Multiplying Integers

Multiplying Integers Preview

What You Will Learn

-Find products of positive integers.

-Find products of positive and negative integers. -Find products of negative integers.

-Evaluate numerical and algebraic expressions involving integer multiplication.

What is a product?

• A product is the answer of a multiplication problem.

• When we talk about products we are talking about multiplying integers.

• Remember that an integer is the set of whole numbers and their opposites, including 0.

Multiple Choice

Product is an answer to a ______________ problem.

• addition

• subtraction

• multiplication

• division

Multiple Choice

When we talk about products we are talking about adding integers.

• True

• False

Let’s look at finding the products of positive integers.

What does it mean to multiply?

Remember that multiplication is repeated addition. When a value is being multiplied repeatedly, we can say that multiplication is a short cut for this repeated addition.

Example 1

3(4) = ____

This means 3 times 4. A set of parentheses is a way to show multiplication.

This means that four is being added three times.

4 + 4 + 4 = 12

The answer is 12.

We can find the product of any two positive integers just as we would multiply any two positive whole numbers.

Example 2

5(7) = ____

7 + 7 + 7 + 7 + 7 = 35

The answer is 35.

These two examples point us to a rule.

Use what you have just learned to multiply the following positive integers.

Multiple Choice

8(3) = ____

• 11

• 24

• -24

• -11

Multiple Choice

5(9) = ____

• 14

• -14

• -45

• 45

Multiple Choice

2(7) = ____

• 14

• -14

• 9

• -9

II. Find Products of Positive and Negative Integers

We can also find products of positive and negative integers.

What does it mean to multiply a positive and a negative integer?

• When we multiply a positive and a negative integer, it means that the negative number is being added so many times.

• Once again, we have an example of repeated addition.

• Let’s look at an example....

Example 1

• 6(-5) = ____

• Here negative five is being added six times.

  -5 + -5 + -5 + -5 + -5 + -5 = -30

• The answer is negative thirty.

Example 2

• 2(-3) = ____

  
  

• Here negative three is being added twice. That is the repeated addition.

  -3 + -3 = -6

  
  

• The answer is -6.

We can write a rule for multiplying positive and negative integers based on these two examples.

Poll

Does it matter if we write the positive number first or the negative number first?

• Yes

• No

Does it matter if we write the positive number first or the negative number first?

No. It doesn’t matter because of the Commutative Property of Multiplication. 

Practice a few of these on your own.

Multiple Choice

3(-7) = ____

• -4

• -21

• 21

• 10

Multiple Choice

5(-9) = ____

• -4

• 45

• -45

• -14

Multiple Choice

4(-3) = ____

• -12

• 1

• -7

• 12

III. Find Products of Negative Integers

We can also find the product of two negative integers.

Let’s say that we wanted to multiply the following two negative integers.

(-5)(-2) = ____

We know that 5 times 2 is 10, but we don’t know what sign to use. Is the answer positive or negative?

Poll

(-5)(-2) = ____

Is the answer positive or negative?

• positive

• negative

Well, what happens if we multiply -5 and 0?

-5(0) = 0

The answer is zero.

What happens if we multiply -5 by 1?

-5(1) = -5

The answer is negative five. We already know that a negative times a positive is a negative.

What happens if we multiply -5 by 2?

-5(2) = -10

Open Ended

What happens if we multiply -5 by 2?

Notice that each time we multiply by a new digit in order, 0, 1, 2, we have a difference of five in our answer.

Here are the three products we just arrived at. These were the products of multiplying by 0, 1 and 2.

-5(0) = 0

-5(1) = -5

-5(2) = -10

We can say that if we multiply by -1 and -2, our answer will go 5 the other way. These moved negative. If we multiply by the opposite sign, the values should move positive.

−5(0)=0

−5(−1)=5

−5(−2)=10

Here is the rule for multiplying two negative integers.

Practice a few of these on your own.

Multiple Choice

-9(-8) = ____

• 72

• -72

• -17

• -1

Multiple Choice

(-4)(-12) = ____

• -16

• 8

• -48

• 48

Multiple Choice

(-5)(-13) = ____

• positive

• negative

You will need the rules for multiplying integers to evaluate expressions.

• Positive × positive = positive

• Negative × positive = negative

• Negative × negative = positive

If you multiply more than 2 integers, remember this...

• EVEN number of negative integers = positive

• EX: -1(-1)(-1)(-1) = 1 or EX: -1(1)(-1)(1) = 1

• ODD number of negative integers = negative

• EX: -1(-1)(-1) = -1 or EX: -1(1)(1) = -1

Multiple Choice

Will my product be positive or negative?

-2(-2)(-2)

• positive

• negative

Multiple Choice

Will my product be positive or negative?

-5(2)(-5)

• positive

• negative

Multiple Choice

Will my product be positive or negative?

3 x (-3) x (-3) x 3

• positive

• negative

Now that you have learned how to multiply integers, you are ready to put this into practice.

You may use your number chart located in your BULLDOG BINDER to help you

Multiple Choice

7 • 4

• 28

• -28

• 11

Multiple Choice

(-7)(-7)

• 14
• -14
• 49
• -49

Multiple Choice

-88 • 0

• 88
• -88
• 0
• -880

Multiple Choice

4(-20)

• 80
• -80
• 24
• -24

Multiple Choice

(-9)(-8)

• -72
• 72
• 81
• -81

Multiple Choice

What is Ms. Peyton's daughter's name?

• Kolbi

• Mikaela

• Peyton

• Ice

Multiple Choice

A negative times a positive equals

• zero

• a negative answer

• a positive answer

• one

Multiple Choice

A negative times a negative equals

• one

• a negative answer

• zero

• a positive answer

Multiple Choice

3(-3)(-3)

• 27
• -27
• 9
• -9

Multiple Choice

-4(-1)(-2)

• -8

• 8

• -7

• 7

Multiple Choice

Solve:
(-2)(-1)(-3)(-4)(-1)

• -11
• 24
• -24
• 11

Multiple Choice

Multiply
(5) • (–9) • (–2)

• 90
• -45
• -90
• 47