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# Adding and Subtracting Rational Numbers

Adding and Subtracting Rational Numbers. 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.

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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 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:

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

8. { Common Denominator Divide to Simplify. More Examples Cross Multiply & Add.

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

10. Change Subtraction to Addition (Keep-Change_Change.). More Examples Change Mixed Numbers to Improper Fractions. Get Common Denominator, Cross Multiply & Add. Simplify.

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

12. Solutions

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