Dividing Integers
Objectives
• I can divide integers
• I can Interpret quotients of rational numbers by
describing real world situations
• I can use the rules for multiplying integers to develop
the rules for dividing integers
• I can explain why −
𝑝
𝑞
=
−𝑝
𝑞
=
𝑝
−𝑞
Round 1: Multiplication as Repeated
Addition
• Recalling that multiplication
• . is repeated
addition, use your Starburst counters to
create a display representing the following
expression:
3 groups of (-5)
• What is the product?
• How do we express this problem as repeated
addition?
• As multiplication?
• We added groups together
to get the total when we
multiplied.
• -5+-5+-5
• This is the same as 3(-5)
• Both gave us a total of -15
Round 2: Let’s Switch It Up!
• Now, push all of your
Starburst counters back
into 1 big group on the
right side of your desk.
• Take away 5 Starburst by
moving them in a group to
your left.
• Take away 5 more
Starburst.
• Take away 5 more Starburst
• This was repeated
subtraction. You
subtracted 5 repeatedly
until you reach zero.
Each subtraction is a group
of 5.
• How many Starburst do we
have left to take away?
• How many groups of 5 do
you have now??
• We just divided by 5!
That is the answer to the
division problem
• -15 ÷-5=3
Yay! Starburst!!!
“I pledge not to eat Starburst during the lesson.”
• Y
Summing It Up
• For the first round, we
added groups together
to get the total when
we multiplied.
• 3(-5)=-15
• For the second round,
we began with -15 and
subtracted in groups of
-5.
Division as Repeated Subtraction
• DIVISION is simply
repeated subtraction
• 20 ÷ 4 = 20
• 20 − 4 − 4 − 4 − 4
− 4 = 0.
I subtracted 4 five
times,
so 20 ÷ 4 = 5.
• Now you try it:
a) 20 + 20 + 20 + 20 +
20 =____
Therefore, ____ × ___ =
______
b)____ − 20 − 20 − 20
− 20 − 20 = 0
• ___ ÷ ___ = ___
• Based on all of our examples, we should
begin to see that multiplication is simply
adding groups together, while division is
pulling those groups back apart.
• Division is simply multiplication inverted!
Division is simply multiplication inverted!
• Since multiplication and division are
“inverse” (opposite) operations, this means
that we can create fact families like this:
If 4 • 3 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3.
If 2 • 5 = 10, then 10 ÷ ___ = ___ and 10 ÷ ___ = ___.
Division Sign Rules
• If division is multiplication inverted, then
what do you think that might mean for the
sign rules of division?
Dividing Integers:
The Rules
• That’s right! The sign rules for division are
the same as for multiplication…
Integer Division Tips
• The easiest way to divide integers is to divide the
absolute value (positive) of a signed number to
get a quotient, and then add the sign to the
answer at the end byusing the sign rules for
division.
• Remember!!! Division by zero is undefined:
You cannot find 10/0
Why? If you have 10 Starburst, you cannot divide
it between 0 people.
14 ÷ 2
Dividing Integers:
Try It Out
-40/(-8)
-32/(-4)
0 ÷ (-6)
−49
7
−21
−3
Reflection Questions – Talk with
your group
• How are quotients of signed numbers used in real world
situations? An $800.00 debt divided into 4 payments
-$800/4=-$200 per payment
• A 30 degree temperature increase divided over 6 hours
30/6=5 degrees increase per hour
• Can you come up with a story problem of your own using -50/2
??? (Hint: think of the (-) as a loss of something!)
Exit Ticket
• Mrs. McIntire, a seventh grade math teacher, is
grading papers. Three students gave the following
responses to the same math problem:
1
Student one:
−2
1
Student two: -( )
2
−1
Student three:
2
On Mrs. McIntire’s answer key for the assignment, the
correct answer is: −0.5. Which student answer(s) is/ are
correct? Explain.