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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.
6 = 6, 12, 18, 24, 30, 36
5 = 5, 10, 15, 20, 25, 30
Adding Fractions With Unlike Denominators
Step 1: Find the multiples of each denominator.
1= 5, 10, 15, 20, 25, 30
1= 10, 20, 30, 40, 50+
5
10
Step 2: Determine the LCD. (Remember the LCD = LCM)
15 = 5, 10, 15 ,20 ,25 ,301
10 = 10, 20, 30, 40, 50+
Adding Fractions With Unlike Denominators
Adding Fractions With Unlike Denominators
Step 3: Make equivalent fractions using the LCD as the new denominator.
151
10 +
10
10
=
=
Adding Fractions With Unlike Denominators
151
10 +
10
10
You know that 1/10 is equal to 1/10 so
Put a 1 over theBottom 10.
1=
=
Adding Fractions With Unlike Denominators
151
10 +
10
10
To find the topnumber, ask yourselfwhat do you multiply
the 5 by to get 10.1
Adding Fractions With Unlike Denominators
151
10 +
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
x 2 =x 2 = 2
Adding Fractions With Unlike Denominators
Step 4: Add/subtract the numerators and keep the denominators the same.
151
10 +
10
10
Remember whenadding fractions the
denominators always stay the
same!!!!!
1=
= 2
103
+
Step 5: Check to make sure your answer is in simplest form.
Adding Fractions With Unlike Denominators
103 3:
1 x 310:
1 x 102 x 5
Common Factors: 1
3/10 is in simplest form
Add these Fractions
2513+
Find the common
Multiples for5 and 3. WriteThis numberAs your newdenominator.
15
15
3 = 3, 6, 9, 12, 155 = 5, 10, 15, 20, 25, 30
Add these Fractions
2513+
Ask yourselfwhat you
multiply thebottom number
by to get 15.
15
15x 5 =
x 3 =
Add these Fractions
2513+
Multiply thetop numberby the samenumber you
did in thebottom.
15
15x 5 =
x 3 =x 5 =
x 3 =
5
6
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
1319+
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.
3 will divide evenly into 9, so 9 is your LCD or LCM.
Add these Fractions
1218+
Now find theequivalent
fractions for1/2 & 1/8.
8
8x 1 =
x 4 =
Ask what do you multiply 2 by to get 8and what do you multiply 8 by to get 8.
Add these Fractions
1218+
Since you arewriting equivalent
fractions, nowmultiply the topnumbers by the
same number you did in the bottom.
8
8x 1 =
x 4 =x 1 =
x 4 =
Subtracting 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.
Follow the same 5 steps that you did to add fractions with unlike denominators.
Subtract these Fractions
3512-
Find the common
Multiples for5 and 2. WriteThis numberAs your newdenominator.
10
10
2 = 2, 4, 6, 8, 105 = 5, 10, 15, 20
Subtract these Fractions
3512-
Ask yourselfwhat you
multiply thebottom number
by to get 10.
10
10x 5 =
x 2 =
Subtract these Fractions
3512-
Multiply thetop numberby the samenumber you
did in thebottom.
10
10x 5 =
x 2 =x 5 =
x 2 =
5
6
Subtract these Fractions
3512-
Now, subtract
your newnumerators.
10
10x 5 =
x 2 =x 5 =
x 2 =
5
6
110
Is this fraction in simplest form?
Subtract these Fractions
4613-
6
6x 2 =
x 1 =x 2 =
x 1 =
2
4
26
Don’t forgetto put your answer in
simplest form!.
= 13
22÷
Subtract these Fractions
5618-
24
24x 3 =
x 4 =x 3 =
x 4 =
3
20
1724
Is this fraction in simplest form?
Subtract these Fractions
3512-
10
10x 5 =
x 2 =x 5 =
x 2 =
5
6
110
Is this fraction in simplest form?
Subtract these Fractions
71214-
12
12x 3 =
x 1 =x 3 =
x 1 =
3
7
412
Is this fraction in simplest form?
= 13
44÷
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 =