Adding and Subtracting Rational Numbers

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Adding and Subtracting Rational Numbers
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Rational Numbers

• The term, Rational Numbers, refers to any number
  that can be written as a fraction.
• This includes fractions that are reduced,
  fractions that can be reduced, mixed numbers,
  improper fractions, and even integers and whole
  numbers.
• An integer, like 4, can be written as a fraction
  by putting the number 1 under it.

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Types of Rational Numbers

• Reduced Fractions
• Not Reduced Fractions
• Mixed Numbers
• Improper Fractions
• Integers and Whole Numbers

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Simplifying Fractions

• Simplifying fractions by dividing the numerator
  (top number) and denominator (bottom number) by
  the same value.
• Repeat this until there are no more numbers that
  divide into both the numerator denominator.
• Example
• Example
• Example

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Simplifying Fractions

• Example
• Example(Rewrite mixed numbers as improper
  fractions before you simplify.)
• Example(If after you divide, the fraction can
  still be simplified, keep going.)

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Adding Fractions

• To add fractions, they must have a common
  denominator.
• If the denominators are the same, add the
  numerators, and put the result over the
  denominator.
• If the answer can be simplified, then simplify
  it.
• Example
• Example

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Getting a Common Denominator

• Use this formula to get two fractions to have a
  common denominator

Cross Multiply Add.
Simplify if possible.
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More Examples
Cross Multiply Add.
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More Examples
Change Subtraction to Addition.
(Keep-Change_Change.)
Note A fraction with a negative numerator or
denominator is a negative fraction.
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More Examples
Change Mixed Numbers to Improper Fractions.
Get Common Denominator, Cross Multiply Add.
Simplify.
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You Try It!
Find each sum or difference.
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Solutions