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 1Positive 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 4
4 4 4 4 4 4
Opposite of…
Opposite of…
Opposite of…
Opposite of…
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 2Multiplying 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 2Negative 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?
5 5 5 5 5
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
5 5
Opposite of…
Opposite of…
5
-40
Example 3Multiplying 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…
2 2 2 2 2
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
2 2
Opposite of…
Opposite of…
2 2
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
Opposite of…
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