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Solving Multiplication and
1-4 Division Equations
Learn to solve equations using multiplication
and division.
Pre-Algebra
Solving Multiplication and
1-4 Division Equations
Vocabulary
Division Property of Equality
Multiplication Property of Equality
Pre-Algebra
Solving Multiplication and
1-4 Division Equations
You can solve a multiplication equation using the
Division Property of Equality.
DIVISION PROPERTY OF EQUALITY
Words
You can divide both
sides of an equation
by the same
nonzero number,
and the equation
will still be true.
Pre-Algebra
Numbers
Algebra
4 • 3 = 12
4 • 3 = 12
2
2
12 = 6
2
x=y
x=y
z z
Solving Multiplication and
1-4 Division Equations
Additional Example 1: Solving Equations Using
Division
Solve 8x = 32.
8x = 32
8x = 32
8
8
1x = 4
x=4
Divide both sides by 8.
1•x=x
Check
8x = 32
? 32
8(4) =
Substitute 4 for x.
? 32
32 =

Pre-Algebra
Solving Multiplication and
1-4 Division Equations
Try This: Example 1
Solve 9x = 36.
9x = 36
9x = 36
9
9
1x = 4
x=4
Divide both sides by 9.
1•x=x
Check
9x = 36
? 36
9(4) =
Substitute 4 for x.
? 36
36 =

Pre-Algebra
Solving Multiplication and
1-4 Division Equations
You can solve a division equation using the
Multiplication Property of Equality.
MULTIPLICATION PROPERTY OF EQUALITY
Words
You can multiply
both sides of an
equation by the
same number, and
the statement will
still be true.
Pre-Algebra
Numbers
2•3=6
4• 2•3=4•6
8 • 3 = 24
Algebra
x=y
z x = zy
Solving Multiplication and
1-4 Division Equations
Additional Example 2: Solving Equations Using
Multiplication
Solve n = 7.
7
n = 7• 7
7•7
n = 49
Multiply both sides by 7.
Check
n =7
7
?
49 =
7
7
? 7
7=

Pre-Algebra
Substitute 49 for n.
Solving Multiplication and
1-4 Division Equations
Try This: Example 2
Solve n = 16
4
n = 4 • 16
4•4
n = 64
Multiply both sides by 4.
Check
n = 16
4
64 =? 16
4
? 16
16 =

Pre-Algebra
Substitute 64 for n.
Solving Multiplication and
1-4 Division Equations
Additional Example 3: Food Application
Joe has enough flour to bake one sheet
cake but would rather make cookies. How
many dozen cookies can he make?
Dessert
Apple crisp
Pre-Algebra
Cups of Flour
1.5
Bread pudding
4
Cookies (1 doz.)
2
Pumpkin pie
1
Sheet cake
8
Tiramisu
3
Solving Multiplication and
1-4 Division Equations
Additional Example 3 Continued
cups of flour for
1 dozen cookies
2

number of
dozen cookies
•
2c = 8
2c = 8
2
2
c =4
c
=
cups of flour in
1 cake
=
8
Write the equation.
Divide both sides by 2.
Joe can make 4 dozen cookies with the same
amount of flour that he would need for 1 sheet cake.
Pre-Algebra
Solving Multiplication and
1-4 Division Equations
Try This: Example 3
cups of flour for
number of bread

bread pudding
pudding desserts
=
•
=
4
4b = 8
4b = 8
4
4
c =2
b
cups of flour in
1 cake
8
Write the equation.
Divide both sides by 4.
Joe can make 2 bread pudding desserts with the
same amount of flour that he would need for 1 sheet
cake.
Pre-Algebra
Solving Multiplication and
1-4 Division Equations
Additional Example 4: Money Application
Meg has saved $50, which is one-fourth of the amount
she needs for a school trip. What is the total amount she
needs?
fraction of amount
raised so far
1
4

total amount
needed
=
amount raised so
far
•
x
=
50
1 x = 50
4
4 • 1 x = 4 • 50
4
x = 200
Meg needs $200 total.
Pre-Algebra
Write the equation.
Multiply both sides by 4.
Solving Multiplication and
1-4 Division Equations
Try This: Example 4
The school library needs money to complete a new
collection. So far, the library has raised $750, which is
only one-eighth of what they need. What is the total
amount needed?
fraction of total

amount raised so far
1
8
•
total amount
needed
x
=
=
amount raised so
far
750
1 x = 750
Write the equation.
8
8 • 1 x = 8 • 750 Multiply both sides by 8.
8
x = 6000
The library needs to raise a total of $6000.
Pre-Algebra
Solving Multiplication and
1-4 Division Equations
Sometimes it is necessary to solve equations
by using two inverse operations. For instance,
the equation 6x  2 = 10 has multiplication
and subtraction.
Variable term
Multiplication
6x  2 = 10
Subtraction
To solve this equation, add to isolate the
term with the variable in it. Then divide to
solve.
Pre-Algebra
Solving Multiplication and
1-4 Division Equations
Additional Example 5: Solving a Simple Two-Step
Equation
Solve 3y – 7 = 20.
Step 1:
Step 2:
Pre-Algebra
3y – 7 = 20
+7 +7
3y
= 27
Add 7 to both sides to
isolate the term with y in it.
3y = 27 Divide both sides by 3.
3
3
y=9
Solving Multiplication and
1-4 Division Equations
Try This: Example 5
Solve 4y + 5 = 29.
Step 1:
Step 2:
Pre-Algebra
4y + 5 = 29 Subtract 5 from both sides to
– 5 – 5 isolate the term with y in it.
4y
= 24
4y = 24 Divide both sides by 4.
4
4
y=6