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Lesson 3.5
Core Focus on
Introductory Algebra
Solving Multiplication and Division
Equations
Warm-Up
Solve each equation. Show all work and check your solution.
1. m + 72 = 100
m = 28
2. 220 = y − 101
y = 321
3. a − 6.6 = 8.9
a = 15.5
4. x + 84 = 233
x = 149
Lesson 3.5
Solving Multiplication and
Division Equations
Solve equations involving multiplication
or division.
Explore!
Multiplication Equations
Step 1 If you do not have an equation mat, draw one like the one seen below on a
blank sheet of paper.
Step 2 On the equation mat, place two variable
cubes on one side. On the other side of the
mat, place 6 chips. This represents the
equation 2x = 6.
Step 3 Divide the chips into two equal groups since there are two variable cubes.
How many chips are equal to one variable cube? This is the value of x.
Step 4 Clear the mat and place counters on the mat to represent the equation 4x = 8.
Draw this on your paper.
Step 5 How can you determine how many chips are equal to one variable cube?
Step 6 Create a multiplication equation on the mat. Record the algebraic equation on
your paper.
Step 7 Solve the equation. What does the variable equal?
Step 8 Write a few sentences that describe how to solve a multiplication equation
using the equation mat, chips and variable cubes.
The Multiplication Property of
Equality
For any numbers a, b and c:
If a = b, then a · c = b · c
The Division Property of Equality
For any numbers a, b and c:
a b
If a = b, then  .
c c
The fraction bar is used to show
division when solving equations.
Example 1
Solve each equation. Show your work and check your solution.
m
a.
3
8
m
8  38
8
m  24
24
3

8
y
b. 6.2 
3
y
3  6.2   3
3
18.6  y
18.6
 6.2 
3
Example 1 Continued…
Solve each equation. Show your work and check your solution.
c. 11p = 99
11 11a
p=9a
d. 12x = 60
12 12a
x=5 a
 11(9) = 99a
 12(5) = 60a
Example 2
Peter is four times older than his son, Matthew. Peter is 52
years old. Write a multiplication equation and solve the
equation to determine Matthew’s age.
Let m represent Matthew’s age. Write the equation that
represents this situation.
Peter’s age
Four times
4m = 52
Solve the equation by using division
(the inverse operation of multiplication).
Matthew is 13 years old.
4m = 52
4
4a
m = 13
Communication Prompt
You have learned how to solve four types of equations
in this Block (addition, subtraction, multiplication and
division). Explain how you are able to tell which
operation to use to solve an equation.
Exit Problems
Solve each equation. Show all work and check your solution.
1. 9x = 81
x=9
k
2. 7 =
4
k = 28
3. 1.5y = 6
y=4
4. Ethan is 4 times older than Juan. Ethan is 44 years old.
Let j represent Juan’s age. Write and solve a multiplication
equation to determine Juan’s age.
4j = 44; j = 11