Difference

Definition

The difference between two numbers is the amount by which one number exceeds or falls short of the other. It is the result of subtracting one number from another and represents the distance or separation between the two values.

5 Must Know Facts For Your Next Test

1. The difference between two numbers can be positive, negative, or zero, depending on the relative values of the numbers.
2. When subtracting a larger number from a smaller number, the result is a negative number, which represents the amount by which the smaller number falls short of the larger number.
3. The absolute value of a difference represents the magnitude or size of the difference, ignoring the positive or negative sign.
4. Differences are an essential concept in integer operations, as they are used to perform subtraction and determine the relative position of numbers on the number line.
5. Understanding the concept of difference is crucial for solving problems involving the addition and subtraction of integers, as it helps in determining the direction and magnitude of the change.

Review Questions

• Explain how the concept of difference relates to the addition and subtraction of integers.
  • The concept of difference is fundamental to the addition and subtraction of integers. When adding integers, the difference between the two numbers determines the direction and magnitude of the result. For example, adding a positive integer to a negative integer results in a difference that is smaller in magnitude than the original numbers. Conversely, subtracting a larger integer from a smaller integer results in a negative difference, which represents the amount by which the smaller number falls short of the larger number. Understanding the concept of difference is crucial for performing operations with integers and interpreting the results.
• Describe how the absolute value of a difference can be used to determine the magnitude of the change between two numbers.
  • The absolute value of a difference represents the distance or separation between two numbers on the number line, regardless of their sign (positive or negative). This is important in the context of integer operations because it allows you to determine the magnitude or size of the change, without being influenced by the direction of the change. For example, the absolute value of the difference between -5 and 3 is 8, which represents the distance between the two numbers on the number line. Understanding the concept of absolute value and how it relates to the difference between integers is crucial for solving problems involving the addition and subtraction of integers.
• Analyze how the concept of difference can be used to compare and order integers on the number line.
  • The concept of difference is closely tied to the ordering and comparison of integers on the number line. The difference between two integers represents their relative position and distance on the number line. A positive difference indicates that the first number is greater than the second, while a negative difference indicates that the first number is less than the second. The absolute value of the difference represents the distance between the two numbers, regardless of their order. By understanding how the concept of difference relates to the ordering and comparison of integers, you can effectively solve problems that involve comparing, ordering, or determining the relative position of integers on the number line.

Related terms

Subtraction: The mathematical operation of removing one number from another to find the difference between them.

Negative Number: A number less than zero, representing a quantity that is the opposite or inverse of a positive number.

Absolute Value: The distance of a number from zero on the number line, regardless of its sign (positive or negative).