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Fraction XI
Adding Mixed Numbers
With Unlike Denominators
By Monica Yuskaitis
Common Multiple

A number that is a multiple
of two or more numbers.
Some multiples of 3 & 4
12, 24, 36, 48,
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
Mixed Numbers

Mixed numbers are whole
numbers and fractions together.
1
3 2
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 2
1
+ 1 8
2 will divide evenly into 8,
so 8 is your LCD or LCM.
To Add Fractions Mixed
Numbers With Unlike
Denominators

Find the multiples of each
denominator.
1
3
4 = 4, 8, 12, 16, 20, 30
1
1
+ 10 = 10, 20, 30, 40, 50
To Add Mixed Fractions With
Unlike Denominators

Compare the lists of multiples.
Circle the common multiples
between the two lists.
1
3
4 = 4, 8, 12, 16, 20, 24
1
1
+ 10 = 10, 20, 30, 40, 50
To Add Mixed Fractions With
Unlike Denominators
Use the least common
multiple as the denominator.

1
3
4 = 4, 8, 12, 16, 20, 24
1
1
+ 10 = 10, 20, 30, 40, 50
To Add Mixed Fractions With
Unlike Denominators
This number is also called
the least common denominator.

1
3
4 = 4, 8, 12, 16, 20, 24
1
1
+ 10 = 10, 20, 30, 40, 50
To Add Mixed Fractions With
Unlike Denominators

Find the equivalent fractions for 1/4
& 1/10 with 20 as the denominator.
1
3
4 x 5 =20
1
1
+ 10
20
Ask yourself what
you multiply 4 by
to get 20.
To Add Mixed Fractions With
Unlike Denominators

Find the equivalent fractions for 1/4
& 1/10 with 20 as the denominator.
1
x
5
=
3
4 x 5 =20
1
1
+ 10
20
That’s right 5. Since
you are looking for
the equivalent fraction
you know the top
number must also be
multiplied by 5.
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
=
3
4 x 5 =20
1
1
+ 10
20
To find the top number
just multiply 1 x 5 to
get your equivalent
fraction.
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
=
3
4 x 5 =20
1
1
+ 10x 2 =20
Now ask what you
multiply the 10 by
to get 20.
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
=
3
4 x 5 =20
1
2
x
2
=
1
+ 10x 2 =20
That’s right 2. Since
you are looking for the
equivalent fraction you
know the top number
must also be multiplied
by 2.
To Add Mixed Fractions With
Unlike Denominators

Now just add the numerators.
1
5
x
5
=
3
4 x 5 =20
1x 2 = 2
+1 10x 2 =20
7
20
Remember! We
never add the
denominators.
To Add Mixed Fractions With
Unlike Denominators

Now add the whole numbers.
1
5
x
5
=
3
4 x 5 =20
1x 2 = 2
+1 10x 2 =20
7
4 20
Add These Mixed Numbers
1
10 3
1
+3 6
6
6
Use the short
cut to find the
Least Common
Denominator
(LCD).
Add These Mixed Numbers
1
10 3 x 2 = 6
1
3
+ 6 x 1 =6
Now find the
equivalent
fractions for
1/3 & 1/6.
Ask what do you multiply 3 by to get 6
and what do you multiply 6 by to get 6.
Add These Mixed Numbers
1
x
2
=
10
3x 2 = 6
1
x
1
=
+ 3 6 x 1 =6
Since you are
writing equivalent
fractions, now
multiply the top
numbers by the
same number you
did in the
bottom.
Add These Mixed Numbers
1
2
x
2
=
10
3x 2 = 6
1
1
x
1
=
3
+ 6x 1 =6
Now multiply
across.
Add These Mixed Numbers
1
2
x
2
=
10 3 x 2 = 6
1
1
x
1
=
3
+ 6x 1 =6
3
6
Add your
new
numerators.
Add These Mixed Numbers
1
2
x
2
=
10 3 x 2 = 6
1
1
x
1
=
3
+ 6x 1 =6
3
13
6
Add your
whole
numbers.
Simplify Your Answer
3
3
1
÷
13
13
=
6 ÷3
2
Add These Mixed Numbers
4
11
5
1
2
+ 3
15
15
Find the
common
multiples for
5 and 3. Write
this number
as your new
denominator.
Add These Mixed Numbers
4
11 5 x 3 = 15
1
+ 2 3 x 5 =15
Ask yourself
what you
multiply the
bottom number
by to get 15.
Add These Mixed Numbers
4
x
3
=
11
5 x 3 = 15
1
x
5
=
+ 2 3 x 5 =15
Multiply the
top number
by the same
number you
did in the
bottom.
Add These Mixed Numbers
4
12
x
3
=
11
5 x 3 = 15
1x 5 =5
+ 2 3 x 5 =15
Multiply
across.
Add These Mixed Numbers
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
15
Now add
your new
numerators.
Change Your Improper Fraction
to a Mixed Number
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
15
2
1 15
15) 17
15
2
Add Your 1 to Your Whole
Numbers
1
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
14
15
2
1 15
15) 17
15
2
Put Your Remainder Fraction
Next to Your Answer
1
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
14 2
15
15
2
1 15
15) 17
15
2
Your Final Answer Is 14 2/15
1
4
12
x
3
=
11
5 x 3 = 15
1
5
x
5
=
2
+ 3 x 5 =15
17
14 2
15
15
2
1 15
15) 17
15
2
Add These Mixed Numbers
1
24 5 x 4 = 20
6 x 4 = 24
5
15
x
3
=
3
+ 8 x 3 =24
11
35
28
24 24
11
1 24
24) 35
24
11