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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
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

Adding Fractions With Unlike Denominators
To find the top number, ask yourself what do you multiply the 5 by to get 10. 1 5 10 1 1 + 10 10

Adding Fractions With Unlike Denominators
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

Adding Fractions With Unlike Denominators
Step 4: Add/subtract the numerators and keep the denominators the same. 1 2 = 5 10 Remember when adding fractions the denominators always stay the same!!!!! 1 1 = + + 10 10 3 10

Adding Fractions With Unlike Denominators
Step 5: Check to make sure your answer is in simplest form. 3: 1 x 3 10: 1 x 10 2 x 5 3 10 Common Factors: 1 3/10 is in simplest form

2 5 15 1 + 3 15 Add these Fractions 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

2 5 15 1 + 3 15 Add these Fractions x 3 = x 5 = Ask yourself what you
multiply the bottom number by to get 15. 2 5 15 x 3 = 1 + 3 x 5 = 15

2 6 5 15 1 5 + 3 15 Add these Fractions x 3 = x 3 = x 5 = x 5 =
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

2 6 5 15 1 5 + 3 15 11 15 Add these Fractions x 3 = x 3 = x 5 = x 5 =
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 6 12 1 3 + 4 12 5 12 Add these Fractions x 2 = x 2 = x 3 = x 3 =
Is this fraction in simplest form? 12

5 20 6 24 1 3 + 8 24 23 24 Add these Fractions x 4 = x 4 = x 3 = x 3 =
Is this fraction in simplest form? 24

2 6 3 9 1 1 + 9 9 7 9 Add these Fractions x 3 = x 3 = x 1 = x 1 =
Is this fraction in simplest form? 9

4 12 5 15 2 10 + 3 15 22 15 Add these Fractions x 3 = x 3 = x 5 =
Is this fraction in simplest form? 15

Simplify Your Answer 1 R7 22 15) 1 22 1 15 15 7 7 1 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/ /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/ /3 =

1 3 1 + 9 Check to see if the smaller denominator
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 will divide evenly into 9, so 9 is your LCD or LCM. 3 1 + 9

1 2 8 1 + 8 8 Add these Fractions Use the short cut to find the
Least Common Denominator (LCD). 1 2 8 1 + 8 8

1 2 8 1 + 8 8 Add these Fractions x 4 = x 1 = 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.

1 2 8 1 + 8 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =
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 2 8 1 1 + 8 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =
Now multiply across. x 4 = 2 8 x 4 = 1 1 x 1 = + 8 x 1 = 8

1 4 2 8 1 1 + 8 8 5 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =
Add your new numerators. x 4 = 2 8 x 4 = 1 1 x 1 = + 8 x 1 = 8 5 8

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
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

Subtract these Fractions
Ask yourself what you multiply the bottom number by to get 10. 3 5 10 x 2 = 1 - 2 x 5 = 10

Subtract these Fractions
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

Subtract these Fractions
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

Subtract these Fractions
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

Subtract these Fractions
5 20 x 4 = 6 24 x 4 = 1 3 x 3 = - 8 x 3 = 24 17 Is this fraction in simplest form? 24

Subtract these Fractions
3 3 x 1 = 4 4 x 1 = 1 2 x 2 = - 2 x 2 = 4 1 Is this fraction in simplest form? 4

Subtract these Fractions
3 6 x 2 = 5 10 x 2 = 1 5 x 5 = - 2 x 5 = 10 1 Is this fraction in simplest form? 10

Subtract these Fractions
7 7 x 1 = 12 12 x 1 = Is this fraction in simplest form? 1 3 x 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? /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/ /6 =

Independent Practice:
Math Book pg # 8-15 & 22-23

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