Homeschool Math, www.HomeschoolMath.net website logo

Home | Blog | Amazon Store | Newsletter  

Ebooks | Worksheets | Curriculum Guide | Lessons & Articles | Reviews |
May newsletter     An online tutor helps you teach math at home!

The ideas in this fraction lesson are taken from the Fractions 1 ebook sold on this website. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.


 Adding and subtracting unlike fractions
Free lesson plan from HomeschoolMath.net

Can you add the following fractions?  Use pictures or some manipulatives to help you.  
Discuss with your teacher.

+ =

1

3

+

1

2

=

What fraction 
would this be?

      
+ =

1

3

+

1

4

=

What fraction 
would this be?

 

Did you solve the problems?  See what happens below:

+
+ =

2

6

+

3

6

=

5

6

      
+
+ =

4

12

+

3

12

=

7

12

So what happened?  Discuss with your teacher and write an explanation below.

 

To add unlike fractions, we must first convert them all to

__________________________________, and then adding is easy.


Example problem types

1.  Write the fractions below the pictures.  Add.  Color parts where needed.  

+ = + =
 

 

+ = + =
+ = + =
 

 

+ = + =


2.  Fill in the table based on the two examples above and the four problems in exercise 1. 

fractions to add converted to fractions to add converted to

1

3

1

2

6th parts        

1

2

1

4

____ parts

1

3

1

4

____parts

2

5

1

2

____ parts

Now think.  How can we know to which kind of parts we need to convert the fractions we are adding?  Can you see any patterns or rules in the table?

3.  Change the fraction pictures by splitting the existing parts (both colored ones and white ones) so that both fractions have same kind of parts.  Underneath write the addition sentence.

 

4. If you think you know to which kind of parts to convert the fractions, try these problems.  In other words, try to convert the fractions so they have a common denominator. Write down the intermediate step, too.
Otherwise go to exercise 5 first.  

1

2

+

2

3

=                                     

1

5

+

1

3

=                                     

1

6

+

1

2

=

1

6

+

1

3

=

5.  This exercise is in the end of the lesson.  Complete it first before continuing on.  

6.  Subtract the fractions.  First convert them so that they have the same denominator.

1

3

-

1

5

=                                    

6

7

-

1

4

=                                    

2

3

-

1

9

=

10

7

-

2

9

=

 
7.  Add and subtract.  Write the intermediate steps in your notebook.  Write your answer as a mixed number if possible.  If you have three addends, the common denominator needs to be a common multiple of all three. 

a.   

4

7

+

10

11

b.  

7

10

+

5

3

c.  

14

5

+

9

4

d.  

3

10

+

7

9

5.  How do we find a common denominator?

Common denominator
   

fractions to add   converted to   addition sentence

1

3

+

1

2

  6th parts

2

6

+

3

6

=

1

3

+

1

4

  12th parts

4

12

+

3

12

=

1

8

+

1

4

  8th parts

 

8

+

 

8

=

The parts to which we convert the fractions to be added tells us the denominator
of the new fractions.  In other words, we convert the fractions so that they have 
a common denominator, or the same denominator.  Maybe you have noticed that

The common denominator has to be in both multiplication tables of 
the denominators 
(or in all of them if there are more than two fractions).
 
In other words: 
The common denominator is a multiple of all the denominators.

"Multiple" refers to "times something".  For example, multiples of 4 are numbers 
that are 4 times something, namely 4, 8, 12, 16, 20, and so on, which are in the
multiplication table of 4.

  • For example, if you add 5th parts and 3rd parts, the common denominator
    must be in  the table of 5, and also in the table of 3.  
    So 15 will work since  15 = 3 × 5  and  15 = 5 × 3.
     
  • If you add 4th parts and 8th parts, 8 will work as the common denominator
    since 8 = 1 × 8  and  8 = 2 × 4.  16 will work also, since  16 = 2 × 8  and
    16 = 4 × 4.   But 8 of course is easier!
     
  • If you can't think of the multiplication tables or the numbers are quite big,
    you can make lists of multiples, one for each denominator, and find a number
    that appears in all of them.

a)  Use this exercise to check your understanding.  Find a common denominator (c.d) that will work for adding these fractions.  

Fractions c.d Fractions c.d Fractions c.d

4

5

and

2

4

                

1

3

and

21

2

                

15

4

and

7

8

     

2

3

and

5

9

           

4

7

and

31

2

           

7

4

and

9

11

     

b)  Add the fractions in the above exercise (write in your notebook).

 

What fractions go into the puzzles? 

         +   =

13

15

                      +   =

13

42

 +     +   +     + 
  +   =

5

12

  +   =

17

72

=
5

6

=

9

20

=
7

24

=

16

63

 

Next lesson: adding mixed numbers


The ideas in this fraction lesson are taken from the Fractions 2 ebook sold on this website. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

FREE math homework help on www.PhatMath.com
  • 40 Math forums for grades K-12 & College
  • Post/view math problems & solutions
  • Blogs for students, parents, teachers


- Learn subtraction concept
- fact families
- memorize basic facts
- word problems
- colorful pages.
- download & print.
Self-teaching worktext.

Download today!






Times Tales

Learn the upper
times tables with
mnemonic stories.

Learn more!




 

 

Math Mammoth Fractions 2 ebook
Don't just memorize fraction rules - learn fractions visually!
Download Fractions 2 self-teaching worktext.

 

 

 

 

 

Teaching Tips and Math Lessons menu

All grades

Teaching math
Is your curriculum coherent?
How to motivate & prevent math anxiety
Keeping math skills sharp in the summer
Setting up equations for word problems
Interview with an astronomer
ADD/ADHD and diet
Omega-3 fats & intelligence

Elementary

Using calculator in elementary grades?
Teaching word problems

Middle

Balance illustrates equation solving
Why are fractions so difficult?
Negative or zero exponents
Number to zero power is one - 2 proofs
How to teach proportions
How to teach integers
Hands-on with pi
Sine in a right triangle
Rational numbers & converting repeating decimals into fractions
Why study math? square roots? algebra?
Square roots without a calculator?

High School

Why high school geometry is difficult
Help with high school geometry
What is proof?
Two-column proof vs. paragraph proof
Proving is a process - logarithm problem
Fascinating irrational numbers
Proof that square root of 2 is irrational
Rational numbers are countable
How does calculator find values of sine?
Fibonacci numbers and golden section
Why does the square root algorithm work?

 

 




HOMESCHOOL MATH NEWSLETTER

Homeschool Math Newsletter comes out once monthly, and includes math teaching articles and tips, Math Mammoth news, and all kinds of little "tidbits" such as math news, interesting links, or humor. The content is equally good for all of us who teach math (not just homeschooling parents).

When you subscribe, you will alsoreceive a GIFT of over 280 FREE math worksheets and sample pages from Math Mammoth books for grades 1-8.

Note: This is a double opt-in list. You will FIRST get an email that asks you to confirm your email address. PLEASE check also your SPAM/JUNK folder for this confirmation email.

Take a peek at the previous volumes here!.

The newsletter service is by Aweber.com. Your email address will not be shared, sold, or distributed to anyone else.

Google

Download 280+ QUALITY math worksheets
Link to us    Sitemap    Contact    About    Privacy    Advertise    Homeschool links    Educational links
Best Homeschool Sites on the Internet - Homeschool Top Sites
Copyright 2003-2008 Homeschool math
http://www.homeschoolmath.net/


 

 

P.S. ....

 

Check out these short video clips from my favorite band - Rockabilly.US. They play oldies, Elvis, country, and top hits of the 50s and 60s. It's a show with large band, costumes, choreography, little skits, "Kid Kritters", 6 dancing/singing girls, junior dancer troupe, etc.

"Be My Baby"
originally by the Ronettes

Impossible Dream (Elvis song)
Most importantly, the band wants to use the uplifting and energetic music to bring some fun, happiness and encouragement into people's lives. They're doing it selflessly to help others, and don't get paid for any of it themselves. And I admire that!

=> See more video clips at YouTube