Negative Integers: Definition, Rules & Examples

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  • 0:02 Defining Negative Integers
  • 0:35 Rules for Negative Integers
  • 2:55 Practice
  • 5:19 Lesson Summary
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Lesson Transcript
Ellen Manchester
Expert Contributor
Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

This lesson will be covering the world of negative integers. What is a negative integer? How do they work? Also, we will be looking at real world examples.

Definition of Negative Integers

Usually we think of water freezing at 32 degrees F, but sometimes water doesn't freeze until -40 degrees F or even -55 degrees F, depending on what is going on with the surrounding temperature. What about the lowest point in North America? Badwater Basin, in Death Valley, California, is -282 feet, or 282 feet below sea level. These negative integers, which are simply all the integers less than zero, are all around us in our world!

Rules for Negative Integers

There are some rules for negative integers that you'll need to keep in mind when doing calculations.

Rule #1: Adding Unlike Signs

When adding positives and negatives, unlike signs, we subtract the numbers and give the answer the sign of the larger absolute value. Remember that absolute value is just the number of steps from zero. Large positive plus small negative equals positive, as seen in 120 + (-20) = 100. Large negative plus small positive equals negative, as seen in -7 + 3 = -4.

Rule #2: Adding Like Signs

When adding the same signs, like signs, we add the numbers and give the answer the sign of the original values. Negative plus negative is equal to negative, as seen in -20 + (-10) = -30. Positive plus positive equals positive, as seen in 10 + 30 = 40.

Rule #3: Subtraction of Signed Numbers

When a subtraction sign is used, think of the subtraction sign as a negative sign. So if you are subtracting a positive number, it's the same thing as adding the negative of that number. -10 - 15 is equivalent to -10 + (-15) which is equal to -25.

If you are subtracting a negative number, it's the same thing as adding the positive of that number. 13 - (-14) is equivalent to 13 + 14 which equals 27.

Rule #4: Multiplying and Dividing Negatives

When multiplying or dividing signed numbers, there are only two rules. You multiply and divide as usual, then like signs equal positive, which we see in: -4 * -4 which equals 16 and -120 / -10 equals 12. Similarly, unlike signs equal negative, which we see in -2 * 5 = -10 and -15 / 3 = -5.


Now that we've covered the rules, let's do some practice questions:

1) -3 + (-3)

Because a negative plus a negative equals a negative, and 3 plus 3 is 6, the answer is -6.

2) 4 + (-5)

First, we know that a small positive plus a large negative will be a negative, so we know right away that this answer will be negative. Also, we know that when combining 4 and negative 5, we can think of the problem as 4 minus 5, which results in an answer of -1.

3) -16 ÷ 4

Because unlike signs result in a negative when we're doing division, we know our answer will be negative and because 16 divided by 4 is 4, we know that the answer will be -4.

4) (-9) * (-8)

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Additional Activities

Adding and Subtracting Positive and Negative Integers Poker Game


  • To add a positive and a negative integer together, we subtract the two integers and then place the sign of the larger absolute value of the integers on the answer.
  • To add integers that are both positive, we add the integers and the sum has a positive sign.
  • To add integers that are both negative, we add the integers and the sum has a negative sign.

Materials Needed

  • A deck of cards
  • Poker chips
  • A piece of notebook paper
  • A pencil


  • Let each red card represent a negative number.
  • Let each black card represent a positive number.
  • Aces are considered to have a value of 1.
  • Face card values are as follows: Jack = 11, Queen = 12, King = 13
  • The object of the game is to get the highest hand to win the poker chips.


  1. Shuffle the cards and give each player 5 cards.
  2. Have each player add up the total value of their cards, and place an opening bet based on that value.
  3. Each player can then either match the highest bet, or they can fold, meaning they bow out of this hand.
  4. For the players still in the game, each player can request to have up to two cards from the remaining cards in the deck to replace two of the cards in their hand.
  5. Have each player add up the total value of their cards again, and then decide whether or not to bet more chips based on their new value.
  6. Each player can then either match the highest bet, or they can fold.
  7. Each player shows their cards, and the highest hand wins the poker chips.

Example Hand:

There are three players; Sara, Missy, and Angela. The hands initially dealt, along with their total hand values are as follows:

  • Sara: Reds: 3, 2, and 10, Blacks: Queen, 2 (Total Hand Value = -3 + -2 + -10 + 12 + 2 = -1)
  • Missy: Reds: Ace, 7, Blacks: King, 4, 9 (Total Hand Value = -1 + -7 + 13 + 4 + 9 = 18)
  • Angela: Blacks: 2, 5, 7, King, Queen (Total Hand Value = 2 + 5 + 7 + 13 + 12 = 39)

The players then place their bets. Angela knows she has a high hand, so she places the highest bet with 5 chips. Both Sara and Missy decide to match the bet. Angela chooses not to replace any cards. Missy replaces one card, which is the red 7, and she gets a red 4. Sara asks to replace two cards, the red 10 and the red 3, and she gets a black Jack and a Black 10. Their new hands, along with their total values are as follows:

  • Sara: Reds: 2, Blacks: 10, Jack, Queen, 2 (Total Hand Value = -2 + 10 + 11 + 12 + 2 = 33)
  • Missy: Reds: Ace, 4, Blacks: King, 4, 9 (Total Hand Value = -1 + -4 + 13 + 4 + 9 = 21)
  • Angela: Blacks: 2, 5, 7, King, Queen (Total Hand Value = 2 + 5 + 7 + 13 + 12 = 39)

Angela chooses to raise the pot by adding in 2 more chips, and Sara and Missy both decide to stay in the game by matching her bet. When they show their cards, they see that Angela has the highest hand, so she wins the poker chips in the pot.

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