5.NF.3 Dividing Whole Numbers Using Picture Models that Lead to Mixed Number Quotients 7 ÷ 4 = 1¾ 8 ÷ 3 = 2 ⅔ 9 ÷ 4 = 2¼ 11 ÷ 3 = 3 ⅔

5.NF.3 Dividing Whole Numbers Using Picture Models that Lead to Mixed Number Quotients

7 ÷ 4 = 1¾

8 ÷ 3 = 2⅔

9 ÷ 4 = 2¼11 ÷ 3 = 3⅔

This skill is part of the Georgia Common Core Standard5.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.

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.

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.

8 ÷ 4 =

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

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?

Your problem will look like this.

We can use picture models to show the division.

8 ÷ 4 =

8 pieces ofcandy

among you and 3 friends

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?

Next, we will divide the candy to show the division.

We will divide the 8 pieces of candy equally among 4 friends.

8 ÷ 4 = 2

8 pieces ofcandy

among you and 3 friends

There are 2 piecesof candy in eachof the 4 circles.

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?

Friend 1

Friend 4Friend 3

Friend 2

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.

4__8

The division problem, 8 ÷ 4, can also be written as a fraction.

8 ÷ 4 means the same as

Fracti

on Division

Division as Fractions

A mixed number is a whole number and a fraction added together.

2 2__1

The 2 represents two wholes.

The fraction represents a part of a whole.

Sometimes when we divide whole numbers, the quotient, or answer, will be a mixed number.

+ =+ 2 2__1

Example:

1 ½1

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 thedividend, 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.

What do we want to divide amongthe group in this problem?

How many groups will the dividend be separated into?

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?

8 blueberry cupcakes 3 groups for 3 team members

We can write this division problem two ways:

8 blueberry cupcakes divided among 3 team members


8 ÷ 3

dividend divisor

or 3__8

dividend

divisor

Next, we will begin using picture models to divide the problem.

We know that we want to divide 8 cupcakes among 3 team members.

8765

432


1

We will use picture models to begin our division.We start with the 8 cupcakes, our dividend, or our numerator in a fraction.


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 2 left.

This is not enough

for each team member.


We will divide each of the 2 remaining cupcakes into 3 equalparts to distribute among the team players. Why 3 parts? We are sharing among 3 team members, so we need to dividethe remaining cupcakes into 3 equal parts to share.


We will distribute the remaining cupcakes equally among the 3. These cupcakes are now divided into 3 parts, or thirds.

All cupcakes have been distributed equally. We can now find the quotient, 0r our answer. Since all 3 groups have equal amounts, count the amountin one of the groups.

Each group has an equal amount:


1 1 ⅓ ⅓+ ++

8 ÷ 3 = 2⅔1 + 1 + ⅓ + ⅓ = 2⅔.

Let’s do another problem dividing whole numbers that will leadto 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 thedividend, 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?

Which number will be the divisor, or denominator? Hint: How many brothers?

Guided Practice

7 chocolate chip cookies – 7 is the dividend

4 brothers – 4 is the divisor

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.

There are 7 chocolate chip cookies left to be shared among 4 brothers. How many cookies will each brother get?

7 ÷ 4, 4__7

Guided Practice

Draw picture models of 7 chocolate chip cookies to be divided among the brothers.


You ca

n draw

some r

ound

circle

s.

Guided Practice


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


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

Guided Practice

and can be distributed equally among the brothers.


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


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.

Each of the 4 groups has an equal amount:

1 ¼¼¼ + ++ = 1¾

Guided Practice

1 + ¼ + ¼ + ¼ = 1¾. 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.

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.

Write the operation as a division problem. Then write it as a fraction.

Dividend: 11 Divisor: 3

Division: 11 ÷ 3 Fraction: 3

_____11

Practice

11 pieces of candy 3 friends


Draw picture models for the dividend.

Draw pictures for the items to be divided among the group.

You can draw

rectangles.

Practice

Practice

Distribute the candy equally among each person.

You will have some pieces left over.


Divide the remaining pieces of candy into equal parts.

Determine how many equal parts you will need then divide the remaining pieces of candy.

Practice

Each of the remaining will need three equal parts to share among the three friends.


Distribute the parts of each remaining pieces of candy.

Each person will get an equal number of parts.

Practice


Determine the quotient.

Each group has the same amount. Remember to count the parts as fractions.

Practice

++ + + = 3⅔

11 ÷ 3 = 3⅔


1 1 1 ⅓ ⅓

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.

Documents

5.NF.3 Dividing Whole Numbers Using Picture Models that Lead to Mixed Number Quotients 7 ÷ 4 = 1¾ 8 ÷ 3 = 2 ⅔ 9 ÷ 4 = 2¼ 11 ÷ 3 = 3 ⅔