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Adding Fractions
  • By: Angela Pope-Martin
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 Standard
  •    6.1.spi.3 Students will represent numbers using a variety of models and equivalent forms (i.e., whole numbers, mixed numbers, fractions, decimals, and percents)
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Parts of a Fraction
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Parts of a Fraction
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Adding Fractions With
Common Denominators
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Simplifying Answers
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Simplify the answer.
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Add these fractions.
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Simplify the answer.
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Add these fractions.
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Simplify the answer.
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Add these fractions.
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Simplify the answer.
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Add these fractions.
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Simplify the answer.
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Adding Fractions With
Different Denominators
    • For fractions to be added, they must have a common denominator.


    • The common denominator will be the least common multiple of the denominators.

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Review of Multiples
  • Multiples of a number are found by multiplying the number times one, two, three, and so on.
  • A number that is a multiple of two or more numbers is called a common multiple.
  • The least common multiple is the smallest whole number that is a multiple of two or more numbers.


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Here is a list of some of the multiples of 3 and 4.
  • Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, …


  • Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, …


  • Common multiples of 3 and 4 include 12, 24, 36, …


  • The least common multiple is 12 because it is the smallest number that is a multiple of both 3 and 4.
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Add these fractions.
  • The denominators are different, so a common denominator must be found.
  • To find the common denominator, find the multiples of each denominator.
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Adding Fractions With
Different Denominators
  • Compare the lists of multiples, and find the least common multiple.
  • The least common multiple will also be the least common denominator.
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Adding Fractions With
Different Denominators
  •   Because 20 is the least common denominator, rename 1/4 and 1/10 as fractions with denominators of 20.
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Adding Fractions With
Different Denominators
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Adding Fractions With
Different Denominators
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Adding Fractions With
Different Denominators
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Adding Fractions With
Different Denominators
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Adding Fractions With
Different Denominators.
  •   Add the numerators.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Add these fractions.
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Simplify your answer by
changing the improper fraction
to a mixed number.
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Review of Mixed Numbers
  •   Mixed numbers are whole numbers and fractions together.
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Adding Mixed Numbers
  • When adding mixed numbers with different denominators, a common denominator must be found.
  • To find a common denominator, find the multiples of each denominator.
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Adding Mixed Numbers
  • Compare the lists of multiples, and find the least common multiple.
  • The least common multiple will also be the least common denominator.
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Adding Mixed Numbers
  •   Because 20 is the least common denominator, rename 1/4 and 1/10 as fractions with denominators of 20.
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Adding Mixed Numbers
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Adding Mixed Numbers
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Adding Mixed Numbers
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Adding Mixed Numbers
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Adding Mixed Numbers
  •   Add the numerators.
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Adding Mixed Numbers
  •  Add the whole numbers.
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Add these mixed numbers.
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Add these mixed numbers.
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Add these mixed numbers.
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Add these mixed numbers.
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Add these mixed numbers.
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Simplify your answer.
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