How To Cheat Sheet for Positive and Negative Numbers

Negative and Positive Number Rules to Know

Integers consist of zero, positive whole numbers, and negative whole numbers.
Integers consist of zero, positive whole numbers, and negative whole numbers. Jeffrey Coolidge, Getty Images

Here is your cheat sheet to help you remember what to do with positive and negative numbers (integers) with adding, subtracting, multiplying and dividing.

Review Integers

You should have an overview of integer basics.

Remember, positive numbers are those with values greater than zero. Zero is neither positive nor negative. Negative numbers are ones with a value less than zero. If there is no fraction or portion after the decimal point, the positive and negative numbers are called integers.

The rules of how to work with positive and negative numbers are important because you'll encounter them in daily life, such as balancing a bank account, losing weight, and preparing recipes.

Difficulty: N/A

Time Required: 20 Minutes & Practice

What You Need for a Positive and Negative Numbers Cheat Sheet

  • Calculator
  • Free Worksheets Below
  • An Understanding of the 4 Operations
  • A Number Line
  • Pencil and Eraser

Positive and Negative Number Rules

  1. Adding Rules:

    Positive + Positive = Positive: 5 + 4 = 9
    Negative + Negative = Negative: (- 7) + (- 2) = - 9

    Sum of a negative and a positive number: Use the sign of the larger number and subtract

    (- 7) + 4 = -3
    6 + (-9) = - 3
    (- 3) + 7 = 4
    5 + ( -3) = 2
    The sign will be that of the larger number. Remember adding a negative number is the same as subtracting a positive one!

  2. Subtracting Rules:

    Negative - Positive = Negative: (- 5) - 3 = -5 + (-3) = -8
    Positive - Negative = Positive + Positive = Positive: 5 - (-3) = 5 + 3 = 8
    Negative - Negative = Negative + Positive = Use the sign of the larger number and subtract (Change double negatives to a positive)
    (-5) - (-3) = ( -5) + 3 = -2
    (-3) - ( -5) = (-3) + 5 = 2
    If you get confused, it often helps to write a positive number in an equation first and then the negative number. This can make it easier to see whether or not a sign change occurs.

  1. Multiplying Rules:

    Positive x Positive = Positive: 3 x 2 = 6
    Negative x Negative = Positive: (-2) x (-8) = 16
    Negative x Positive = Negative: (-3) x 4 = -12
    Positive x Negative = Negative: 3 x (-4) = -12
    If you're multiplying a larger series of positive and negative numbers, you can add up how many are positive and how many are negative. The final sign will be the one in excess. 

  1. Dividing Rules:

    Positive ÷ Positive = Positive: 12 ÷ 3 = 4
    Negative ÷ Negative = Positive: (-12) ÷ (-3) = 4
    Negative ÷ Positive = Negative: (-12) ÷ 3 = -4
    Positive ÷ Negative = Negative: 12 ÷ (-3) = -4

Tips for Success

  1. When working with rules for positive and negative numbers, try and think of weight loss or poker games to help solidify 'what this works'.
  2. Using a number line showing both sides of 0 is very helpful to help develop the understanding of working with positive and negative numbers/integers.
  3. It's easier to keep track of the negative numbers if you enclose them in brackets.

Edited by Anne Marie Helmenstine, Ph.D.