Difference

Definition

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

5 Must Know Facts For Your Next Test

1. The difference between two whole numbers is always a whole number.
2. When subtracting a larger number from a smaller number, the result is a negative number.
3. The absolute value of the difference between two numbers represents the distance between them on the number line.
4. Subtracting integers follows the same rules as subtracting whole numbers, with the added consideration of positive and negative signs.
5. Identifying the difference is a key step in problem-solving strategies, as it helps determine the unknown quantity or the relationship between given values.

Review Questions

• Explain how the concept of difference is applied when subtracting whole numbers.
  • When subtracting whole numbers, the difference represents the amount by which the minuend (the number being subtracted from) exceeds the subtrahend (the number being subtracted). The difference is always a whole number, and if the subtrahend is larger than the minuend, the result will be a negative number. Understanding the concept of difference is crucial in performing subtraction operations with whole numbers accurately.
• Describe how the concept of difference is extended to the context of integers.
  • The concept of difference is similarly applied when subtracting integers, but with the added consideration of positive and negative signs. When subtracting a negative integer, the process is equivalent to adding the absolute value of the negative integer. Conversely, when subtracting a positive integer, the process is equivalent to adding the negative of that integer. The difference between two integers can result in a positive, negative, or zero value, depending on the relative magnitudes and signs of the numbers involved.
• Analyze how the understanding of difference can be utilized in a problem-solving strategy.
  • Identifying the difference between two or more quantities is a crucial step in many problem-solving strategies. By recognizing the difference, one can determine the unknown quantity or the relationship between the given values. For example, in a word problem involving the subtraction of whole numbers or integers, the difference can help identify the missing information or the amount by which one quantity exceeds another. Applying the concept of difference effectively can lead to the successful resolution of a wide range of mathematical problems.

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 value that is less than the reference point.

Absolute Value:

The distance of a number from zero on the number line, regardless of its sign.