Absolute Value

Definition

Absolute value is a mathematical concept that represents the distance of a number from zero on the number line, regardless of the number's sign. It is a way to describe the magnitude or size of a number without considering its positive or negative direction.

5 Must Know Facts For Your Next Test

1. The absolute value of a number is always a non-negative value, as it represents the distance from zero on the number line.
2. The absolute value of a positive number is the number itself, while the absolute value of a negative number is the opposite of the number.
3. Absolute value is used to compare the size or magnitude of numbers, regardless of their sign.
4. Absolute value is an important concept in operations with integers, such as addition, subtraction, multiplication, and division.
5. Absolute value is denoted using vertical bars, such as |x|, which means the absolute value of the number x.

Review Questions

• Explain how the absolute value of a number is determined on the number line.
  • The absolute value of a number represents the distance of that number from zero on the number line, regardless of whether the number is positive or negative. For example, the absolute value of 5 is 5, as it is 5 units away from zero on the number line. Similarly, the absolute value of -3 is also 3, as it is 3 units away from zero on the number line. The absolute value of a number is always a non-negative value, as it focuses on the magnitude or size of the number without considering its direction.
• Describe how absolute value is used in the context of integer operations, such as addition and subtraction.
  • Absolute value is an important concept in performing operations with integers, as it allows for the comparison and manipulation of numbers regardless of their sign. When adding or subtracting integers, the absolute value of the numbers is used to determine the magnitude of the result. For example, when adding |3| + |-5|, the absolute value of 3 (which is 3) and the absolute value of -5 (which is also 5) are used to calculate the result, which is 8. Similarly, when subtracting |7| - |-2|, the absolute value of 7 (which is 7) and the absolute value of -2 (which is 2) are used to determine the difference of 5.
• Analyze how the concept of absolute value is applied in the context of multiplying and dividing integers.
  • The absolute value of a number plays a crucial role in the multiplication and division of integers. When multiplying integers, the absolute value of the numbers is used to determine the magnitude of the result, while the signs of the original numbers are used to determine the overall sign of the product. For instance, when multiplying |-4| × |6|, the absolute values of 4 and 6 are used to calculate the result of 24, and the overall sign is positive since both original numbers were positive. Similarly, when dividing integers, the absolute value of the numbers is used to determine the magnitude of the quotient, while the sign of the division is determined by the original signs of the numbers. For example, when dividing |15| ÷ |-3|, the absolute value of 15 (which is 15) is divided by the absolute value of -3 (which is 3), resulting in a quotient of 5 with a negative sign.

Related terms

Integer:

An integer is a whole number, including positive, negative, and zero values.

Number Line:

A number line is a visual representation of the set of real numbers, where each point on the line corresponds to a unique real number.

Magnitude: Magnitude refers to the size or amount of a number, without regard to its positive or negative direction.