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Daily Goals
• Today you will learn:
• How to multiply positive and negative numbers.
• How to Divide positive and negative numbers.
• Review for Exam on Monday
Class Work
Notes
Handout
Multiplication
Using Arrays
How many paper clips are here? I could count them,
but there is an easier way!
4 paper clips in each column
Now, how many paper clips are here? I can count
them by groups.
3 columns. That is 3 sets of 4. I can add 4 + 4 + 4 or
I could say 3 x 4. Now how many are there?
How many are here? What is the number
sentence?
You could have said 3 + 3 or 2 + 2 + 2. Using multiplication
You might have said 2 x 3 or 3 x 2. The answer will be the same for
all!
Try this one. What is the number sentence using
multiplication?
If you said 3 x 4 or 4 x 3 you are correct. What is the answer?
Now try this one. What is the multiplication fact?
Recorder/Reporter
Task Manager
Facilitator
Resource Manager
Great! 2 x 4 or 4 x 2. What is the product?
(that means answer when you are multiplying!
To find out how many stars there are, you could add.
2 yellow + 2 red + 2 blue = 6
stars
However, if you have equal groups of
something you can use
I see three groups of two.
3 groups x 2 = 6
stars
If you are having a party and you want
to have lots of sodas, you can use
multiplication.
Sodas come in groups of six.
Five groups of six would be 30 sodas.
5 x 6 = 30 sodas
Sometime multiplication can be used
when objects are in rows or columns,
or arrays.
Here is an array of flowers.
There are 3 rows of 6 flowers.
3 x 6 = 18 flowers.
How many groups?
How many in each group?
There are 3 groups of 4 balloons.
Equal numbers are in each group.
Multiplication can be used!
3 x 4 = 12 balloons
How many groups?
How many in each group?
There are 4 groups of 3 tires.
Equal numbers are in each group.
Multiplication can be used!
4 x 3 = 12 tires
When combining EQUAL groups,
the fastest way to get the total
is by using…
I know how to do
multiplication, but
what about division?
Don’t worry Woody,
it is easy to relate
multiplication and
division.
Multiplication is a shortcut for addition.
When you add, you combine amounts.
When you have equal amounts to add, you can
multiply to find the total.
There are 5 bicycles that need new tires.
How many tires is that?
Sample
2
+
2
You could add
2+2+2+2+2 to
find the total.
+
2
+
2
+
2
2 + 2 + 2 + 2 + 2 = 10
2 x 5
2 is the number of
tires on each bike.
= 10
Total number of tires
5 is the number
of bikes.
Division
is the operation of making equal
groups and finding the number in each group
or the number of groups.
Wow!!!!!!!
That sounds cool!
There are 12 stickers and 3 students. How many
stickers can each student get so that they
each have the same amount?
12 ÷
Total number of
stickers
3
=
4
Total number
of students
Number of stickers for
each student.
Sample
There are 18 cupcakes. How many cupcakes
can you put into 3 boxes so each
box has the same amount of cupcakes?
18 ÷ 3 = 6
Total number of cupcakes
Total number of boxes
Total number of
cupcakes for each box.
Just like subtraction is the
opposite of addition,
division is the opposite
of multiplication.
You can use what you know about multiplication
to help you with division.
Multiplication Facts
Related Division Facts
4 x 5 = 20
20 ÷ 5 = 4
5 x 4 = 20
20 ÷ 4 = 5
I’ll do
the multiplication
facts.
Ok, I’ll do the
related
division facts
24 ÷ 8 =
Think:
X
8 = 24
The number you need to write here
is called the missing factor.
=3
because
So, you know
Answer
24
=
3
3
x
÷
8
8
=
= 24
3
Yeah! We did it!
Multiplying and Dividing
Integers
Ms. Iovino
Lisa Iovino
Multiplying and Dividing Integers
To Multiply and Divide
Integers,
We use the same set of rules.
Lisa Iovino
Multiplying and Dividing Integers
Meet the Negative Family
The negative people live in
negativeland. In
negativeland, you must follow
the rules that are listed here.
Lisa Iovino
Multiplying and Dividing Integers
Rules to NegativeLand
• There are only two things that you can do
in negativeland (Shop or Math)
• You can only go shopping in negativeland,
if you have ONE other friend to go with.
• If you don’t go shopping you stay home
and do math (meaning you are in the
answer).
Let’s try a problem…..
4 x –2=
Lisa Iovino
Multiplying and Dividing Integers
Multiply, like you would
without the negative sign.
4 x 2=8
How many negative signs do
you see?
Lisa Iovino
Multiplying and Dividing Integers
One negative sign……
4 x –2=
One negative sign represents
one negativeland resident.
Does he have anyone to shop
with?
Lisa Iovino
Multiplying and Dividing Integers
Nope, He doesn’t…..
So he stays home in the
answer.
4 x –2= -8
Lisa Iovino
Multiplying and Dividing Integers
Try these problems…..
•
•
•
•
•
•
-5 x –3=
-8 x 3=
10/-2=
-14/-2=
-20/5=
-3 x –4 x –1=
Here are the answers…..
• -5 x –3= 15 The two negative people go
shopping.
• -8 x 3= -24 One negative sign makes a
negative answer.
• 10/-2= -5 One negative sign, negative answer.
• -14/-2= 7 Two negative signs cancel out.
• -20/5= -4 One negative sign, negative answer.
• -3 x -4 x-1= -12 Two negative signs cancel out
and one is left in the answer.
In conclusion, when
multiplying and dividing
integers, every two negative
signs cancel each other out.
Lisa Iovino
Multiplying and Dividing Integers
If you have an even number
of negative signs, your
answer is negative.
Lisa Iovino
Multiplying and Dividing Integers
If you have an odd number of
negative signs, your answer is
positive.
Lisa Iovino
Multiplying and Dividing Integers
Lisa Iovino
Multiplying and Dividing Integers