ADDING FRACTIONS WITH DIFFERENT DENOMINATORS

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ADDING FRACTIONS WITH DIFFERENT DENOMINATORS

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Back to the Basics

• Bill has five pets and two of them are dogs and
  three of them are cats.
• Jenny has 2 pets and one is a dog and one is a
  cat.
• You want to know what fraction of their pets put
  together are dogs.

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• Two out of five (2/5) of Bills pets are dogs and
  one out of two (1/2) of Jennys pets are dogs.
• You cannot add these fractions until the
  denominator is the same.
• To get the denominators the same you need to find
  the Least Common Denominator (LCD).

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• The LCD is the smallest number that both
  denominators can go into.
• You need to find the smallest number that both 5
  and 2 go into.
• The next highest number that 5 goes into is 10,
  and 2 also goes into 10.
• Because 10 is the smallest number that 5 and 2 go
  into it is the LCD.

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• Now that you know that 10 must be the denominator
  you use to add the fractions, lets change the
  numerators to fit.
• 2/5 of Bills pets are dogs. To change the
  denominator to 10 both the top and bottom numbers
  must be multiplied by 2.
• 2/5 x 2/2 4/10

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• Lets do the same for Jennys pets.
• 1/2 of her pets are dogs.
• To change the bottom number to 10 you must
  multiply both the top and bottom number by 5.
• 1/2 x 5/5 5/10
• Now you are ready to add Bills number of dogs to
  Jennys number of dogs.

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• 4/10 of Bills pets are dogs, and 5/10 of Jennys
  pets are dogs.
• Out of all of their pets added together, how many
  of them are dogs?
• Look back to the presentation about adding
  fractions with the same denominator if you need
  more help.

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• 4/10 5/10 ?
• Because the bottom number is the same it does not
  change or get added together.
• Only the top numbers get added together.
• 4 5 9
• So 4/10 5/10 9/10!!!