5.NF.3 Dividing Whole Numbers Using Picture Models
that Lead to Mixed Number Quotients
This PowerPoint lesson will demonstrate how to solve
word problems involving division of whole numbers
that lead to answers in the form of mixed numbers.
This skill is part of the Georgia Common Core Standard
5.NF.3 Interpret a fraction as division of the numerator by the
denominator (a/b =a ÷ b). Solve word problems involving division of
whole numbers leading to answers in the form of fractions or mixed
numbers, e.g., by using visual fraction models or equations to
represent the problem.
Let’s review the meaning of division.
o
Division is a math term used to refer to distributing an
equal amount among a group.
Division word problem:
If you had 8 pieces of candy and you shared them equally with
3 of your friends, how many pieces would
each of you get?
o A division problem has three parts:
the dividend – the number being divided into groups
the divisor – the number of groups the dividend will be separated into
the quotient – the answer, or the number that each receives
Let’s review continued.
To solve the problem, your will need to determine which number is the
dividend and which is the divisor. Then you can find the quotient.
If you had 8 pieces of candy and you shared them equally with 3 of
your friends, how many pieces would each of you get?
Determine the dividend and the divisor of this word problem.
dividend – the number being divided into groups
8 pieces of candy
divisor – the number of groups the dividend will be separated into
you and 3 of your friends = 4
Your problem will look like this.
8 ÷4=
If you had 8 pieces of candy and you shared them equally with 3 of
your friends, how many pieces would each of you get?
 We can use picture models to show the division.
8 pieces of
candy
among you
and 3 friends
8 ÷4=
Next, we will divide the candy to show the division.
If you had 8 pieces of candy and you shared them equally among
you and 3 of your friends, how many pieces would each of you get?
 We will divide the 8 pieces of candy equally among 4 friends.
8 pieces of
candy
among you
and 3 friends
Friend 1
Friend 3
Friend 2
Friend 4
8 ÷4=2
There are 2 pieces
of candy in each
of the 4 circles.
Division as Fractions
The division problem, 8 ÷ 4, can also be written as a fraction.
A fraction is another way of representing the division of whole numbers.
o The numerator of a fraction, the number on top, is the dividend.
o The line is the divided by sign.
o The denominator, the number on the bottom, the is the divisor.
8
__
4
means the same as
8÷4
Sometimes when we divide whole numbers, the quotient,
or answer, will be a mixed number.
A mixed number is a whole number and a fraction added together.
1
__
Example: 2
2
The 2 represents two wholes.
The fraction represents a part of a whole.
1
+
1
+
½
1
__
= 2
2
Let’s solve a division word problem using pictures models
that will have a mixed number for the answer.
Word problem:

There are 8 blueberry cupcakes to share among 3 team members.
How many cupcakes will each team member get.?
To solve this problem we first need to figure out which number is the
dividend, or numerator, and which number is the divisor, or denominator.
 The dividend is the number of cupcakes that will be divided among
the group.
 The divisor is the number of team members that will get the
cupcakes.
Remember:
 The dividend the number being divided into groups
 The divisor is the number of groups the dividend will be
separated into

There are 8 blueberry cupcakes to share among 3 team members.
How many cupcakes will each team member get?
What do we want to divide among
the group in this problem?
8 blueberry cupcakes
How many groups will the
dividend be separated into?
3 groups for 3 team members

There are 8 blueberry cupcakes to share among 3 team members.
How many cupcakes will each team member get?
We can write this division problem two ways:
8 blueberry cupcakes divided among 3 team members
8 ÷3
or
8
__
3
Next, we will begin using picture models to divide the problem.

There are 8 blueberry cupcakes to share among 3 team members.
How many cupcakes will each team member get?
We know that we want to divide 8 cupcakes among 3 team members.
We will use picture models to begin our division.
We start with the 8 cupcakes, our dividend, or our numerator in a fraction.
1
2
3
4
5
6
7
8

There are 8 blueberry cupcakes to share among 3 team members.
How many cupcakes will each team member get?
Now we’ll divide the cupcakes equally among the three. We will use ovals to
represent the 3 team member then distribute the cupcakes among the three.
We will stop when we don’t have an equal amount for each oval.

There are 8 blueberry cupcakes to share among 3 team members.
How many cupcakes will each team member get?
We will divide each of the 2 remaining cupcakes into 3 equal
parts to distribute among the team players. Why 3 parts?
We are sharing among 3 team members, so we need to divide
the remaining cupcakes into 3 equal parts to share.

There are 8 blueberry cupcakes to share among 3 team members.
How many cupcakes will each team member get?
We will distribute the remaining cupcakes equally among
the 3. These cupcakes are now divided into 3 parts, or thirds.

There are 8 blueberry cupcakes to share among 3 team members.
How many cupcakes will each team member get?
All cupcakes have been distributed equally. We can now find the quotient,
0r our answer. Since all 3 groups have equal amounts, count the amount
in one of the groups.
1
+ 1 +⅓ + ⅓
Each group has an equal amount:
1 + 1 + ⅓ + ⅓ = 2⅔.
8 ÷ 3 = 2⅔
Guided Practice
Let’s do another problem dividing whole numbers that will lead
to an answer that is a mixed number. For this example, get your
paper and pencil and follow along with each step of the problem.
Word problem:
 There are 7 chocolate chip cookies left to be shared among 4 brothers.
How many cookies will each brother get?
To solve this problem, we first need to figure out which number is the
dividend, or numerator, and which number is the divisor, or denominator.
 Which number will be the dividend, or numerator?
Hint: What’s divided among the brothers?
7 chocolate chip cookies – 7 is the dividend
 Which number will be the divisor, or denominator?
Hint: How many brothers?
4 brothers – 4 is the divisor
Guided Practice
 There are 7 chocolate chip cookies left to be shared among 4 brothers.
How many cookies will each brother get?
We have determined the dividend and the divisor.
Dividend – 7
Divisor 4
 Write the problem first as a division problem and then as a fraction.
For the fraction, the dividend is the numerator and the divisor is the
denominator.
7
__
7 ÷ 4, 4
Guided Practice
 There are 7 chocolate chip cookies left to be shared among 4 brothers.
How many cookies will each brother get?
 Draw picture models of 7 chocolate chip cookies to be
divided among the brothers.
Guided Practice
 There are 7 chocolate chip cookies left to be shared among 4 brothers.
How many cookies will each brother get?
Now distribute the cookies.
 Draw 4 circles to represent the four brothers and put one cookie
in each until they all have the same number of cookies. Some cookies
will be left over.
Hint: On your paper, mark an ‘X’ to show you have distributed a cookie.
Guided Practice
 There are 7 chocolate chip cookies left to be shared among 4 brothers.
How many cookies will each brother get?
Divide the remaining cookies.
 There are 3 cookies left. Divide each of the 3 cookies into 4 equal pieces.
Each of the cookies are now divided into fourths
and can be distributed equally among the brothers.
Guided Practice
 There are 7 chocolate chip cookies left to be shared among 4 brothers.
How many cookies will each brother get?
Distribute the divided pieces of cookies.
 Put one fourth of each cookie into each circle until all pieces are gone.
Hint: Mark each fourth of a cookie with an ‘X’ as you distribute them.
Guided Practice
 There are 7 chocolate chip cookies left to be shared among 4 brothers.
How many cookies will each brother get?
Each group has an equal amount of cookies. Determine your answer.
 Count the cookies in one of the groups to find how many each will get.
+ ¼ +
¼ + ¼ = 1¾
Each of the 4 groups has an equal amount:
1 + ¼ + ¼ + ¼ = 1¾.
1
7 ÷ 4 = 1¾
Practice
Get ready to show how easy it is to divide whole numbers
leading to answers in the form of mixed numbers. You will be
given a problem to solve one step at a time. Then you can
check your work against the slide after each step.
Practice
Word problem
Three friends were given a pack of candy to share equally among each other.
There were 11 pieces of candy in the pack. How many pieces of candy will each
receive?
 Decide which number is the dividend and which is the divisor.
Dividend: 11
11 pieces of candy
Divisor: 3
3 friends
 Write the operation as a division problem. Then write it as a fraction.
Division: 11 ÷ 3
Fraction:
11
3
_____
Practice
 Three friends were given a pack of candy to share equally among each other.
There were 11 pieces of candy in the pack. How many pieces of candy will
each receive?
 Draw picture models for the dividend.
Draw pictures for the items to be divided among the group.
Practice
 Three friends were given a pack of candy to share equally among each other.
There were 11 pieces of candy in the pack. How many pieces of candy will
each receive?
 Distribute the candy equally among each person.
You will have some pieces left over.
Practice
 Three friends were given a pack of candy to share equally among each other.
There were 11 pieces of candy in the pack. How many pieces of candy will
each receive?
 Divide the remaining pieces of candy into equal parts.
Determine how many equal parts you will need then
divide the remaining pieces of candy.
Each of the remaining will need three equal parts to share among the three friends.
Practice
 Three friends were given a pack of candy to share equally among each other.
There were 11 pieces of candy in the pack. How many pieces of candy will
each receive?
 Distribute the parts of each remaining pieces of candy.
Each person will get an equal number of parts.
Practice
 Three friends were given a pack of candy to share equally among each other.
There were 11 pieces of candy in the pack. How many pieces of candy will
each receive?
 Determine the quotient.
Each group has the same amount. Remember to count the
parts as fractions.
1
+
1
+
1
+ ⅓ + ⅓ = 3⅔
11 ÷ 3 = 3⅔
 You have learned in this lesson how you can divide whole
numbers leading to answers in the form of mixed numbers.
 You have also learned that a fraction is also a division
problem and to interpret a fraction as division of the
numerator by the denominator.