Part 2: Addition and Subtraction

# 2.2: Adding and subtracting with negative integers

Notes

##### Subtracting a negative integer from a positive integer

The addition algorithm from 3a: Adding and subtracting with positive integers gives us a way to subtract a negative integer from a positive integer. For example, to solve 83 – (–47), write 83 – (–47) = 83 + 47 and use the addition algorithm to obtain the answer 130. More generally, A – (–B) = A + B.

##### Adding a negative integer to a positive integer

The subtraction algorithm from 3a: Adding and subtracting with positive integers gives us a way to add a negative integer to a positive integer. For example, to solve 83 + (–47), write 83 + (–47) = 83 – 47 and use the subtraction algorithm to obtain the answer 36. More generally, A + (–B) = A – B.

##### Adding a positive integer to a negative integer

The subtraction algorithm from 3a: Adding and subtracting with positive integers gives us a way to add a positive integer to a negative integer. For example, to solve –47 + 83, write –47 + 83 = 83 – 47 and use the subtraction algorithm to obtain the answer 36. More generally, –A + B = B – A.

##### Subtracting a larger integer from a smaller integer

What if we’re subtracting a larger integer from a smaller integer, for example, 47 – 83? In this case, write 47 – 83 = –(–47 + 83) = –(83 – 47) and use the subtraction algorithm to calculate 83 – 47 = 36. Then –(83 – 47) must be –36, so 47 – 83 = –36. More generally, A – B = – (B – A).

##### Adding and subtracting with positive and negative integers

The following two tables summarize the various possibilities for adding and subtracting with positive and negative integers.

Expression |
Equivalent expression |
Example |

A + B | 43 + 18 = 61 | |

A – (–B) | A + B | 43 – (–18) = 43 + 18 = 61 |

Expression |
Constraint |
Equivalent expression |
Example |

A – B | A > B | 43 – 18 = 25 | |

A + (–B) | A > B | A – B | 43 + (–18) = 43 – 18 = 25 |

–A + B | A < B | B – A | –18 + 43 = 43 – 18 = 25 |

–A – (–B) | A < B | B – A | –18 – (–43) = 43 – 18 = 25 |

A – B | A < B | –(B – A) | 18 – 43 = –(43 – 18) = – 25 |

A + (–B) | A < B | –(B – A) | 18 + (–43) = –(43 – 18) = –25 |

–A + B | A > B | –(A – B) | –43 + 18 = –(43 – 18) = –25 |

–A – (–B) | A > B | –(A – B) | –43 – (–18) = –(43 – 18) = –25 |

The video below works through some examples of adding and subtracting with negative integers.

Video Tips

Practice Exercises

Do the following exercises to practice adding and subtracting with negative integers.