Download Fraction IX Least Common Multiple Least Common Denominator

Adding and Subtracting
Unlike Denominators
Common Multiple

A number that is a multiple
of two or more numbers.
Some multiples of 3 & 6
6, 12, 18, 24, 30, 36, 42
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
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
1
+ 9
3 will divide evenly into 9,
so 9 is your LCD or LCM.
To Add or Subtract Fractions
With Unlike Denominators

Find the multiples of each
denominator.
1
5 = 5, 10, 15, 20, 25, 30
1
+10 = 10, 20, 30, 40, 50
To Add or Subtract Fractions
With Unlike Denominators

Compare the lists of multiples.
Circle the common multiples
between the two lists.
1
5 = 5, 10, 15, 20, 25, 30
1
+10 = 10, 20, 30, 40, 50
To Add or Subtract Fractions
With Unlike Denominators

Use the lowest common
multiple as the denominator.
1
5 = 5, 10, 15 ,20 ,25 ,30
1
+10 = 10, 20, 30, 40, 50
To Add or Subtract Fractions
With Unlike Denominators

This number is also called the
least common denominator.
1
5 = 5, 10, 15 ,20 ,25 ,30
1
+10 = 10, 20, 30, 40, 50
To Add or Subtract Fractions
With Unlike Denominators

Rewrite the fractions using the
least common denominator or
least common multiple.
1
5
1
+10
10
10
To Add or Subtract Fractions
With Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
You
know
that
1/10
1
is
equal
to
1/10
so
5
10
Put
a
1
over
the
1
1
Bottom
10.
+10
10

To Add or Subtract Fractions
With Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
To
find
the
top
1
number,
ask
yourself
5
10
what
do
you
multiply
1
1
the
5
by
to
get
10.
+10
10

To Add or Subtract Fractions
With Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
That’s right 2. Since
you are looking for
1x 2 =
equivalent fraction
5 x 2 = 10 theyou
know the top
1
1 number must also be
+10
10
multiplied by 2.

To Add or Subtract Fractions
With Unlike Denominators

Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
1 x 2 = 2 To find the top number
just multiply 2 x 1 to
5 x 2 = 10 get your equivalent
1
1
fraction.
+10
10
To Add or Subtract Fractions
With Unlike Denominators

Now just add the numerators.
1x 2 = 2
5 x 2 = 10
1
1
+10
10
3
10
Remember when
adding fractions
you never add the
denominators.
Add these Fractions
1
2
1
+8
8
8
Use the short
cut to find the
Least Common
Denominator
(LCD).
Add these Fractions
1
2x 4 = 8
1
+ 8 x 1 =8
Now find the
equivalent
fractions for
1/2 & 1/8.
Ask what do you multiply 2 by to get 8
and what do you multiply 8 by to get 8.
Add these Fractions
1x 4 =
2x 4 = 8
1x 1 =
+ 8 x 1 =8
Since you are
writing equivalent
fractions, now
multiply the top
numbers by the
same number you
did in the
bottom.
Add these Fractions
1x 4 = 4
2x 4 = 8
1x 1 =1
+ 8x 1 =8
Now multiply
across.
Add these Fractions
1x 4 = 4
2x 4 = 8
1x 1 =1
+ 8x 1 =8
5
8
Add your
new
numerators.
Add these Fractions
2
5
1
+3
15
15
Find the
common
Multiples for
5 and 3. Write
This number
As your new
denominator.
Add these Fractions
2
5 x 3 = 15
1
+ 3 x 5 =15
Ask yourself
what you
multiply the
bottom number
by to get 15.
Add these Fractions
2x 3 =
5 x 3 = 15
1x 5 =
+ 3 x 5 =15
Multiply the
top number
by the same
number you
did in the
bottom.
Add these Fractions
2x 3 = 6
5 x 3 = 15
1x 5 =5
+ 3 x 5 =15
Multiply
across.
Add these Fractions
2x 3 = 6
5 x 3 = 15
1x 5 =5
+ 3 x 5 =15
11
15
Now add
your new
numerators.
Add these Fractions
1x 2 = 2
6 x 2 = 12
1x 3 =3
+ 4 x 3 =12
5
12
Add these Fractions
5 x 4 = 20
6 x 4 = 24
1x 3 =3
+ 8 x 3 =24
23
24
Add these Fractions
2x 3 = 6
3x 3 = 9
1x 1 =1
+ 9x 1 =9
7
9
Add these Fractions
4 x 3 = 12
5 x 3 = 15
2 x 5 = 10
+ 3 x 5 = 15
22
15
Simplify Your Answer
22
15
7
1 15
15) 22
15
7
To Subtract Fractions With
Unlike Denominators

Find the multiples of each
denominator.
1
5 = 5, 10, 15, 20, 25, 30
1
- 10 = 10, 20, 30, 40, 50
To Subtract Fractions With
Unlike Denominators

Compare the lists of multiples.
Circle the common multiples
between the two lists.
1
5 = 5, 10, 15, 20, 25, 30
1
- 10 = 10, 20, 30, 40, 50
To Subtract Fractions With
Unlike Denominators

Use the lowest common
multiple as the denominator.
1
5 = 5, 10, 15 ,20 ,25 ,30
1
- 10 = 10, 20, 30, 40, 50
To Subtract Fractions With
Unlike Denominators

This number is also called the
least common denominator.
1
5 = 5, 10, 15 ,20 ,25 ,30
1
- 10 = 10, 20, 30, 40, 50
To Subtract Fractions With
Unlike Denominators

Rewrite the fractions using the
least common denominator or
least common multiple.
1
5
1
- 10
10
10
To Subtract Fractions With
Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
You
know
that
1/10
1
is
equal
to
1/10
so
5
10
Put
a
1
over
the
1
1
Bottom
10.
- 10
10

To Subtract Fractions With
Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
To
find
the
top
1
number,
ask
yourself
5
10
what
do
you
multiply
1
1
the
5
by
to
get
10.
- 10
10

To Subtract Fractions With
Unlike Denominators
Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
That’s right 2. Since
you are looking for
1x 2 =
equivalent fraction
5 x 2 = 10 theyou
know the top
1
1 number must also be
- 10
10
multiplied by 2.

To Subtract Fractions With
Unlike Denominators

Find the equivalent fractions for
1/5 & 1/10 with 10 as the
denominator.
1 x 2 = 2 To find the top number
just multiply 2 x 1 to
5 x 2 = 10 get your equivalent
1
1
fraction.
- 10
10
To Subtract Fractions With
Unlike Denominators

Now just subtract the numerators.
1x 2 = 2
5 x 2 = 10
1
1
- 10
10
1
10
Remember when
subtracting
fractions you never
subtract the
denominators.
Subtract these Fractions
1
2
1
- 8
8
8
Use the short
cut to find the
Least Common
Denominator
(LCD).
Subtract these Fractions
1
2x 4 = 8
1
- 8 x 1 =8
Now find the
equivalent
fractions for
1/2 & 1/8.
Ask what do you multiply 2 by to get 8
and what do you multiply 8 by to get 8.
Subtract these Fractions
1x 4 =
2x 4 = 8
1x 1 =
- 8 x 1 =8
Since you are
writing equivalent
fractions, now
multiply the top
numbers by the
same number you
did in the
bottom.
Subtract these Fractions
1x 4 = 4
2x 4 = 8
1x 1 =1
- 8x 1 =8
Now multiply
across.
Subtract these Fractions
1x 4 = 4
2x 4 = 8
1x 1 =1
- 8x 1 =8
3
8
Subtract
your new
numerators.
Subtract these Fractions
2
5
1
- 3
15
15
Find the
common
Multiples for
5 and 3. Write
This number
As your new
denominator.
Subtract these Fractions
2
5 x 3 = 15
1
- 3 x 5 =15
Ask yourself
what you
multiply the
bottom number
by to get 15.
Subtract these Fractions
2x 3 =
5 x 3 = 15
1x 5 =
- 3 x 5 =15
Multiply the
top number
by the same
number you
did in the
bottom.
Subtract these Fractions
2x 3 = 6
5 x 3 = 15
1x 5 =5
- 3 x 5 =15
Multiply
across.
Subtract these Fractions
2x 3 = 6
5 x 3 = 15
1x 5 =5
- 3 x 5 =15
1
15
Now subtract
your new
numerators.
Subtract these Fractions
5 x 4 = 20
6 x 4 = 24
1x 3 =3
- 8 x 3 =24
17
24
Subtract these Fractions
2x 3 = 6
3x 3 = 9
1x 1 =1
- 9x 1 =9
5
9
Subtract these Fractions
4 x 3 = 12
5 x 3 = 15
2 x 5 = 10
- 3 x 5 = 15
2
15