Add or Subtract Fractions with Unlike Denominators. 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…. Review: Least Common Multiple.
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Add or Subtract Fractions with Unlike Denominators
Common Multiples of 3 & 6:
3: 3, 6, 9, 12, 15, 18, 21, 24…
6: 6, 12, 18, 24, 30, 36, 42…
5 = 5, 10, 15, 20, 25, 30
6 = 6, 12, 18, 24, 30, 36
1
5
= 5, 10, 15, 20, 25, 30
1
+
10
= 10, 20, 30, 40, 50
Adding Fractions With Unlike Denominators
1
5 = 5, 10, 15 ,20 ,25 ,30
1
+
10 = 10, 20, 30, 40, 50
1
=
5
10
1
=
+
10
10
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
To find the top
number, ask yourself
what do you multiply
the 5 by to get 10.
1
5
10
1
1
+
10
10
That’s 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
1
2
=
5
10
Remember when
adding fractions the denominators always stay the same!!!!!
1
1
=
+
+
10
10
3
10
3:
1 x 3
10:
1 x 10
2 x 5
3
10
Common Factors: 1
3/10 is in simplest form
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
Ask yourself
what you
multiply the
bottom number
by to get 15.
2
5
15
x 3 =
1
+
3
x 5 =
15
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
x 5 =
15
Now, add
your new
numerators.
2
6
x 3 =
5
15
x 3 =
1
5
x 5 =
+
3
x 5 =
15
11
15
1
2
x 2 =
6
12
x 2 =
1
3
x 3 =
+
4
x 3 =
12
5
Is this fraction in simplest form?
12
5
20
x 4 =
6
24
x 4 =
1
3
x 3 =
+
8
x 3 =
24
23
Is this fraction in simplest form?
24
2
6
x 3 =
3
9
x 3 =
1
1
x 1 =
+
9
x 1 =
9
7
Is this fraction in simplest form?
9
4
12
x 3 =
5
15
x 3 =
2
10
x 5 =
+
3
x 5 =
15
22
Is this fraction in simplest form?
15
1
R7
22
15)
1
22
1
15
15
7
7
1
15
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 =
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
Use the short
cut to find the
Least Common
Denominator
(LCD).
1
2
8
1
+
8
8
Now find the
equivalent
fractions for
1/2 & 1/8.
1
2
8
x 4 =
1
+
8
x 1 =
8
Ask what do you multiply 2 by to get 8
and what do you multiply 8 by to get 8.
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
x 1 =
8
1
4
Now multiply
across.
x 4 =
2
8
x 4 =
1
1
x 1 =
+
8
x 1 =
8
1
4
Add your
new
numerators.
x 4 =
2
8
x 4 =
1
1
x 1 =
+
8
x 1 =
8
5
8
Follow the same 5 steps that you did to add fractions with unlike denominators.
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
Ask yourself
what you
multiply the
bottom number
by to get 10.
3
5
10
x 2 =
1

2
10
x 5 =
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
x 5 =
10
Now,
subtract
your new
numerators.
3
6
x 2 =
5
10
x 2 =
1
5
x 5 =

2
x 5 =
10
1
Is this fraction in simplest form?
10
Don’t forget
to put your
answer in
simplest form!.
4
4
x 1 =
6
6
x 1 =
1
2
x 2 =

3
x 2 =
6
2
2
1
=
÷
6
2
3
5
20
x 4 =
6
24
x 4 =
1
3
x 3 =

8
x 3 =
24
17
Is this fraction in simplest form?
24
3
3
x 1 =
4
4
x 1 =
1
2
x 2 =

2
x 2 =
4
1
Is this fraction in simplest form?
4
3
6
x 2 =
5
10
x 2 =
1
5
x 5 =

2
10
x 5 =
1
Is this fraction in simplest form?
10
7
7
x 1 =
12
12
x 1 =
Is this fraction in simplest form?
1
3
x 3 =

4
12
x 3 =
4
4
1
=
÷
12
4
3
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 =