FRACTIONSFRACTIONSAdding & Subtracting Fractions Adding & Subtracting Fractions

with Different Denominatorswith Different DenominatorsBy Timothy LeonardBy Timothy Leonard

Fractions with Same Fractions with Same (Common) (Common) DenominatorsDenominators It's easy to add and subtract like fractions, or fractions with It's easy to add and subtract like fractions, or fractions with

the same the same denominatordenominator. . You just add or subtract the You just add or subtract the numeratorsnumerators and keep the same and keep the same

denominatordenominator. .

1/4 + 1/4 = 2/4 (or ½)

3/5 - 1/5= 2/5

Denominators Denominators that are that are multiples of anothermultiples of another To Add and Subtract Fractions with different To Add and Subtract Fractions with different

denominatorsdenominators, you need to know how to find the , you need to know how to find the least common denominator (LCD). least common denominator (LCD). To find the least common To find the least common denominatordenominator find the find the

least common multiple of the least common multiple of the denominatorsdenominators..

1/5 + 2/3 = ? In the above addition problem the multiples of each In the above addition problem the multiples of each

denominatordenominator are: are:

1515 is the least common multiple (lowest shared number) between the is the least common multiple (lowest shared number) between the two sets of multiples and is your two sets of multiples and is your least common denominator (LCD)least common denominator (LCD)..

5, 10, 15, 20, 25Multiples

of 5

3, 6, 9, 12, 15, 18, 21Multiples

of 3

Adding Fractions with Different Adding Fractions with Different Denominators Denominators (cont’d)(cont’d) Now that you’ve found your Now that you’ve found your least common denominatorleast common denominator

((1515), ask yourself how many times does each starting ), ask yourself how many times does each starting denominatordenominator go into go into 1515. .

1/5 + 2/3 = 1515÷5 = 3 and 15÷3 = 5

Now multiply each result times the corresponding Now multiply each result times the corresponding numeratornumerator. .

3x1 = and 5x2 = 3 10

? ? +

15

10 + 3 = 15

13

AnswerAnswer: :

14

13

Subtracting Fractions with Subtracting Fractions with Different Different DenominatorsDenominators

- =

It’s difficult to determine the exact answer using this animation It’s difficult to determine the exact answer using this animation of 1/3 – 1/4. Now attempt to solve using of 1/3 – 1/4. Now attempt to solve using least common least common denominatordenominator method. Lets take a look at the next slide. method. Lets take a look at the next slide.

?

WHOLE

412

312-

Subtracting Fractions with Subtracting Fractions with Different Different Denominators Denominators (cont’d)(cont’d)

Multiples of 3: 3, 6, 9, 12, 15Multiples of 4: 4, 8, 12, 16Least common multiple: 12

13 - =

14

Multiply numerators by 12÷3=4 and 12÷4=3, respectively

=1

12

?

Now we have

twelfths

Denominators Denominators that are that are multiples of each othermultiples of each other To Add and Subtract Fractions with different To Add and Subtract Fractions with different denominators denominators

which are multiples ofwhich are multiples of each other each other, you have fewer steps to , you have fewer steps to find the find the least common denominator (LCD). least common denominator (LCD). To find the least common To find the least common denominatordenominator in this instance in this instance

the greater of the 2 denominators becomes the the greater of the 2 denominators becomes the LCDLCD..

1/5 + 2/10 =?

Now only 1 division and 1 multiplication operation Now only 1 division and 1 multiplication operation is required:is required:

5, 10, 15, 20, 2510 is a multiple of 5, and 10 is also a multiple

Give It a TryGive It a TryLet’s Practice Adding FractionsLet’s Practice Adding Fractions

Number 1Number 1 2/6 + 2/3 = ?2/6 + 2/3 = ?

a)a) 1/31/3

b)b) 11

c)c) 2/62/6

Number 2Number 2 2/6 + 1/6 = ?2/6 + 1/6 = ?

a)a) 4/64/6

b)b) 3/53/5

c)c) 1/21/2

Number 3Number 3 3/8 + 2/8 = ?3/8 + 2/8 = ?

a)a) 5/85/8

b)b) 3/83/8

c)c) 1/81/8

Number 4Number 4 3/8 + 2/6 = ?3/8 + 2/6 = ?

a)a) 5/145/14

b)b) 6/246/24

c)c) 17/2417/24

What Has Been Given,What Has Been Given,We Now Have to Take Away.We Now Have to Take Away.

It’s Time to Practice Subtracting FractionsIt’s Time to Practice Subtracting FractionsNumber 1Number 1 2/3 - 2/6 = ?2/3 - 2/6 = ?

a)a) 2/32/3

b)b) 1/31/3

c)c) 1/21/2

Number 2Number 2 2/6 - 1/6 = ?2/6 - 1/6 = ?

a)a) 3/63/6

b)b) 1/21/2

c)c) 1/61/6

Number 3Number 3 3/8 - 1/8 = ?3/8 - 1/8 = ?

a)a) 1/81/8

b)b) 3/83/8

c)c) 1/41/4

Number 4Number 4 3/8 - 2/6 = ?3/8 - 2/6 = ?

a)a) 1/241/24

b)b) 5/145/14

c)c) 1/61/6

IncorrectIncorrect

Did you forget to make them Did you forget to make them equivalent fractions?equivalent fractions?

CorrectCorrect

Great Job, move to the next Great Job, move to the next question.question.

IncorrectIncorrect

Did you forget to subtract or did Did you forget to subtract or did you forget to make them you forget to make them equivalent?equivalent?

CorrectCorrect

Great Job, move to the next Great Job, move to the next question.question.

Correct—Done w/Adding, Now Correct—Done w/Adding, Now Let’s Try Something New…Let’s Try Something New…

Great Job, move to the next Great Job, move to the next question.question.

Excellent JobExcellent Job

For further practice or For further practice or explanations on adding and explanations on adding and subtracting fractions, here are subtracting fractions, here are some suggested websites.some suggested websites.

For Further StudyFor Further Study

http://www.visualfractions.com/http://www.visualfractions.com/

http://www.shodor.org/interactivhttp://www.shodor.org/interactivate/activities/FractionSorter/?verate/activities/FractionSorter/?version=skip1&browser=unknownsion=skip1&browser=unknown

http://http://www.funbrain.comwww.funbrain.com//