Download “like” signs, the answer is always positive. Dividing

I positively
have negative
feelings about
this!
are positive and
negative “whole” numbers,
and zero.
…-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7…
Integers do not include fractions
or decimals.
When you think about it, integers
are everywhere.
They represent
temperatures…
and chemical
compounds.
They’re in bank statements…
Date
Withdraw
8/23
–$65
9/24
10/10
11/17
Deposit
Balance
$4,054
+$150
–$220
$4,204
$3,984
+$75
and golf scores.
$4,059
When we multiply or divide integers,
there are just a couple of rules we
need to remember.
Whenever we multiply two integers
with “like” signs, the answer is
always positive.
(+) × (+) = +
𝟕 × 𝟑 = 𝟐𝟏
Whenever we multiply two integers
with “like” signs, the answer is
always positive.
(−) × (−) = +
−𝟓 × (−𝟐) = 𝟏𝟎
Whenever we multiply two integers
with “unlike” signs, the answer is
always negative.
(+) × (−) = −
𝟖 × (−𝟐) = −𝟏𝟔
Whenever we multiply two integers
with “unlike” signs, the answer is
always negative.
(−) × (+) = −
−𝟔 × 𝟒 = −𝟐𝟒
Whenever we divide two integers
with “like” signs, the answer is
always positive.
+ ÷ + =+
𝟏𝟔 ÷ 𝟒 = 𝟒
Whenever we divide two integers
with “like” signs, the answer is
always positive.
(−) ÷ (−) = +
−𝟏𝟐 ÷ (−𝟒) = 𝟑
Whenever we divide two integers
with “unlike” signs, the answer is
always negative.
(+) ÷ (−) = −
𝟗 ÷ −𝟑 = −𝟑
Whenever we divide two integers
with “unlike” signs, the answer is
always negative.
(−) ÷ (+) = −
−𝟏𝟓 ÷ 𝟑 = −𝟓
What did you notice about the rules for
multiplying and dividing integers?
If you said they’re exactly the same,
you’re right!
Multiply or divide the following integers.
1) 𝟓 × −𝟔
=
2) −𝟏𝟐 ÷ −𝟒
=
3) −𝟏𝟎 × 𝟗
=
4) 𝟑𝟔 ÷ −𝟔
=
5) −𝟕 × −𝟓
6) −𝟖𝟖 ÷ 𝟏𝟏
=
=
Multiply or divide the following integers.
1) 𝟓 × −𝟔
= −𝟑𝟎
3) −𝟏𝟎 × 𝟗
= −𝟗𝟎
5) −𝟕 × −𝟓
= 𝟑𝟓
2) −𝟏𝟐 ÷ −𝟒
=𝟑
4) 𝟑𝟔 ÷ −𝟔
= −𝟔
6) −𝟖𝟖 ÷ 𝟏𝟏
= −𝟖
Here are some other ways that multiplying
and dividing integers might appear:
Multiplying with a raised dot or using parenthesis:
−𝟐 𝟔
𝟖(−𝟑)
(−𝟓)(−𝟏𝟏)
Dividing with a fraction bar:
𝟏𝟐
→
−𝟒
𝟏𝟐 ÷ (−𝟒)
−𝟗
→
−𝟑
−𝟗 ÷ (−𝟑)
But what if
I have to multiply
or divide more than
two integers
at once?
An expression with an even number of
negative integers will always produce a
positive answer.
An expression with an odd number of
negative integers will always produce a
negative answer.
Let’s take a look at a few examples!
Example 1:
−𝟐 × −𝟑 × 𝟒 × −𝟐 = −𝟒𝟖
Since there are 3 negative integers (an odd
amount), the answer will be negative.
Then, multiply from left to
right to find the product.
Perform the above calculation as instructed to check the answer given.
Example 2:
−𝟑𝟐 ÷ 𝟐 ÷ 𝟒 ÷ −𝟐 = 𝟐
2 negative integers (an even amount)
result in a positive quotient.
Divide from left to right to simplify.
Perform the above calculation as instructed to check the answer given.
Example 3:
𝟐𝟓 ÷ (−𝟓) × 𝟒 ÷ −𝟒 × (−𝟐) × (−𝟕)
= 𝟕𝟎
4 negative integers produce a
positive answer.
Multiply and divide from left to right
to simplify.
Perform the above calculation as instructed to check the answer given.
So, I just
count negative
signs to determine
the sign of my
answer?
Then I
just multiply or
divide from left
to right?
That’s it! An even number of negative
signs equals a positive answer, and an
odd number equals a negative answer.
Multiply and/or divide.
1) −𝟔 ÷ 𝟐 × 𝟕
2) −𝟒 × −𝟔 ÷ (−𝟐)
=
=
3) 𝟐𝟎 ÷ (−𝟒) × 𝟐 × 𝟖 ÷ (−𝟒)
=
4) −𝟏 × −𝟑 × 𝟏𝟎 ÷ (−𝟐) ÷ (−𝟑)
=
5) −𝟔 ÷ −𝟑 × 𝟕 ÷ (−𝟕) × (−𝟐𝟎) ÷ (−𝟖)
=
Multiply and/or divide.
1) −𝟔 ÷ 𝟐 × 𝟕
2) −𝟒 × −𝟔 ÷ (−𝟐)
= −𝟐𝟏
= −𝟏𝟐
3) 𝟐𝟎 ÷ (−𝟒) × 𝟐 × 𝟖 ÷ (−𝟒)
= 𝟐𝟎
4) −𝟏 × −𝟑 × 𝟏𝟎 ÷ (−𝟐) ÷ (−𝟑)
=𝟓
5) −𝟔 ÷ −𝟑 × 𝟕 ÷ (−𝟕) × (−𝟐𝟎) ÷ (−𝟖)
= −𝟓
Get the booklet from your
teacher and continue your
practice 
The end