Math 5
Unit 2
Lesson 8
Division Equations
Home Organization
Alyssa is well organized. She wants all of her purses to be lined up on 3
shelves in her closet, with 4 purses on each shelf. Alyssa must have
exactly enough purses to organize her closet this way. This means that
Alyssa has 12 purses.
3 Shelves
12 Purses
4 Purses on Each Shelf
In this problem, Alyssa needed to find out how many purses she could
arrange in the way she wanted. This involved filling each position until the
purses were organized.
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Math 5
Unit 2
Lesson 8: Division Equations
Reflection
How does this relate to a multiplication equation?
Objectives for this Lesson
In this lesson you will explore the following concepts:
• S
olve a given single-variable division equation with
an unknown
• Solve problems involving one-step equations
Division Equations
Division equations will look like this:
x ÷ 4 = 6
y
= 12 3
32 = m
2
The inverse operation of multiplication is division. You used this in
solving multiplication equations in Lesson 7. Look at the relationships
in these equations:
Multiplication
Division
4(12) = 48
48 ÷ 12 = 4
3(5) = 15
6(7) = 42
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15 = 3
5
42 = 6
7
Math 5
Unit 2
Lesson 8: Division Equations
The inverse operation of division is multiplication. This property allows
you to solve division equations.
Modelling Division Equations
You can use cups and counters as one way to model a division equation.
Example 1
Solve x ÷ 6 = 3 using cups and counters.
1. Since the variable is divided by 6, you need 6 cups or counters.
2. The right side is 3 so we need to fill each cup with 3 counters.
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Math 5
Unit 2
Lesson 8: Division Equations
3. The answer is the total number of counters in the model.
The answer is: x = 18
Another way to model an equation is to use an area model.
Example 2
Solve c = 5 using a visual model.
4
1. Draw a picture of the variable as a rectangle.
C
2.Since the variable is divided by 4 in the equation, divide the rectangle
into 4 equal parts.
3. Now place 5 in each section.
5
5
5
4. How many are in the total?
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c = 20
5
Math 5
Unit 2
Lesson 8: Division Equations
Look at instruction 3 of this example. There are 4 sections of 5 for a total
of 20. This means that to solve the equation, you multiplied 4 times 5.
The Multiplication Property of Equality
The two sides of an equation remain equal if
both sides are multiplied by the same number.
Remember, the inverse of division is multiplication. You can multiply both
sides of the equation by the divisor to get the solution.
c =5
4
Y c = 5(4)
(4)
Y
c = 20
4
Equation
Multiply both sides by the divisor.
Answer
Let’s Explore
Exploration 1: Division Equations
Materials: Unit 2, Lesson 8, Exploration 1 page from your Workbook, paper, pencil
Solve the following division equations using the rectangle
provided. Separate the rectangle into the sections needed to
model the problem.
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Math 5
Unit 2
1.m = 4
3
Lesson 8: Division Equations
2. m = 3
2
m =3
3.
6
4. m = 4
5
5. What is the operation that you would use to find the answer?
6.Can you find the answer using the operation without the model? Why
or why not?
Solving Division Equations Using the Rule
Now try solving one without a model. To check and see if you are correct,
put the number back in the equation and divide. If the statement is true,
it is correct.
Example 3
Solve n = 8 using the rule for division equations and check.
3
1. Write the equation.
n =8
3
2. Multiply both sides by the divisor 3.
(3)
n = 8(3)
3
3. Write the solution.
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n = 24
Math 5
Unit 2
Lesson 8: Division Equations
4. Check the solution:
n =8
3
(3) n3 = 8(3)
n = 24
24 = 8
3
8=8
This is what the
entire problem
will look like on
your paper.
5. The answer is: n = 24
Now It’s Your Turn
Solve and check each equation.
a. j ÷ 3 = 5
b. h = 2
6
c.
t =7
4
b.
c.
t = 28
Solutions
a. j = 15
h = 12
Let’s Practice
• In your Workbook turn to Unit 2, Lesson 8 and complete 1 to 18.
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Math 5
Unit 2
Lesson 8: Division Equations
Problem Solving with Division Equations
Division equations have clue words to let you know that
you need to divide.
Variable
Equal Sign
Division
a number
some number
what number
is
equals
gives
yields
are
were
will be
per
a
out of
ratio of
quotient of
divided by
You can use the clue words to identify the parts of the equation.
Variable
Division
n = 8
3
Equal Sign
Here are some sentences that have been written as division equations.
Words
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Equations
the quotient of a number and 3 is 5
n÷3=5
n =5
3
a number divided by 4 equals six
y÷4=6
y
=6
4
Math 5
Unit 2
Lesson 8: Division Equations
Here is an example of how to write a division equation from a sentence:
Example 4
Write an equation for the sentence:
A number divided by seven equals nine.
1. Circle the operation and equation words.
A number
divided by seven equals nine.
2. Write the division symbol and equal sign over the clue words.
÷
=
A number divided by seven equals nine.
3. Underline the words for the numbers and for the variable.
÷
=
A number divided by seven equals nine.
4. Write in the variable and numbers.
÷
=
b
7
9
A number divided by seven equals nine.
5. Write the equation.
b÷7=9
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Math 5
Unit 2
Lesson 8: Division Equations
Now It’s Your Turn
Write an equation for each sentence.
a. The quotient of a number and eleven is 10.
b. A number divided by six equals twelve.
c. A number divided by four equals two.
Solutions
a. n ÷ 11 = 10
b. y ÷ 6 = 12
c. b ÷ 4 = 2
Let’s Practice
Go online to watch the Notepad Tutor about Division Equations.
• In your Workbook turn to Unit 2, Lesson 8 and complete 19 to 24.
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