multiply the numbers and make the result negative. Example: (+2) × (-3) = -6
• Division:
  • Same signs: Divide the numbers and keep the sign. Example: (+6) ÷ (+2) = +3
  • Different signs: Divide the numbers and make the result negative. Example: (+6) ÷ (-2) = -3

Directed Numbers

• Directed numbers are used to represent integers with a direction or sign.

Key Concepts

• Positive numbers are greater than zero, represented by a plus sign (+) or no sign at all, e.g., +5, 3.
• Negative numbers are less than zero, represented by a minus sign (-), e.g., -2, -10.
• Zero is neither positive nor negative, represented by 0.

Operations with Directed Numbers

Addition

• When adding numbers with the same sign, add the numbers and keep the sign, e.g., (+3) + (+2) = +5.
• When adding numbers with different signs, subtract the smaller number from the larger number and keep the sign of the larger number, e.g., (+3) + (-2) = +1.

Subtraction

• When subtracting numbers with the same sign, subtract the smaller number from the larger number and keep the sign, e.g., (+5) - (+2) = +3.
• When subtracting numbers with different signs, add the numbers and keep the sign of the first number, e.g., (+3) - (-2) = +5.

Multiplication

• When multiplying numbers with the same sign, multiply the numbers and keep the sign, e.g., (+2) × (+3) = +6.
• When multiplying numbers with different signs, multiply the numbers and make the result negative, e.g., (+2) × (-3) = -6.

Division

• When dividing numbers with the same sign, divide the numbers and keep the sign, e.g., (+6) ÷ (+2) = +3.
• When dividing numbers with different signs, divide the numbers and make the result negative, e.g., (+6) ÷ (-2) = -3.