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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:

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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:

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**Getting a Common Denominator**

Use this formula to get two fractions to have a common denominator: Common Denominator = 3•5=15. Cross Multiply & Add. Simplify if possible.

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**{ More Examples Cross Multiply & Add. Divide to Simplify.**

Common Denominator { Divide to Simplify.

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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 Subtraction to Addition (Keep-Change_Change.).**

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

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