Opposite Method

Definition

The opposite method is a strategy used in integer addition and subtraction operations. It involves applying the opposite operation to the given numbers in order to solve the problem, relying on the inverse relationship between addition and subtraction.

5 Must Know Facts For Your Next Test

1. The opposite method is particularly useful when adding and subtracting integers of different signs.
2. To use the opposite method, you first identify the signs of the given integers, then apply the opposite operation to solve the problem.
3. When adding integers with the same sign, the opposite method involves adding the absolute values of the numbers and keeping the common sign.
4. When subtracting integers, the opposite method involves adding the additive inverse of the subtrahend to the minuend.
5. The opposite method relies on the inverse relationship between addition and subtraction, allowing for efficient problem-solving.

Review Questions

• Explain how the opposite method can be used to add integers with different signs.
  • When adding integers with different signs, the opposite method involves applying the opposite operation. For example, to add a positive integer and a negative integer, you would subtract the absolute value of the negative integer from the absolute value of the positive integer, keeping the sign of the larger number. This leverages the inverse relationship between addition and subtraction to efficiently solve the problem.
• Describe the relationship between subtraction and the addition of the opposite, and how this is utilized in the opposite method.
  • The opposite method relies on the concept that subtracting a number is the same as adding its additive inverse. This means that to subtract an integer, you can instead add the opposite, or additive inverse, of that integer. For example, to subtract 5 from 10, you can add the additive inverse of 5, which is -5, to 10. This allows you to reframe the subtraction as an addition problem, which can be more easily solved using the opposite method.
• Analyze how the opposite method can be applied to solve more complex integer addition and subtraction problems, and explain the advantages of this approach.
  • The opposite method can be extended to solve more complex integer addition and subtraction problems by breaking down the operations into simpler steps. For example, to subtract a negative integer from a positive integer, you can first add the additive inverse of the negative integer, and then apply the opposite method to add the two resulting integers. This approach allows you to leverage the inverse relationship between addition and subtraction, making the problem-solving process more efficient and less prone to errors. The opposite method's flexibility and reliance on fundamental mathematical principles make it a powerful tool for mastering integer operations.

Related terms

Integer: A whole number, including positive, negative, and zero values.

Additive Inverse: The number that, when added to a given number, results in a sum of zero.

Subtraction as Addition of the Opposite: The concept that subtracting a number is the same as adding its additive inverse.