Adding Mixed Numbers With Unlike Denominators

1
Adding Mixed Numbers 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
Lowest 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
Mixed Numbers

• Mixed numbers are whole numbers and fractions
  together.

1
3
2
5
Shortcut for Finding the Lowest Common
Denominator or Lowest 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
2 will divide evenly into 8, so 8 is your LCD or
LCM.
2
1
1

8
6
To Add Fractions Mixed Numbers With Unlike
Denominators

• Find the multiples of each denominator.

1
3
4, 8, 12, 16, 20, 30
4
1
1

10, 20, 30, 40, 50
10
7
To Add Mixed Fractions With Unlike Denominators

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

1
3
4, 8, 12, 16, 20, 24
4
1
1
10, 20, 30, 40, 50

10
8
To Add Mixed Fractions With Unlike Denominators

• Use the lowest common
• multiple as the denominator.

1
3
4, 8, 12, 16, 20, 24
4
1
1
10, 20, 30, 40, 50

10
9
To Add Mixed Fractions With Unlike Denominators

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

1
3
4, 8, 12, 16, 20, 24
4
1
1
10, 20, 30, 40, 50

10
10
To Add Mixed 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
3
4
20
x 5
1
1

10
20
11
To Add Mixed Fractions With Unlike Denominators

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

Thats right 5. Since you are looking for the
equivalent fraction you know the top number must
also be multiplied by 5.
1
x 5
3
4
20
x 5
1
1

10
20
12
To Add Mixed 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.
3
4
20
x 5
1
1

10
20
13
To Add Mixed 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.
3
4
20
x 5
1
1

10
20
x 2
14
To Add Mixed 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
3
4
20
x 5
1
2
x 2
1

10
20
x 2
15
To Add Mixed Fractions With Unlike Denominators

• Now just add the numerators.

1
5
x 5
3
4
20
x 5
1
2
x 2
Remember! We never add the denominators.
1

10
20
x 2
7
20
16
To Add Mixed Fractions With Unlike Denominators

• Now add the whole numbers.

1
5
x 5
3
4
20
x 5
1
2
x 2
1

10
20
x 2
7
4
20
17
Add These Mixed Numbers
Use the short cut to find the Lowest
Common Denominator (LCD).
1
10
3
6
1
3

6
6
18
Add These Mixed Numbers
Now find the equivalent fractions for 1/3 1/6.
1
10
3
6
x 2
1
3

6
6
x 1
Ask what do you multiply 3 by to get 6 and what
do you multiply 6 by to get 6.
19
Add These Mixed Numbers
Since you are writing equivalent fractions,
now multiply the top numbers by the same number
you did in the bottom.
1
x 2
10
3
6
x 2
1
x 1
3

6
6
x 1
20
Add These Mixed Numbers
1
Now multiply across.
2
x 2
10
3
6
x 2
1
1
x 1
3

6
6
x 1
21
Add These Mixed Numbers
1
Add your new numerators.
2
x 2
10
3
6
x 2
1
1
x 1
3

6
6
x 1
3
6
22
Add These Mixed Numbers
1
Add your whole numbers.
2
x 2
10
3
6
x 2
1
1
x 1
3

6
6
x 1
3
13
6
23
Simplify Your Answer
3
3
1

13
13

6
3
2

24
Add These Mixed Numbers
Find the common multiples for 5 and 3.
Write this number as your new denominator.
4
11
5
15
1
2

3
15
25
Add These Mixed Numbers
Ask yourself what you multiply the bottom
number by to get 15.
4
11
5
15
x 3
1
2

3
15
x 5
26
Add These Mixed Numbers
Multiply the top number by the same number
you did in the bottom.
4
x 3
11
5
15
x 3
1
x 5
2

3
15
x 5
27
Add These Mixed Numbers
Multiply across.
4
12
x 3
11
5
15
x 3
1
5
x 5
2

3
15
x 5
28
Add These Mixed Numbers
Now add your new numerators.
4
12
x 3
11
5
15
x 3
1
5
x 5
2

3
15
x 5
17
15
29
Change Your Improper Fractionto a Mixed Number
2
4
12
x 3
11
1
15
5
15
x 3
15)
17
1
5
x 5
2
15

3
15
x 5
2
17
15
30
Add Your 1 to Your Whole Numbers
2
1
4
12
x 3
11
1
15
5
15
x 3
15)
17
1
5
x 5
2
15

3
15
x 5
2
17
14
15
31
Put Your Remainder FractionNext to Your Answer
2
1
4
12
x 3
11
1
15
5
15
x 3
15)
17
1
5
x 5
2
15

3
15
x 5
2
2
17
14
15
15
32
Your Final Answer Is 14 2/15
2
1
4
12
x 3
11
1
15
5
15
x 3
15)
17
1
5
x 5
2
15

3
15
x 5
2
2
17
14
15
15
33
Add These Mixed Numbers
11
1
5
20
x 4
24
1
24
6
24
x 4
24)
35
5
15
x 3
3
24

8
24
x 3
11
11
35
28
24
24