Adding and Subtracting

Designed and Created by Leslie James Click the arrow to get started

Adding and Subtracting Fractions

Tutorials

Guided Practice

Quiz

Help !

Click to see the Program Objective

Equality

Adding fractions with LIKE Denominators

Changing denominators in fractions with UNLIKE Denominators

Changing numerators in fractions with UNLIKE denominators

Click on a topic!

Click to view Objective 1Main Menu

EqualityClick the box below to watch a video about

equality.

Click to continueMain Menu

Equality

Equality in Math is when two items (numbers, equations, fractions, etc.) are equal.

3 x 5 = 15

4 + 2 = 3 x 2

24 – 4 = 5 x 4Click to continueMain Menu

Equality

Click on a topic to see examples of equalities or take the Quiz

Equations

FractionsNumbers

Items

Take the QUIZ!

Main Menu Click here to see the objective

Examples of Equations that are Equal

2 + 3 = 3 + 2 (They both equal 5)

10 – 7 = 20 – 17 (They both equal 3)

6 x 6 = 4 x 9 (They both equal 36)

Equality MenuMain Menu

Examples of Numbers that are Equal

1,045 = 1,045

62 = 62

4 = 4

4,321,092 = 4,321,092

743 = 743

9,782 = 9,782

0 = 0

15 = 15


Examples of Items that are Equal

=

=

=

=


Examples of Fractions that are Equal

2

4

1

2=

3

4

6

8=

=

=


Equality Quiz

Are the following items equal?

ContinueMain Menu

Equality Quiz

4 x 3 = 6 + 6

Are they equal?

YES NO

GOOD! Click

Continue.

Sorry, these are equal. They both equal 12.

Continue

Equality Quiz

14 – 6 = 15 - 8

Are they equal?

YES NO

These are not equal. One

equals 8, and one equals 7.

These are NOT equal.

Continue

Equality Quiz

Are they equal?

YES NO

GOOD! Click

Continue

Sorry, these are equal. They both equal one half.

3

6=

1

2

Continue

Equality Quiz

Are they equal?

4,980,089 = 4,089,980

YES NO

Sorry, these are not equal.

Good! These are not equal. Click next!

Continue

Equality Quiz

Are they equal?

YES NO

GOOD!

Sorry, these are equal. They both equal one half.

2

3=

6

9

Equality Menu

Adding and Subtracting with Like Denominators

Click the box below to watch a video about adding and subtracting fractions



Here are the steps:1. Look at the two fractions. Do the denominators

match? If yes, keep going. If no, click here for steps for adding fractions with unlike denominators

2. Add or subtract the numerators (top numbers).

3. Slide the denominator into the answer. It stays the same.

4. You are finished. If done correctly, you should have an answer that has the same denominator as the two original fractions and the numerator should be the original numerators added or subtracted.

Try Some!Main Menu


1

2

4

4+

1

2+

3

4

Add the numerators

(top numbers)

Keep the denominators

(bottom numbers)

the sameClick to ContinueMain Menu

Try one on your paper and check your answer

2

5

2

5+

4

5

Did you get the correct answer?

If yes, click Main Menu and choose where to

go next.

If no, click here and view the tutorial again

Main Menu Click here to see the objective

Changing denominators in fractions with

UNLIKE Denominators

Click the box below to watch a video about adding and subtracting fractions



Now that you’ve watched the video about adding and subtracting fractions with different

denominators, let’s look at the steps.

Click to continueMain Menu Click here to see the objective


Step 1 – Find a common denominatorTo find a common denominator, you must find a number that is a multiple of both of

the denominators. The lowest one is usually the easiest to work with.

So, if you have the two denominators of 3 and 5 you must find a multiple that they

have in common.



Think about the multiples of 3 and 5

3’s multiples – 3, 6, 9, 12, 15, 18, 21, 24, 27

5’s multiples – 5, 10, 15, 20, 25, 30, 35, 40

Which multiple(s) do they have in common?



The multiple that they have in common is 15

3’s multiples – 3, 6, 9, 12, 15, 18, 21, 24, 27

5’s multiples – 5, 10, 15, 20, 25, 30, 35, 40

We have found a common denominator

Main Menu Click to continue


Now that we have a common denominator, let’s change the numerators.


1

3

1

5+

=

=

15

15

In order to change the numerator, you must find out what you multiplied the denominator by to

get the new denominator.

Click here to see the objective


Now that we have a common denominator, let’s change the numerators.


1

3

1

5+

=

=

15

15

Once you have found what you multiplied the denominator by to get the new denominator,

multiply the numerator by the same number.

X 5

X 3

X 5

X 3

5

3

Click to see the objective

Adding fractions with UNLIKE Denominators

Click to continue

TA DA! That’s all there is to it. Now you just add them together!

515

315

+

Don’t Forget!

Only add the numerators, the

denominators stay the same (15).

8

15Main Menu


Let’s try one more!

12

2

6+

=

=

First, find the common

denominator.

If you need help finding a common denominator click

here.

Main Menu Click to continueClick here to see the objective

Multiplication Chart

This can be helpful if you are having trouble finding a common denominator. Just find the two denominators along the left side and

trace across until you find a number they have in common.

ContinueMain Menu

Multiplication Chart

If you denominators are 2 and 6, just trace across the 2 and the 6 until you find the lowest number that they have in common.

Main Menu Click to Continue



12

2

6+

=

=

Write down the common

denominator.

6

6



1

2

2

6+

=

=

Figure out what you multiplied the

original denominator by to

get the new denominator.

If you need help finding a common denominator click

here.


6

6

X 3

X 1




1

2

2

6+

=

=

Multiply the numerator by the

same thing.

If you need help finding a common

denominator click here.


6

6

X 3

X 1

X 3

X 1

3

2




1

2

2

6+

=

=

Add or subtract.


6

6

X 3

X 1

X 3

X 1

3

2

65


5

6

Is the answer!!

Main MenuClick here to see the objective for this lesson

Guided Practice Menu

Like Denominators

Unlike Denominators

Click which topic you would like to work on

Main Menu

Guided Practice – Like Denominators

2

3

1

3+

Try to solve the following problem on your paper and

check your answers. If you get them wrong,

follow the steps to determine where you mistake was.

Do not click continue until you are

ready to check your answerClick here to see the objective


2

3

1

3+

3

3

Is this the answer that you got?

If yes, click here to try some more.

If no, click here to find your

mistake.

Main Menu


2

3

1

3+

3

First, check your denominators. Do

they match? If yes, then go ahead

and write that number in the

answer.

Click to Continue


2

3

1

3+

3

Second, add or subtract your numerators.

2 + 1 = 3So the answer is 3

3C

Click to Continue

If you are still having trouble with adding and subtracting with like

denominators, click here to go back and review the tutorial.

If you understand now where you made your mistake, click here to continue with the guided practice.

Main Menu


1

4

2

4+







1

4

2

4+

3

4




mistake.

Main Menu


1

4

2

4+

4




answer.

Click to ContinueMain Menu


1

4

2

4+

4



4

Continue




Main Menu


3

7

2

7+







3

7

2

7+

5

7




mistake.

Main Menu


3

7

2

7+

7




answer.

Click to Continue


3

7

2

7+

7



7

Click to continue




Main Menu


5

8

2

8+







5

8

2

8+

7

8




mistake.

Main Menu


5

8

2

8+

8




answer.

Click to Continue


5

8

2

8+

8



8

Click to Continue




Main Menu


3

6

1

6+







3

6

1

6+

4

6


If yes, click here to go back to the guided practice

menu.


mistake.

Main Menu


3

6

1

6+

6




answer.

Click to Continue


3

6

1

6+

6



6

Click to Continue



If you understand now where you made your mistake, click here to go back to the Guided Practice

Menu.

Main Menu

Guided Practice – Unlike Denominators

1

2

1

5+







1

2

1

5+

7

10




mistake.

Main Menu


1

2

1

5+

First, check your denominators. Do they match? If no, you will need to find a common denominator. If you are having trouble finding

the common denominator, click here.

Click to Continue

The blue circles represent other common multiples, but we usually want the smallest one.

Click to continue


1

2

1

5+

The common denominator is 10.

Next you need to figure out what you multiply

the original denominator by to get the new

denominator.

10

=

=

10

10

X 5

X 2



1

2

1

5+

Now multiply the original numerator by the same number that

you multiplied the original denominator by.

10

=

=

10

10

X 5

X 2

X 5

X 2

5

2



1

2

1

5+

Now just add the numerators and keep the denominator the

same.

10

=

=

10

10

X 5

X 2

X 5

X 2

5

2

7

5 + 2 = 7


If you are still having trouble with adding and subtracting with unlike



Main Menu


1

3

1

4+





ready to check your answerMain Menu Click here to see the objective


1

3

1

4+

7

12




mistake.

Main Menu


1

3

1

4+





Click to continue


1

3

1

4+




denominator.

12

=

=

12

12

X 4

X 3



1

3

1

4+



12

=

=

12

12

X 4

X 3

X 4

X 3

4

3



1

3

1

4+


same.

12

=

=

12

12

X 4

X 3

X 4

X 3

4

3

7

4 + 3 = 7





Main Menu


3

4

1

7-







3

4

1

7-

12




mistake.

Main Menu


3

4

1

7-





Click to Continue


3

4

1

7-




denominator.

28

=

=

28

28

X 7

X 4



3

4

1

7-



28

=

=

28

28

X 7

X 4

X 7

X 4

21

4



3

4

1

7-


same.

28

=

=

28

28

X 7

X 4

X 7

X 4

21

4

17

21 – 4 = 17





Main Menu


7

12

1

3-







7

12

1

3-

3

12




mistake.

Main Menu


7

12

1

3-





Click to Continue


7

12

1

3-




denominator.

12

=

=

12

12

X 1

X 4



7

12

1

3-



12

=

=

12

12

X 1

X 4

X 1

X 4

7

4



7

12

1

3-

Now just subtract the numerators and keep the denominator the

same.

12

=

=

12

12

X 1

X 4

X 1

X 4

7

4

3

7 – 4 = 3





Main Menu


6

7

5

8+







6

7

5

8+


If yes, click here to return to the

Main Menu


mistake.32

56


6

7

5

8+





Click to Continue


6

7

5

8+




denominator.

56

=

=

56

56

X 8

X 7



6

7

5

8+



56

=

=

56

56

X 8

X 7

X 8

X 7

48

35



6

7

5

8-

Now just subtract the numerators and keep the denominator the

same.

56

=

=

56

56

X 8

X 7

X 8

X 7

48

35

13

48 - 35 = 13




If you understand now where you made your mistake, click here to

go back to the Main Menu.

Quiz Menu

Like Denominators

Unlike Denominators

Mixed Questions

Main Menu

Quiz – Like Quiz – Like Denominators

Number you paper from 1 – 5 and solve the problem. At the end of the quiz the answers will be shown so that you can

grade your own quiz.

Ready? Click the light to begin.

Main Menu

Quiz – Like Denominators

3

5

1

5+

Main Menu


1

7

4

7+

Main Menu


1

2

1

2+

Main Menu


2

9

3

9+

Main Menu


4

9

3

9+

Main Menu Continue to answers

Quiz Answers – Like Denominators

1. 4

5

2. 5

7

3. 2

2

4. 5

9

5. 7

9


How many did you get correct?

All 5 – Click to go back to the Main Menu to try something different

3 or 4 – Click here to review Guided Practice

0,1,or 2 – Click here to review the Tutorial

Main Menu

Quiz – Like Quiz – Unlike Denominators

Number your paper from 1 – 5 and solve the problem. At the end of the quiz the answers will be shown so that you can


Ready? Click the green light to begin.

Main Menu

Quiz – Unlike Denominators

3

4

1

5+

Main Menu


2

3

1

2+

Main Menu


4

7

3

4+

Main Menu


2

4

1

2+

Main Menu


1

5

3

8+

Main Menu Continue to answers

Quiz Answers – Unlike Denominators

1. 19

20

2. 7

6

3. 37

28

4. 4

4

5. 23

40






Main Menu

Quiz – Like Quiz – Mixed Denominators

Number your paper from 1 – 5 and solve the problem. At the end of the quiz the answers will be shown so that you can


Ready? Click the green light to begin.

Main Menu

Quiz – Mixed Denominators

3

4

1

8+

Main Menu


3

5

2

3+

Main Menu


1

4

2

4+

Main Menu


7

9

3

6+

Main Menu


7

9

1

9+

Main Menu Click to check your answers

Quiz Answers – Unlike Denominators

1. 7

8

2. 19

15

3. 3

4

4. 23

18

5. 8

9

Main Menu





Main Menu

HELP MENU

Definitions

Symbols

Credits

Main Menu

DefinitionsClick on the word to see the definition

Denominator

Numerator

Fractions

Multiple

Main Menu Back to Help MenuObjective

Denominator

•The bottom number of a fraction

• The total number of parts that the item is divided into

4

8Definitions Menu

Numerator

•The top number of a fraction

• The number of parts of the whole

4

8Definitions Menu

Fraction•A whole that is broken into pieces

•Made up of a numerator and denominator

• Expressed as a/b

4

8Definitions Menu

Multiple

The count bys of a number.

Definitions Menu

SymbolsContinue to next page

Return to previous menu (not Main Menu)

Return to Main Menu

This button will let you view the objective

Return to Help MenuReturn to Main Menu

There is a sound on the page

This button allows you to continue to the next page of the quiz.

Credits

Created by Leslie James for the Virginia Tech ITMA Program. This project is for the course “Multimedia

Authoring”.

All of the clip art came from Microsoft Clip Art. Except for the Hokie clip art which came from footballfanatics.com

Return to Main Menu

Objective

What it is that the user is expected to learn

What the user is supposed to be able to do after using this program

You can view the objective for the lesson by clicking on the

button.

Return to Help MenuMain Menu

Objective

Main Menu Return to previous menu

Program Objective:

Given paper and pencil and/or manipulatives, students will be able to add and subtract fractions with like and unlike denominators to an accuracy of

80% or better.

Objective


Objective 1:

Given examples of adding and subtracting fractions problems, students will determine if they need to change the denominators before adding/subtracting

to an accuracy of 80%.

Main Menu Return to previous page

Objective 1.1Given pairs of fractions, students will identify if the fractions have like

or unlike denominators, to an accuracy of 100%. Objective 2.1

Given addition and subtraction problems with like denominators, students will correctly add together the numerators, to an accuracy of 100%.

Objective 2.2Given addition and subtraction problems with like denominators, students will correctly place the denominator in the solution, to an

accuracy of 100%. Objective 2.0

Given addition and subtraction problems with like denominators, students will correctly solve, to an

accuracy of 100%.

Objective 3.0


Given an addition/subtraction problem with unlike denominators, students will correctly change the fractions so that both denominators

are the same, to an accuracy of 80% or better.

Objective 3.1


Using paper and pencil, students will correctly list multiples of

numbers 1-12, to an accuracy of 80% or better.

Objective 3.2


Using paper and pencil, students will correctly record the

common denominator, to an accuracy of 100%.

Objective 3.1a


Given many different examples of numbers, items, and equations, students will identify the equalities and

inequalities, to an accuracy of 80% or better.

Objective 4.0


After correctly changing the denominators of fractions, students will successfully change the numerator to match

the denominator, to an accuracy of 80% or better.

Objective 4.1


After correctly changing the denominators of the fractions, students will correctly multiply the original numerator by

the same number that the denominator was multiplied by, to an accuracy of 80 % or better.

Objective 4.2


After correctly changing the numerators in the fractions, students will record those new numerators above the

denominators, to an accuracy of 80 % or better.

Objective 5.0

Main Menu Return to previous screen

After changing the numerators and denominators, students will correctly add and subtract the fractions,

to an accuracy of 80% or better.

So why do we need to learn this stuff??

There are many reasons why it is useful to learn to add and subtract fractions.

Some examples of when you may use these skills are when you are cooking, building, drawing (blueprints or maps), measuring, splitting something into pieces,

and many many other examples!

Click to Continue

So why do we need to learn this stuff??

So besides being able to use these skills in numerous different types of activities, adding and subtracting fractions is also useful when you are trying

to solve certain word problems and certain real life problems.

For example:

I bought a pizza with 8 slices. 3/8 of them were eaten, how many slices are left?

I bought ½ gallon of milk and my daughter drink ¼ of it, how much is left?

The recipe calls for ¼ cup of white sugar and ¼ cup of brown sugar. How much sugar is needed in all?

I am supposed to drink 8 ½ cups of water a day and 1 ¼ cups of milk a day. How much fluid is that in all?

You can solve all sorts of problems with adding and subtracting fractions!! Click to Continue

Before we begin…

Let’s think about what we already know about adding fractions.

Pretend you have 2/8 of a pizza (two slices out of 8). Someone decided to give you another piece. How many pieces have you eaten? You may have solved this problem in real life. 2/8 + 1/8 = 3/8

Now pretend that you have a cake that is cut into 12 equal pieces. At the party 7 pieces are eaten. How many pieces are left?

What if you needed to buy paint. Each item that you needed to paint needed ¼ pint of paint. A container of paint holds one pint. You need to paint 4 items. How many containers of paint will you need?See, you already may know how to solve some

of these problems!

Before we begin…

Let’s think about what we already know about adding fractions.

Pretend you are baking a cake. You need 1/3 cup of flour and then later you need another ½ cup. How much flour will we need in all?

Now pretend that you have a cake that is cut into 12 equal pieces. At the party ¼ of the cake is eaten. How many pieces are left?

What if you needed to buy paint. Each item that you needed to paint needed ¼ pint of paint. A container of paint holds one pint. You need to

paint 6 items. How many containers of paint will you need?

You may have encountered situations like these in real life. You may have also developed strategies to use to help you solve these problems. If you have that is great! They will help you when you learn to add and subtract fractions. If you have not been able to figure these out on

your own, don’t worry, the tutorial will teach you some strategies.

Documents

Adding and Subtracting