#### Integers - Multiplication and Division

**Multiplying of Two Integers (Positive and Negative Numbers)**

1) Multiply as usual

2) Determine the sign

(- 4) x (-5) = 6 x 3 =

……. If both signs are the same, the product or the answer is positive.

…….If the signs are different, the product or the answer is negative.

Memory Tip Story for Determining the Sign: Pretend you and a friend decide to share your favorite bag of candy. Your friend ends up with a different amount of candy than you. In fact he / she has a lot more than you, that’s a negative situation! On the other hand, if you both receive the same amount of candy, all is well. That’s a positive situation! The friendship is saved.

(- 4) x (-5) = +20 6 x 3 = 18

Recall, a number without a sign is considered positive.

**Division of Two Integers (Positive and Negative Numbers)**

1) Divide as usual (“/ ” represents a division sign)

2) Determine the sign

(- 32) / (-4) = 50 / 2 =

……. If both signs are the same, the quotient or the answer is positive.

…….If the signs are different, the quotient or the answer is negative.

Memory Tip Story for Determining the Sign: Pretend you and a friend decide to share your favorite bag of candy. Your friend ends up with a different amount of candy than you. In fact he / she has a lot more than you, that’s a negative situation! On the other hand, if you both receive the same amount of candy, all is well. That’s a positive situation! The friendship is saved.

(- 32) / (-4) = + 8 50 / 2 = 25

Recall, a number without a sign is considered positive.

**Multiplication and Division of Several Integers (Positive and Negative Numbers)**

1) Multiply or divide two numbers at a time

2) Then, follow above rules

**Example: 5 x (-2) x (-3) x 4 =**

Multiply 5 x (-2) = - 10 ..... negative, because the signs are different

Then, -10 x (-3) = 30 ........ positive, because the signs are the same

Then, 30 x 4 = 120 ............ positive, because the signs are the same

**Example: - 40 / (- 5) x 2 / - 4 =**

Divide (– 40) by -5 get + 8 .. positive, because the signs are the same

Next, 8 x 2 = 16 ............. positive, because the signs are the same

Then, 16 x (-4) = - 4 ....... negative, because the signs are different

**Alternative Method:**

1) Temporarily ignore the signs and multiply or divide

2) Count the negative signs

3) An odd number of negative signs produces a negative answer

An even, number of negative signs produces a positive answer

In the previous examples,

**5 x (-2) x (-3) x 4 =**, there are two negative signs which is an even number; thus, the answer is positive.

AND

**- 40 / (- 5) x 2 / - 4 =**has three negative signs which is odd number; thus, the answer is negative

**You Should Also Read:**

Integers - Adding Integers

Integers - Positive and Negative Numbers

Introducing Algebra - Unknown Variables

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