Multiplying and Dividing Integers

The lesson below is still images taken from the fully animated PowerPoint I created that is available in my Teachers Pay Teachers store page. If the PowerPoint is not one of my freebies, you may also head over to my YouTube channel to see the slideshow fully animated and can pause as needed to be sure you grasp each concept before moving forward (each lesson will always be free there!).

This lesson will continue our work with integers by explaining how to multiply and divide with both positive and negative numbers. Cheer up, this part is actually easier to remember than adding and subtracting! Just remember two rules: same signs mean a positive answer, and different signs mean a negative answer.

So without further ado, read through the slides below to get a feel for how to multiply and divide integers so that you’ll have a complete understanding of what to do with these new numbers!

Mult and Div Int 1Mult and Div Int 2Mult and Div Int 3Mult and Div Int 4Mult and Div Int 5Mult and Div Int 6Mult and Div Int 7Mult and Div Int 8Mult and Div Int 9

Phew, that’s a lot to take in. Once you’ve gone over this and found some practice problems to cement the idea in your head what integers are, you may move on to the next lesson below!

Properties of Numbers

Just in case the slides aren’t your thing, here is a text outline of the main points of the lessons above!

  • Integers
  • Multiplying and dividing integers
  • Objectives
  • By the end of this lesson you should feel comfortable:
  • Multiplying and dividing integers
  • Recognizing the Commutitive Property of mulitiplication
  • Signs signs signs
  • As you may have guessed by the title of this lesson, it is now time to expand our integer knowledge by multiplying and dividing these new numbers.
  • Luckily, the rules for these two operations are not only simpler, but they are also the same for both multiplication and division!
  • So let’s introduce the rules first, then really dive into what they mean.
  • Positive with positive
  • Ok, you’re skeptical after all those rules from the last lesson, right? That’s fair.
  • Let’s think critically about this then thanks to that healthy skepticism.
  • Our first rule seems to make sense with what we already know:
  • Two positive factors
  • Positive product
  • So the same signs made a positive answer.
  • Positive with positive
  • Multiplication isn’t the only place this works, however.
  • Let’s look at a division problem.
  • Again we have two positives to work with.
  • What about our quotient?
  • Also positive.
  • So division works exactly the same!
  • Negative with negative
  • But two positives isn’t the only way to have the same signs.
  • We may also see two negatives together.
  • First, we need something concrete to work with:
  • We have a negative and negative, so same signs.
  • Now we need to think critically about what is happening here.
  • We start with a negative number.
  • Then we are multiplying it by a negative quantity.
  • Remember, negatives negate, or make opposite, which makes our answer, the product, positive!
  • Positive with negative
  • The rule for dividing two negatives is the same as for multiplication (just like with two positives), so let’s move on to our other case:
  • As the title of this slide suggests, let’s observe what happens when we multiply a positive number by a negative number. Example:
  • So positive 2 and negative 3.
  • Different signs, so what happens?
  • Well, the negative changes our sign, which began positive.
  • So our answer has to be negative!
  • Negative with positive
  • Much like with adding integers, the order does not affect the product.
  • For example, let’s observe our last problem:
  • What would happen if we switched the order?
  • We still have 3 and 2 multiplied together which gives us 6.
  • Here, however, we begin with a negative number.
  • Simply multiplying by 2 cannot change our sign, so our answer must also be negative.
  • Now you can see that as long as the signs remain different, regardless of the order, the answer will be negative!
  • More examples
  • With what we now know, how about trying out a few problems that we might encounter?
  • In our first problem we have negative and negative, so same signs mean a positive answer.
  • 12 divided by 3 is 4, so that is our answer!
  • Next we have a positive and negative, so different signs means:
  • And our negative answer is 5×3=15, so:
  • Lastly, see if you can solve this one before clicking for the solution:
  • conclusion
  • Both multiplying and dividing integers follow the same two rules:
  • Same Signs = Positive Answer
  • Different Signs = Negative Answer
  • Positive x Positive = Positive
  • Negative x Negative = Positive
  • Positive ÷ Positive = Positive
  • Negative ÷ Negative = Positive
  • Positive x Negative = Negative
  • Negative x Positive = Negative
  • Positive ÷ Negative = Negative
  • Negative ÷ Positive = Negative