Download Fraction IX Least Common Multiple Least Common Denominator

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
 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
Adding Fractions With
Unlike Denominators
 Step 1: Find the multiples of
each denominator.
1
5 = 5, 10, 15, 20, 25, 30
1
+10 = 10, 20, 30, 40, 50
Adding Fractions With
Unlike Denominators
 Step 2: Determine the LCD.
(Remember the LCD = LCM)
1
5 = 5, 10, 15 ,20 ,25 ,30
1
+10 = 10, 20, 30, 40, 50
Adding Fractions With Unlike
Denominators
 Step 3: Make equivalent
fractions using the LCD as the
new denominator.
1 =
5
10
1 =
+10
10
Adding Fractions With Unlike
Denominators
1 =
5
10
1 = 1
+10
10
You know that 1/10
is equal to 1/10 so
Put a 1 over the
Bottom 10.
Adding Fractions With Unlike
Denominators
1
5
1
+10
10
1
10
To find the top
number, ask yourself
what do you multiply
the 5 by to get 10.
Adding Fractions With Unlike
Denominators
1x 2 = 2
5 x 2 = 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.
Adding Fractions With Unlike
Denominators
 Step 4: Add/subtract the numerators
and keep the denominators the same.
1 = 2
5
10
1 = 1
+10 + 10
3
10
Remember when
adding fractions the
denominators
always stay the
same!!!!!
Adding Fractions With Unlike
Denominators
 Step 5: Check to make sure
your answer is in simplest form.
3
10
3:
1x3
10:
1 x 10
2x5
Common Factors: 1
3/10 is in simplest form
Add these Fractions
2
5
1
+3
15
15
5 = 5, 10, 15, 20, 25, 30
3 = 3, 6, 9, 12, 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 = 6
5 x 3 = 15
1x 5 =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
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
Is this fraction in
simplest form?
Add these Fractions
5 x 4 = 20
6 x 4 = 24
1x 3 =3
+ 8 x 3 =24
23
24
Is this fraction in
simplest form?
Add these Fractions
2x 3 = 6
3x 3 = 9
1x 1 =1
+ 9x 1 =9
7
9
Is this fraction in
simplest form?
Add these Fractions
4 x 3 = 12
5 x 3 = 15
2 x 5 = 10
+ 3 x 5 = 15
22
15
Is this fraction in
simplest form?
Simplify Your Answer
22
15
1 R7
1 1
15) 22
15
7
1
7
15
Word Problem Practice:
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 =
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.
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.
Independent Practice:
Math Book pg. 450 # 8-17
Subtracting Fractions With
Unlike Denominators:
Follow the same 5 steps that you did to
add fractions with unlike denominators.
Step 1: Find the multiples of each
denominator.
Step 2: Determine the LCD.
Step 3: Make equivalent fractions using the
LCD as the new denominator.
Step 4: Add/subtract the numerators and keep
the denominators the same.
Step 5: Check to make sure your answer is in
simplest form.
Subtract these Fractions
3
5
1
- 2
5 = 5, 10, 15, 20
2 = 2, 4, 6, 8, 10
10
10
Find the
common
Multiples for
5 and 2. Write
This number
As your new
denominator.
Subtract these Fractions
3
5 x 2 = 10
1
- 2 x 5 =10
Ask yourself
what you
multiply the
bottom number
by to get 10.
Subtract these Fractions
3x 2 = 6
5 x 2 = 10
1x 5 =5
- 2 x 5 =10
Multiply the
top number
by the same
number you
did in the
bottom.
Subtract these Fractions
3x 2 = 6
5 x 2 = 10
1x 5 =5
- 2 x 5 =10
1
10
Now,
subtract
your new
numerators.
Is this fraction in
simplest form?
Subtract these Fractions
4x 1 = 4
6x 1 = 6
1x 2 =2
- 3x 2 =6
Don’t forget
to put your
answer in
simplest form!.
2 ÷ 2 = 1
6
2
3
Subtract these Fractions
5 x 4 = 20
6 x 4 = 24
1x 3 =3
- 8 x 3 =24
17
24
Is this fraction in
simplest form?
Subtract these Fractions
3x 1 = 3
4x 1 = 4
1x2= 2
- 2x 2 = 4
1
4
Is this fraction in
simplest form?
Subtract these Fractions
3x 2 = 6
5 x 2 = 10
1x5= 5
- 2 x 5 = 10
1
10
Is this fraction in
simplest form?
Subtract these Fractions
7x 1 = 7
12x 1 = 12 Is this fraction in
simplest
form?
1x3= 3
- 4 x 3 = 12
4÷ 4 = 1
12 4
3
Word Problem Practice:
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 =
Independent Practice:
Math Book pg. 454-455 # 8-15 & 22-23