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Questions and Answers
What is represented by a plus sign (+) or no sign at all?
What is represented by a plus sign (+) or no sign at all?
What happens when you add two positive numbers with the same sign?
What happens when you add two positive numbers with the same sign?
What is the result of multiplying two numbers with different signs?
What is the result of multiplying two numbers with different signs?
What happens when you subtract a negative number from a positive number?
What happens when you subtract a negative number from a positive number?
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What is the result of dividing a positive number by a negative number?
What is the result of dividing a positive number by a negative number?
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What is represented by a zero?
What is represented by a zero?
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Study Notes
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.
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Description
Understand directed numbers, including positive numbers, negative numbers and zero, and how to perform operations with them.
