Add or Subtract Fractions with Unlike Denominators.

Add or Subtract Fractions with

Unlike Denominators

Review: Common Multiple

A number that is a multiple of two or more numbers.

Common Multiples of 3 & 6:

3: 3, 6, 9, 12, 15, 18, 21, 24…6: 6, 12, 18, 24, 30, 36, 42…

Review: Least Common Multiple

The smallest common multiple of a set of two or more numbers.

6 = 6, 12, 18, 24, 30, 36

5 = 5, 10, 15, 20, 25, 30

Adding Fractions With Unlike Denominators

Step 1: Find the multiples of each denominator.

1= 5, 10, 15, 20, 25, 30

1= 10, 20, 30, 40, 50+

5

10

Step 2: Determine the LCD. (Remember the LCD = LCM)

15 = 5, 10, 15 ,20 ,25 ,301

10 = 10, 20, 30, 40, 50+



Step 3: Make equivalent fractions using the LCD as the new denominator.

151

10 +

10

10

=

=


151

10 +

10

10

You know that 1/10 is equal to 1/10 so

Put a 1 over theBottom 10.

1=

=


151

10 +

10

10

To find the topnumber, ask yourselfwhat do you multiply

the 5 by to get 10.1


151

10 +

10

10

That’s right 2. And we know that if we

multiply by 2 at the bottom then we must also multiply by 2 at

the top.1

x 2 =x 2 = 2


Step 4: Add/subtract the numerators and keep the denominators the same.

151

10 +

10

10

Remember whenadding fractions the

denominators always stay the

same!!!!!

1=

= 2

103

+

Step 5: Check to make sure your answer is in simplest form.


103 3:

1 x 310:

1 x 102 x 5

Common Factors: 1

3/10 is in simplest form

Add these Fractions

2513+

Find the common

Multiples for5 and 3. WriteThis numberAs your newdenominator.

15

15

3 = 3, 6, 9, 12, 155 = 5, 10, 15, 20, 25, 30

Add these Fractions

2513+

Ask yourselfwhat you

multiply thebottom number

by to get 15.

15

15x 5 =

x 3 =

Add these Fractions

2513+

Multiply thetop numberby the samenumber you

did in thebottom.

15

15x 5 =

x 3 =x 5 =

x 3 =

5

6

Add these Fractions

2513+

Now, addyour new

numerators.15

15x 5 =

x 3 =x 5 =

x 3 =

5

6

1115

Add these Fractions

1614+

12

12x 3 =

x 2 =x 3 =

x 2 =

3

2

512

Is this fraction in simplest form?

Add these Fractions

5618+

24

24x 3 =

x 4 =x 3 =

x 4 =

3

20

2324


Add these Fractions

2319+

9

9x 1 =

x 3 =x 1 =

x 3 =

1

6

79


Add these Fractions

4523+

15

15x 5 =

x 3 =x 5 =

x 3 =

10

12

2215


Simplify Your Answer

2215

15) 221

157

R7

15

1 1

1 7

Word Problem Practice:Mrs. Walker graded 2/3 of the class’ math test and then stopped to take a phone call. When she returned, she graded 1/6 of the math test. What amount of the math test has she graded?

2/3 + 1/6 =

Mrs. Andrea is planning on having her art classes paint a picture. She will need 1/5 of a gallon of paint for her first period art class and 2/3 of a gallon for her second period art class. How much paint will be needed in all?

1/5 + 2/3 =

Shortcut for Finding the Least Common Denominator or

Least Common Multiple

1319+

Check to see if the smaller denominator divides evenly into the larger denominator.If it does, use the larger denominator for your LCD or LCM.

3 will divide evenly into 9, so 9 is your LCD or LCM.

Add these Fractions

1218+

Use the shortcut to find the

Least CommonDenominator

(LCD).

8

8

Add these Fractions

1218+

Now find theequivalent

fractions for1/2 & 1/8.

8

8x 1 =

x 4 =

Ask what do you multiply 2 by to get 8and what do you multiply 8 by to get 8.

Add these Fractions

1218+

Since you arewriting equivalent

fractions, nowmultiply the topnumbers by the

same number you did in the bottom.

8

8x 1 =

x 4 =x 1 =

x 4 =

Add these Fractions

1218+

Now multiplyacross.

8

8x 1 =

x 4 =x 1 =

x 4 =

1

4

Add these Fractions

1218+

Add yournew

numerators.

8

8x 1 =

x 4 =x 1 =

x 4 =

1

4

58

Independent Practice:

Math Book pg. 450 # 8-17

Subtracting Fractions With Unlike Denominators:

Step 1: Find the multiples of each denominator.

Step 2: Determine the LCD.Step 3: Make equivalent fractions using the LCD as the new denominator.

Step 4: Add/subtract the numerators and keep the denominators the same.

Step 5: Check to make sure your answer is in simplest form.

Follow the same 5 steps that you did to add fractions with unlike denominators.

Subtract these Fractions

3512-

Find the common

Multiples for5 and 2. WriteThis numberAs your newdenominator.

10

10

2 = 2, 4, 6, 8, 105 = 5, 10, 15, 20


3512-

Ask yourselfwhat you

multiply thebottom number

by to get 10.

10

10x 5 =

x 2 =


3512-

Multiply thetop numberby the samenumber you

did in thebottom.

10

10x 5 =

x 2 =x 5 =

x 2 =

5

6


3512-

Now, subtract

your newnumerators.

10

10x 5 =

x 2 =x 5 =

x 2 =

5

6

110



4613-

6

6x 2 =

x 1 =x 2 =

x 1 =

2

4

26

Don’t forgetto put your answer in

simplest form!.

= 13

22÷


5618-

24

24x 3 =

x 4 =x 3 =

x 4 =

3

20

1724



3412-

4

4x 2 =

x 1 =x 2 =

x 1 =

2

3

14



3512-

10

10x 5 =

x 2 =x 5 =

x 2 =

5

6

110



71214-

12

12x 3 =

x 1 =x 3 =

x 1 =

3

7

412


= 13

44÷

Word Problem Practice:Johnny fed his two dogs. He fed the big dog 11/12 of a cup of dog food. He fed the little dog 1/4 of a cup of dog food. How much more food did the big dog get than the little dog?

1112 - 1/4 =

Susan is training for a 5K run. She ran 5/12 of a mile on Saturday and 5/6 of a mile on Sunday. What is the difference in the distance she ran?

5/12 - 5/6 =

Independent Practice:

Math Book pg. 454-455 # 8-15 & 22-23

Add or Subtract Fractions with Unlike Denominators.

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