Add or Subtract Fractions with Unlike Denominators

1
Add or Subtract Fractions with Unlike
Denominators
2
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
3
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
4
Adding Fractions With Unlike Denominators

• Step 1 Find the multiples of each denominator.

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

10, 20, 30, 40, 50
10
5
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
6
Adding Fractions With Unlike Denominators

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

1

5
10
1


10
10
7
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
8
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
9
Adding Fractions With Unlike Denominators
Thats 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
10
Adding Fractions With Unlike Denominators

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

1
2

5
10
Remember when adding fractions the denominators
always stay the same!!!!!
1
1



10
10
3
10
11
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
12
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
13
Add these Fractions
Ask yourself what you multiply the bottom
number by to get 15.
2
5
15
x 3
1

3
15
x 5
14
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
15
x 5
15
Add these Fractions
Now, add your new numerators.
2
6
x 3
5
15
x 3
1
5
x 5

3
15
x 5
11
15
16
Add these Fractions
1
2
x 2
6
12
x 2
1
3
x 3

4
12
x 3
5
Is this fraction in simplest form?
12
17
Add these Fractions
5
20
x 4
6
24
x 4
1
3
x 3

8
24
x 3
23
Is this fraction in simplest form?
24
18
Add these Fractions
2
6
x 3
3
9
x 3
1
1
x 1

9
9
x 1
7
Is this fraction in simplest form?
9
19
Add these Fractions
4
12
x 3
5
15
x 3
2
10
x 5

3
15
x 5
22
Is this fraction in simplest form?
15
20
Simplify Your Answer
1
R7
22
15)
22
1
1
15
15
7
7
1
15
21
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

22
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
23
Add these Fractions
Use the short cut to find the Least
Common Denominator (LCD).
1
2
8
1

8
8
24
Add these Fractions
Now find the equivalent fractions for 1/2 1/8.
1
2
8
x 4
1

8
8
x 1
Ask what do you multiply 2 by to get 8 and what
do you multiply 8 by to get 8.
25
Add these Fractions
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
8
x 1
26
Add these Fractions
1
Now multiply across.
4
x 4
2
8
x 4
1
1
x 1

8
8
x 1
27
Add these Fractions
1
Add your new numerators.
4
x 4
2
8
x 4
1
1
x 1

8
8
x 1
5
8
28
Independent Practice

• Math Book pg. 450 8-17

29
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.

30
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
31
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
32
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
10
x 5
33
Subtract these Fractions
Now, subtract your new numerators.
3
6
x 2
5
10
x 2
1
5
x 5
-
2
10
x 5
1
Is this fraction in simplest form?
10
34
Subtract these Fractions
Dont forget to put your answer in simplest
form!.
4
4
x 1
6
6
x 1
1
2
x 2
-
3
6
x 2
2
1
2


6
3
2
35
Subtract these Fractions
5
20
x 4
6
24
x 4
1
3
x 3
-
8
24
x 3
17
Is this fraction in simplest form?
24
36
Subtract these Fractions
3
3
x 1
4
4
x 1
1
2
x 2
-
2
4
x 2
1
Is this fraction in simplest form?
4
37
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
38
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
1
4


12
3
4
39
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

40
Independent Practice

• Math Book pg. 454-455 8-15 22-23