key term - Signed Numbers

Definition

Signed numbers are a way of representing positive and negative quantities using a sign (+ or -) to indicate the direction or value of a number. They are essential in the context of adding and subtracting integers, as the sign determines whether the number is to be added or subtracted.

5 Must Know Facts For Your Next Test

1. The sign of a signed number determines whether the number is positive or negative, and how it will be used in mathematical operations.
2. When adding or subtracting signed numbers, the signs must be taken into account to determine the direction and magnitude of the result.
3. Positive numbers are always greater than negative numbers, with zero being neither positive nor negative.
4. The absolute value of a number is the distance of that number from zero on the number line, regardless of its sign.
5. Signed numbers are essential in understanding and working with integers, which can be used to represent quantities, positions, and changes in direction.

Review Questions

• Explain how the sign of a signed number affects its value and how it is used in mathematical operations.
  • The sign of a signed number determines whether the number is positive or negative. Positive numbers are greater than zero and are added to other positive numbers, while negative numbers are less than zero and are subtracted from other numbers. The sign is crucial in determining the direction and magnitude of the result when performing addition and subtraction operations with signed numbers. For example, adding a positive number increases the overall value, while subtracting a negative number also increases the value.
• Describe the relationship between positive and negative numbers on the number line and how the absolute value of a number is determined.
  • Positive numbers are located to the right of zero on the number line, while negative numbers are located to the left. The absolute value of a number represents the distance of that number from zero on the number line, regardless of its sign. For example, the absolute value of -5 is 5, as it is the same distance from zero as the positive number 5. Understanding the relationship between positive and negative numbers on the number line and the concept of absolute value is essential for working with signed numbers and performing operations such as addition and subtraction.
• Analyze how the use of signed numbers is essential in the context of adding and subtracting integers, and explain how the signs of the numbers affect the final result.
  • Signed numbers are fundamental in the context of adding and subtracting integers because the sign of each number determines whether it is to be added or subtracted. When adding two positive numbers, the result is a positive number. When adding a positive and a negative number, the result depends on the relative magnitudes of the numbers - if the positive number is greater, the result is positive, and if the negative number is greater, the result is negative. When subtracting a positive number, it is equivalent to adding the negative of that number, and when subtracting a negative number, it is equivalent to adding the positive of that number. Understanding how the signs of signed numbers interact in addition and subtraction is crucial for accurately performing these operations with integers.

Related terms

Positive Numbers: Positive numbers are numbers greater than zero, represented with a positive sign (+) or no sign at all.

Negative Numbers: Negative numbers are numbers less than zero, represented with a negative sign (-).

Absolute Value:

The absolute value of a number is the distance of that number from zero on the number line, regardless of its sign.