key term - Adding the Opposite

Definition

Adding the opposite, also known as additive inverse, is a mathematical operation where a number is added to its negative counterpart, resulting in a sum of zero. This concept is particularly relevant in the context of subtracting integers, as it allows for the simplification of subtraction problems by converting them into addition problems.

5 Must Know Facts For Your Next Test

1. Adding the opposite is a fundamental concept in the context of subtracting integers, as it allows for the simplification of subtraction problems.
2. The additive inverse of a number is the number with the same absolute value but the opposite sign, which when added to the original number, results in a sum of zero.
3. Subtracting a number is equivalent to adding the opposite of that number, which is a useful property for simplifying subtraction problems.
4. When subtracting a negative integer, the operation can be rewritten as adding the positive counterpart of the negative integer.
5. The use of adding the opposite is a key strategy in solving subtraction problems involving integers, as it helps to convert the problem into a simpler addition problem.

Review Questions

• Explain how adding the opposite can be used to simplify subtraction problems involving integers.
  • Adding the opposite, or the additive inverse, is a key concept in simplifying subtraction problems involving integers. The additive inverse of a number is the number with the same absolute value but the opposite sign. By adding the opposite of the number being subtracted, the subtraction problem can be converted into an addition problem, which is often easier to solve. For example, to subtract 5 from 8, you can instead add the opposite of 5, which is -5, resulting in the expression 8 + (-5) = 3. This process of adding the opposite allows you to simplify subtraction problems and perform the operations more efficiently.
• Describe the relationship between adding the opposite and the concept of integers.
  • The concept of adding the opposite is closely tied to the understanding of integers, which are whole numbers that can be positive, negative, or zero. When subtracting a negative integer, the operation can be rewritten as adding the positive counterpart of the negative integer. For instance, to subtract -3 from 7, you can instead add the opposite of -3, which is 3, resulting in the expression 7 + 3 = 10. This relationship between adding the opposite and integers is a fundamental principle in performing subtraction operations with integers, as it allows for the conversion of subtraction problems into simpler addition problems.
• Analyze how the use of adding the opposite can be a strategic approach in solving subtraction problems involving integers.
  • The use of adding the opposite is a highly strategic approach in solving subtraction problems involving integers. By recognizing that subtracting a number is equivalent to adding the opposite of that number, you can convert subtraction problems into simpler addition problems. This strategy is particularly useful when dealing with negative integers, as it allows you to avoid the complexities of subtracting a negative number. Additionally, adding the opposite can help you identify patterns and relationships between integers, further enhancing your problem-solving skills. The ability to effectively utilize this concept is a valuable tool in mastering the subtraction of integers and developing a deeper understanding of mathematical operations.

Related terms

Additive Inverse:

The additive inverse of a number is the number with the same absolute value but the opposite sign, which when added to the original number, results in a sum of zero.

Integer:

An integer is a whole number, which can be positive, negative, or zero, and does not include fractions or decimal points.

Subtraction:

Subtraction is the mathematical operation of finding the difference between two numbers, where one number is taken away from the other.