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➕pre-algebra review

Keep-Change-Change Rule

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The keep-change-change rule is a method used to subtract integers, where the sign of the second number is changed, and the absolute values of the numbers are then subtracted. This rule helps simplify the process of subtracting integers and ensures consistent and accurate results.

5 Must Know Facts For Your Next Test

  1. The keep-change-change rule is specifically applicable when subtracting integers, where the signs of the numbers may be different.
  2. The first step in using the keep-change-change rule is to keep the sign of the first number, the minuend, the same.
  3. The second step is to change the sign of the second number, the subtrahend, from positive to negative or from negative to positive.
  4. The third step is to change the absolute values of the numbers and subtract them, following the standard rules of subtraction.
  5. The keep-change-change rule helps simplify the process of subtracting integers and ensures consistent and accurate results.

Review Questions

  • Explain the step-by-step process of the keep-change-change rule when subtracting integers.
    • The keep-change-change rule for subtracting integers involves three steps: 1) Keep the sign of the first number (the minuend) the same, 2) Change the sign of the second number (the subtrahend) from positive to negative or from negative to positive, and 3) Change the absolute values of the numbers and subtract them. For example, to subtract -5 from 8 using the keep-change-change rule, you would keep the sign of 8 (positive), change the sign of -5 to positive (making it 5), and then subtract 8 - 5 to get the answer 3.
  • How does the keep-change-change rule help simplify the process of subtracting integers?
    • The keep-change-change rule simplifies the process of subtracting integers by providing a consistent and systematic approach. By keeping the sign of the first number, changing the sign of the second number, and then subtracting the absolute values, the rule eliminates the need to memorize complex subtraction rules for different combinations of positive and negative integers. This makes the subtraction process more straightforward and less prone to errors, especially when dealing with larger or more complex integer subtraction problems.
  • Explain how the keep-change-change rule ensures accurate results when subtracting integers.
    • The keep-change-change rule ensures accurate results when subtracting integers by adhering to the fundamental properties of integer subtraction. By changing the sign of the second number, the rule effectively converts the subtraction problem into an addition problem, which is generally easier to perform and less prone to mistakes. Additionally, the rule's emphasis on working with absolute values helps to eliminate any potential confusion or errors that may arise from the signs of the numbers. By following the consistent steps of the keep-change-change rule, students can be confident that their integer subtraction results will be accurate and reliable.