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Adding and Subtracting Rational Numbers

Learn about rational numbers, including fractions, mixed numbers, improper fractions, and integers, and how to simplify fractions. Explore the process of adding and subtracting rational numbers with common denominators. Practice examples included.

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Adding and Subtracting Rational Numbers

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  1. Adding and Subtracting Rational Numbers

  2. 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.

  3. Types of Rational Numbers • Reduced Fractions: • Not Reduced Fractions: • Mixed Numbers: • Improper Fractions: • Integers and Whole Numbers:

  4. 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:

  5. 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.)

  6. Adding Rational Numbers • First they must have a common denominator. • Next, look at the signs. If they have the same signs you add the absolute values and keep the sign. • If they have different signs subtract the absolute values keep the sign of the larger absolute value. Use the song to help remind you if you need to: http://www.teachertube.com/viewVideo.php?video_id=286228

  7. Subtracting Rational Numbers • First they must have a common denominator. • Next, rewrite subtraction as addition – keep-change-change. • Follow the rules for adding rational numbers. Use the song to help remind you if you need to: http://www.teachertube.com/viewVideo.php?video_id=286228

  8. Common Denominator = 3•5=15. Getting a Common Denominator • Use this formula to get two fractions to have a common denominator: Simplify if possible.

  9. { Common Denominator Divide to Simplify. More Examples

  10. More Examples Change Subtraction to Addition. (Keep-Change_Change.) Note: A fraction with a negative numerator or denominator is a negative fraction.

  11. More Examples Change Subtraction to Addition (Keep-Change-Change.). Change Mixed Numbers to Improper Fractions. Simplify. Get Common Denominator

  12. You Try It! Find each sum or difference.

  13. Solutions

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