MULTIPLYING INTEGERS By Rose Eisenmenger

What Is Multiplication?  A number of groups of a number  Example: 6 x 3 is the same as saying 6 groups of 3  This could be shown as:

What Is Multiplication?  It could also be said in a word problem, Mary had 5 friends coming over, and she wanted each person, including herself, to have 3 chocolates. How many chocolates would she need to buy?  Therefore, multiplication can be shown as:  an equation 6 x 3  word problem Mary had 5 friends …  picture

Example 1 Multiplying A Positive By A Negative  Let’s try another problem using equation, word problem, and a picture  Equation  6 x -4  Word Problem  Suzie owed 6 of her friends 4 dollars. How much money did she owe?

Example 1 Positive x Negative Picture  Here are 6 boxes of 4, but we need six boxes of negative four  Another way to say negative is, the opposite of, so we need the opposite of Opposite of… *Since we are doing the opposite of 6 x 4 which equals 24, our product will be the opposite! What do you think the answer is? -24

Example 2 Multiplying A Negative By A Positive  We will also use an equation, word problem, and picture for this problem  Equation  -8 x 5  Word Problem  8 people got a letter in the mail from the bank stating that they received 5$. One week later, the same eight people got another letter saying that the bank made a mistake and meant to say that they owed the bank 5$.

Example 2 Negative x Positive Picture  Here are 8 boxes of 5, but we need negative 8 boxes of 5  Another way to say negative is, the opposite of, so we need the opposite of 8 boxes   Since we are doing the opposite of 8 x 5 where we would get a positive answer, we will get an negative product. What do you think the answer is? Opposite of…

Example 3 Multiplying A Negative By A Negative  Guess what? We are going to use the same method for this problem too!  Equation  -9 x -2  Word Problem  There were many people at the dog park, but only nine of the people brought two dogs each. All 18 of those dogs found a way to escape under a fence, and became lost. The owners of the dogs went home dog-less and felt “negative” or sad. The next day, all the dogs returned home, which made the owners feel positive!

Example 3 Negative x Negative  We have 9 boxes of two, but we need negative nine boxes of negative two.  Another way to say that is… Opposite of… *We have one “opposite of” for each negative number per box *Since there are two negative numbers or “Opposite of…” per box, they cancel each other out *Therefore, your answer will be positive *What do you think your answer will be? 18

Let’s Try Some!  6 x -7  -8 x 4  -3 x 5  -6 x -1  Challenge: -2 x 0 = -42 = -15 =6 = -32 =0

Multiplying Integers Rules  A positive times a negative equals a negative(pxn)  A positive times a positive equals a positive (pxp)  A negative times a negative equals a positive(nxn)  Between the two factors and the product, there should either be 2 negative numbers or zero negative numbers