Algebra2go®
Division with Negative Numbers
Objective 1
Perform Division with Negative Numbers
Remember that multiplication represents
repetitive addition of a number.
Recall 4 ⋅ 3 = 4 + 4 + 4 = 12
This means that “4 goes into 12” three times!
4
4
4
0
1
2
3 4
5
6
7 8
9 10 11 12 13 14
We can see that it takes three 4’s to make 12.
3.
12 , this means 12 ÷ 4 =
Since 4 ⋅ 3 =
12
12
Note: 4 = 3 since 4 ⋅ 3 =
Do you see a pattern in the above note?
( −4) + ( −4) + ( −4) =−12
Recall: −4 ⋅ 3 =
We can see that it takes three -4’s to make -12.
3.
− 12 , this means − 12 ÷(− 4) =
Since − 4 ⋅ 3 =
Note: −−12
4 = 3 since − 4 ⋅ 3 =− 12
Do you see a pattern in the above note? Notice
that negative divided by negative is positive!
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Algebra2go®
Understanding our multiplication tables can
help us with mentally determining basic
division problems.
Notice that since 7 ⋅ 3 = 3 ⋅ 7 =21 we can
conclude that
21 3=
21 7
=
d
an
.
3
7
Similarly, since -7 ⋅ 3= 7 ⋅(-3)= -21 we can
conclude that
-21 -3
-21 -7
an
=
=
d
.
3
7
We can now make a general conclusion
regarding division with integers.
When dividing two numbers with the same
sign, the quotient will be positive.
When dividing two numbers with different
signs, the quotient will be negative.
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Algebra2go®
Example 1: Find each quotient and then rewrite
it as an equivalent multiplication problem by
filling in the blank.
15
=
a) 5
-42
=
b) 7
45
=
c) -9
-54
=
d) -6
since 7 ⋅( ___) -42
=
since -9 ⋅ ___ 45
=
=
since -6 ⋅ ___ -54
0
=
e) -12
=
since -12 ⋅ ___ 0
-84
=
f) 4
=
since 4 ⋅( ___) -84
-128
=
g) 8
since 8 ⋅( ___) -128
=
162
=
h) -9
=
since -9 ⋅ ___ 162
216
=
i) -12
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since 5 ⋅ ____ 15
=
=
since -12 ⋅ ___ 216
Algebra2go®
Answer the following homework questions.
In Exercises 1 – 6, find each quotient.
÷ (-7)
132 ÷ (-11)
÷ (-8)
-54 ÷ 9
÷ (-4) ÷ 5
-56 ÷ (-7) ÷ 8
1) 28
3) -32
5) 40
2)
4)
6)
In Exercises 7 – 10, write each word statement as a mathematical
expression then find the value of the expression.
7) The quotient of -30 and 5.
8) Subtract -3 from the quotient of 27 and -9.
9) The quotient of -3 squared and -9.
10) The product of -1 and -4 squared, divided by -2.
In Exercises 11 – 19, evaluate each expression.
20
4(-6)
11) -4
14) -3
17) (-2)2 + 20 ÷ 4
0
7(-6)
2
12) -8
15) -3(-2)
18) -3 + 24 ÷( −8)
-6
2
2
2
13) 0
16) (-3) + 21 ÷ 7 19) -2 −(-8) ÷(-4)
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