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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.

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Add or subtract fractions with unlike denominators

Add or Subtract Fractions with Unlike Denominators


Review common multiple
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
Review: Least Common Multiple

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

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

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


Adding fractions with unlike denominators
Adding Fractions With Unlike Denominators

  • Step 1: Find the multiples of each denominator.

1

5

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

1

+

10

= 10, 20, 30, 40, 50


Adding Fractions With Unlike Denominators

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

1

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

1

+

10 = 10, 20, 30, 40, 50


Adding fractions with unlike denominators1
Adding Fractions With Unlike Denominators

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

1

=

5

10

1

=

+

10

10


Adding fractions with unlike denominators2
Adding Fractions With Unlike Denominators

You know that 1/10

is equal to 1/10 so

Put a 1 over the

Bottom 10.

1

=

5

10

1

1

=

+

10

10


Adding fractions with unlike denominators3
Adding Fractions With Unlike Denominators

To find the top

number, ask yourself

what do you multiply

the 5 by to get 10.

1

5

10

1

1

+

10

10


Adding fractions with unlike denominators4
Adding Fractions With Unlike Denominators

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

2

x 2 =

5

10

x 2 =

1

1

+

10

10


Adding fractions with unlike denominators5
Adding Fractions With Unlike Denominators

1

2

=

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

5

10

Remember when

adding fractions the denominators always stay the same!!!!!

1

1

=

+

+

10

10

3

10


Adding fractions with unlike denominators6
Adding Fractions With Unlike Denominators

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

3:

1 x 3

10:

1 x 10

2 x 5

3

10

Common Factors: 1

3/10 is in simplest form


Add these fractions
Add these Fractions

Find the

common

Multiples for

5 and 3. Write

This number

As your new

denominator.

2

5

15

1

+

3

15

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

3 = 3, 6, 9, 12, 15


Add these fractions1
Add these Fractions

Ask yourself

what you

multiply the

bottom number

by to get 15.

2

5

15

x 3 =

1

+

3

x 5 =

15


Add these fractions2
Add these Fractions

Multiply the

top number

by the same

number you

did in the

bottom.

2

6

x 3 =

5

15

x 3 =

1

5

x 5 =

+

3

x 5 =

15


Add these fractions3
Add these Fractions

Now, add

your new

numerators.

2

6

x 3 =

5

15

x 3 =

1

5

x 5 =

+

3

x 5 =

15

11

15


Add these fractions4
Add these Fractions

1

2

x 2 =

6

12

x 2 =

1

3

x 3 =

+

4

x 3 =

12

5

Is this fraction in simplest form?

12


Add these fractions5
Add these Fractions

5

20

x 4 =

6

24

x 4 =

1

3

x 3 =

+

8

x 3 =

24

23

Is this fraction in simplest form?

24


Add these fractions6
Add these Fractions

2

6

x 3 =

3

9

x 3 =

1

1

x 1 =

+

9

x 1 =

9

7

Is this fraction in simplest form?

9


Add these fractions7
Add these Fractions

4

12

x 3 =

5

15

x 3 =

2

10

x 5 =

+

3

x 5 =

15

22

Is this fraction in simplest form?

15


Simplify your answer
Simplify Your Answer

1

R7

22

15)

1

22

1

15

15

7

7

1

15


Word problem practice
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
Shortcut for Finding the Least Common Denominator or Least Common Multiple

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.

1

3 will divide evenly into 9,

so 9 is your LCD or LCM.

3

1

+

9


Add these fractions8
Add these Fractions

Use the short

cut to find the

Least Common

Denominator

(LCD).

1

2

8

1

+

8

8


Add these fractions9
Add these Fractions

Now find the

equivalent

fractions for

1/2 & 1/8.

1

2

8

x 4 =

1

+

8

x 1 =

8

Ask what do you multiply 2 by to get 8

and what do you multiply 8 by to get 8.


Add these fractions10

Since you are

writing equivalent

fractions, now

multiply the top

numbers by the

same number you

did in the

bottom.

Add these Fractions

1

x 4 =

2

8

x 4 =

1

x 1 =

+

8

x 1 =

8


Add these fractions11
Add these Fractions

1

4

Now multiply

across.

x 4 =

2

8

x 4 =

1

1

x 1 =

+

8

x 1 =

8


Add these fractions12
Add these Fractions

1

4

Add your

new

numerators.

x 4 =

2

8

x 4 =

1

1

x 1 =

+

8

x 1 =

8

5

8


Independent practice
Independent Practice:

  • Math Book pg. 450 # 8-17


Subtracting fractions with unlike denominators
Subtracting Fractions With Unlike Denominators:

Follow the same 5 steps that you did to add 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.


Subtract these fractions
Subtract these Fractions

Find the

common

Multiples for

5 and 2. Write

This number

As your new

denominator.

3

5

10

1

-

2

10

5 = 5, 10, 15, 20

2 = 2, 4, 6, 8, 10


Subtract these fractions1
Subtract these Fractions

Ask yourself

what you

multiply the

bottom number

by to get 10.

3

5

10

x 2 =

1

-

2

10

x 5 =


Subtract these fractions2
Subtract these Fractions

Multiply the

top number

by the same

number you

did in the

bottom.

3

6

x 2 =

5

10

x 2 =

1

5

x 5 =

-

2

x 5 =

10


Subtract these fractions3
Subtract these Fractions

Now,

subtract

your new

numerators.

3

6

x 2 =

5

10

x 2 =

1

5

x 5 =

-

2

x 5 =

10

1

Is this fraction in simplest form?

10


Subtract these fractions4
Subtract these Fractions

Don’t forget

to put your

answer in

simplest form!.

4

4

x 1 =

6

6

x 1 =

1

2

x 2 =

-

3

x 2 =

6

2

2

1

=

÷

6

2

3


Subtract these fractions5
Subtract these Fractions

5

20

x 4 =

6

24

x 4 =

1

3

x 3 =

-

8

x 3 =

24

17

Is this fraction in simplest form?

24


Subtract these fractions6
Subtract these Fractions

3

3

x 1 =

4

4

x 1 =

1

2

x 2 =

-

2

x 2 =

4

1

Is this fraction in simplest form?

4


Subtract these fractions7
Subtract these Fractions

3

6

x 2 =

5

10

x 2 =

1

5

x 5 =

-

2

10

x 5 =

1

Is this fraction in simplest form?

10


Subtract these fractions8
Subtract these Fractions

7

7

x 1 =

12

12

x 1 =

Is this fraction in simplest form?

1

3

x 3 =

-

4

12

x 3 =

4

4

1

=

÷

12

4

3


Word problem practice1
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 practice1
Independent Practice:

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


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