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Arithmetic with Integers

Learning how to add and subtract integers

Introduction to Integers

  • Negative numbers are part of a special set called integers
  • Arithmetic with integers is more complicated than with whole numbers
  • Two key rules: adding a negative is the same as subtracting a positive
  • Subtracting a negative is the same as adding a positive

Case 1: Making a Positive Number More Positive

  • Adding positive numbers is regular addition
  • Adding a negative number can be rewritten as subtraction
  • Answer will always be positive in this case

Case 2: Making a Positive Number More Negative

  • Subtraction makes a positive number more negative
  • Answer can be positive, negative, or zero
  • Adding a negative can be rewritten as subtracting a positive

Case 3: Making a Negative Number More Negative

  • Adding a negative number makes a negative number more negative
  • Answer will always be negative in this case
  • Adding a negative can be rewritten as subtracting a positive

Case 4: Making a Negative Number More Positive

  • Adding a positive number makes a negative number more positive
  • Answer can be positive, negative, or zero
  • Adding a negative can be rewritten as subtracting a positive

Strategy for Adding and Subtracting Integers

  • Ask three key questions: starting sign, direction of change, resulting sign
  • First question: starting with a positive or a negative number
  • Second question: making the value bigger or smaller
  • Third question: will the answer be positive, negative, or zero

Practice and Conclusion

  • Practice is key to mastering integer arithmetic
  • Try a variety of problems with an answer key
  • Don't get discouraged and rewatch the video for clarification

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