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How do you subtract integers quickly?

Published in Integer Subtraction 3 mins read

To subtract integers quickly, the key is to change the subtraction problem into an addition problem.

Here's a breakdown of the process, leveraging the provided reference:

The core concept, as stated in the reference, is to change the sign of the number being subtracted (the subtrahend) and then add the numbers. Let's illustrate with a step-by-step approach and examples.

Steps for Quick Integer Subtraction

  1. Identify the Subtrahend: Determine which number is being subtracted. This is the number that follows the minus sign (-).

  2. Change the Sign: Reverse the sign of the subtrahend. If it's positive, make it negative. If it's negative, make it positive.

  3. Convert to Addition: Replace the subtraction operation with an addition operation.

  4. Apply Addition Rules:

    • Same Signs: If both numbers now have the same sign (both positive or both negative), add their absolute values and keep the common sign.
    • Different Signs: If the numbers have different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.

Examples

Let's go through some examples to demonstrate the process:

Example 1: 5 - 3

  1. Subtrahend: 3
  2. Change the sign: -3
  3. Convert to addition: 5 + (-3)
  4. Apply addition rules: Different signs. |5| - |-3| = 5 - 3 = 2. Since |5| is larger and positive, the answer is 2.

Example 2: 2 - (-4)

  1. Subtrahend: -4
  2. Change the sign: 4
  3. Convert to addition: 2 + 4
  4. Apply addition rules: Same signs (both positive). 2 + 4 = 6.

Example 3 (From the Reference): 1 - (-9)

  1. Subtrahend: -9
  2. Change the sign: 9
  3. Convert to addition: 1 + 9
  4. Apply addition rules: Same signs (both positive). 1 + 9 = 10.

Example 4: -7 - 2

  1. Subtrahend: 2
  2. Change the sign: -2
  3. Convert to addition: -7 + (-2)
  4. Apply addition rules: Same signs (both negative). |-7| + |-2| = 7 + 2 = 9. Keep the negative sign, so the answer is -9.

Example 5: -3 - (-5)

  1. Subtrahend: -5
  2. Change the sign: 5
  3. Convert to addition: -3 + 5
  4. Apply addition rules: Different signs. |5| - |-3| = 5 - 3 = 2. Since |5| is larger and positive, the answer is 2.

Table Summary

Original Problem Subtrahend Sign Change Converted Problem Solution
5 - 3 3 -3 5 + (-3) 2
2 - (-4) -4 4 2 + 4 6
1 - (-9) -9 9 1 + 9 10
-7 - 2 2 -2 -7 + (-2) -9
-3 - (-5) -5 5 -3 + 5 2

By consistently applying these steps, you can subtract integers more quickly and accurately. The key is to internalize the sign change and conversion to addition, which simplifies the process.

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