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# Add or Subtract Fractions with Unlike Denominators PowerPoint PPT Presentation

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

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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

• 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

• 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 Denominators

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

1

=

5

10

1

=

+

10

10

### 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 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 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 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 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

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

Ask yourself

what you

multiply the

bottom number

by to get 15.

2

5

15

x 3 =

1

+

3

x 5 =

15

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

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 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 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 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 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

1

R7

22

15)

1

22

1

15

15

7

7

1

15

### 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

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

Use the short

cut to find the

Least Common

Denominator

(LCD).

1

2

8

1

+

8

8

### 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.

Since you are

writing equivalent

fractions, now

multiply the top

numbers by the

same number you

did in the

bottom.

1

x 4 =

2

8

x 4 =

1

x 1 =

+

8

x 1 =

8

1

4

Now multiply

across.

x 4 =

2

8

x 4 =

1

1

x 1 =

+

8

x 1 =

8

1

4

Add your

new

numerators.

x 4 =

2

8

x 4 =

1

1

x 1 =

+

8

x 1 =

8

5

8

### Independent Practice:

• Math Book pg. 450 # 8-17

### 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

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

Ask yourself

what you

multiply the

bottom number

by to get 10.

3

5

10

x 2 =

1

-

2

10

x 5 =

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 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

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 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 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 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 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 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