Multipling Integers 1-6

​Lesson 1-6:
Multiplying Integers

By Reese Henrie

Multiplication

​How many times you add a number!

Multiplying integers is a shorthand way of adding the same number to itself a certain number of times.
Imagine the expression 4x5. How would you write this as an addition exression? Go to the next slide when you have your answer.

Multiple Select

How would you write 4x5 as an addition problem?

• 4+4+5+5

• 5+5+5+5

• 4+4+4+4+4

That's right!

4x5 would be written as 4+4+4+4+4 or 5+5+5+5. That's five fours, or four fives. All multiplication works this way. Let's practice a few more multiplication questions!

Quick Tip!

​Use number lines for multiplication!

You can recreate the addition setup we did for 4x5 with a number line. Try marking out 4 points of 5 on a number line to fine 4x5!

Multiple Select

What is 4x5?

• 9

• 20

• 45

Multiple Choice

What is 9x10?

• 109

• 19

• 90

Multiple Choice

What is 10x9?

• 19

• 90

• 109

Multiple Choice

Story problem!

A beach erodes 4 inches every year. How many years will it take for the beach to erode by 3 feet?

• 9 years

• 3 years

• 4 years

Open Ended

What did you notice while doing the problems?

​What did you notice?

Multiplication is commutative - that is, AxB is the same as BxA. You should have noticed this with questions 2 and 3, which had the same answer. Keep this in mind for the next section.

What happens when you multiply a positive and negative number? Try writing out -5x4 in the addition style like we did earlier. Think hard about how this would look!

Negative x Positive

Multiplying Negative Integers

Multiple Select

What does -5x4 look like?

• -5-5-5-5

• -(4+4+4+4+4)

Multiplying Negative Integers

Negative x Negative

If a negative integer times a positive integer results in a negative integer product, then what do you think a negative integer times another negative integer looks like?

Multiple Select

What does -5x(-4) look like?

• -(-5-5-5-5)

• -(-4-4-4-4-4)

Open Ended

What did you notice during your negative multiplication?

Multiplying Negative Integers

​What did you notice?

A positive times a negative is negative, but a negative times a negative is positive.
Here's an easy way to think about it - if the two numbers have the same sign, it's positive! But if they have different signs, it's negative.

Open Ended

How do the signs of factors affect their product?

Multiplying <2 Integers

​All positive

When multiplying more than two integers, work left to right and follow the same process as before. For example, take 4x5x2. How would you write this out in addtiton form?
To start, take 4x5, which we've already done. We know that this goes to 20. Now, what would 20x2 looks like?

Multiplying <2 Integers

All positive

That's right! 4x5x2 becomes 20x2, which can be written as 20+20. This equals 40!

Multiplying <2 Integers

Including Negatives

Let's say you have more than 2 integers and at least one of them is negative. How would you multiply this? Think about how you multiply more than 2 integers when there only positives, and apply that to this.

Open Ended

How would you multiply more than 2 integers when there's a negative integer involved?

Multiplying <2 Integers

​Including Negatives

That's right! Go left to right like you did earlier, taking into account the same sign = positive and different signs = negative rule like we learned.

Now, let's finish with some practice questions! Once you've finished problems X through X on pages X and X, go ahead to the next slide!

Poll

Did you finish the lesson?

• Yes, I am a good student

• No, I got to the end of the slideshow without finishing the lesson somehow