Adding Fractions With Unlike Denominators

1
Adding Fractions with Unlike Denominators
2
Common Multiple

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

Some multiples of 3 4 12, 24, 36, 48,
3
Least Common Multiple

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

4 4, 8, 12, 16, 20, 24, 28
5 5, 10, 15, 20, 25, 30
4
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
2 will divide evenly into 8, so 8 is your LCD or
LCM.
2
1

8
5
To Add Fractions With Unlike Denominators

• Find the multiples of each denominator.

1
4, 8, 12, 16, 20, 30
4
1

10, 20, 30, 40, 50
10
6
To Add Fractions With Unlike Denominators

• Compare the lists of multiples. Circle the
  common multiples between the two lists.

1
4, 8, 12, 16, 20, 24
4
1
10, 20, 30, 40, 50

10
7
To Add Fractions With Unlike Denominators

• Use the least common
• multiple as the denominator.

1
4, 8, 12, 16, 20, 24
4
1
10, 20, 30, 40, 50

10
8
To Add Fractions With Unlike Denominators

• This number is also called
• the least common denominator.

1
4, 8, 12, 16, 20, 24
4
1
10, 20, 30, 40, 50

10
9
To Add Fractions With Unlike Denominators

• Find the equivalent fractions for 1/4 1/10
  with 20 as the denominator.

Ask yourself what you multiply 4 by to get 20.
1
4
20
x 5
1

10
20
10
To Add Fractions With Unlike Denominators

• Find the equivalent fractions for 1/4 1/10
  with 20 as the denominator.

1
x 5
Thats right 5. Since you are looking for the
equivalent fraction you know the top number must
also be multiplied by 5.
4
20
x 5
1

10
20
11
To Add Fractions With Unlike Denominators

• Find the equivalent fractions for 1/4 1/10
  with 20 as the denominator.

1
5
x 5
To find the top number just multiply 1 x 5 to get
your equivalent fraction.
4
20
x 5
1

10
20
12
To Add Fractions With Unlike Denominators

• Find the equivalent fractions for 1/4 1/10
  with 20 as the denominator.

1
5
x 5
Now ask what you multiply the 10 by to get 20.
4
20
x 5
1

10
20
x 2
13
To Add Fractions With Unlike Denominators

• Find the equivalent fractions for 1/4 1/10
  with 20 as the denominator.

Thats right 2. Since you are looking for the
equivalent fraction you know the top number must
also be multiplied by 2.
1
5
x 5
4
20
x 5
1
2
x 2

10
20
x 2
14
To Add Fractions With Unlike Denominators

• Now just add the numerators.

1
5
x 5
4
20
x 5
Remember! We never add the denominators.
1
2
x 2

10
20
x 2
7
20
15
To Add Fractions With Unlike Denominators
1
5
x 5
4
20
x 5
1
2
x 2

10
20
x 2
7
20
16
Add These Fractions
Use the short cut to find the Least
Common Denominator (LCD).
1
3
6
1

6
6
17
Add These Fractions
Now find the equivalent fractions for 1/3 1/6.
1
3
6
x 2
1

6
6
x 1
Ask what do you multiply 3 by to get 6 and what
do you multiply 6 by to get 6.
18
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 2
3
6
x 2
1
x 1

6
6
x 1
19
Add These Fractions
1
Now multiply across.
2
x 2
3
6
x 2
1
1
x 1

6
6
x 1
20
Add These Fractions
1
Add your new numerators.
2
x 2
3
6
x 2
1
1
x 1

6
6
x 1
3
6
21
Add These Fractions
1
2
x 2
3
6
x 2
1
1
x 1

6
6
x 1
3
6
22
Add These Fractions
Find the common multiples for 5 and 3.
Write this number as your new denominator.
4
5
15
1

3
15
23
Add These Fractions
Ask yourself what you multiply the bottom
number by to get 15.
4
5
15
x 3
1


3
15
x 5
24
Add These Fractions
Multiply the top number by the same number
you did in the bottom.
4
x 3
5
15
x 3
1
x 5


3
15
x 5
25
Add These Fractions
Now add your new numerators.
4
12
x 3
5
15
x 3
1
5
x 5

3
15
x 5
17
15
26
Change Your Improper Fractionto a Mixed Number
2
4
12
x 3
1
15
5
15
x 3
15)
17
1
5
x 5
15

3
15
x 5
2
17
15
27
Put Your Remainder FractionNext to Your Answer
2
4
12
x 3
1
15
5
15
x 3
15)
17
1
5
x 5
15

3
15
x 5
2
2
17
1
15
15
28
Your Final Answer Is 1 2/15
2
1
4
12
x 3
1
15
5
15
x 3
15)
17
1
5
x 5
15

3
15
x 5
2
2
17
1
15
15
29
1. Add 3/7 1/2

• 4/9
• 10/14
• 9/14
• 13/14

30
2. Add 1/3 1/2

• 2/5
• 5/6
• 4/6
• 3/5

31
3. Add 2/7 1/14

• 3/14
• 3/21
• 4/14
• 10/49

32
4. Add 2/3 1/9

• 3/12
• 3/9
• 7/9
• 4/9

33
5. Add 2/9 3/5

• 5/14
• 37/45
• 5/9
• 35/45

34
6. Add 1/3 1/4

• 5/12
• 7/12
• 4/7
• 4/12

35
7. Add 3/10 2/6

• 5/16
• 19/30
• 15/30
• 5/10