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8.8 Mixed Expressions and Complex Fractions

8.8 Mixed Expressions and Complex Fractions. CORD Math Mrs. Spitz Fall 2006. Objective. Simplify mixed expressions and complex fractions. Upcoming. 8.8 Friday 10/27 8.9 Monday 10/30 8.10 Tuesday/Wed Chapter 8 Review Wed/Thur Chapter 8 Test Friday. Assignment. Pgs. 336-337 #3-29 all.

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8.8 Mixed Expressions and Complex Fractions

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  1. 8.8 Mixed Expressions and Complex Fractions CORD Math Mrs. Spitz Fall 2006

  2. Objective • Simplify mixed expressions and complex fractions.

  3. Upcoming • 8.8 Friday 10/27 • 8.9 Monday 10/30 • 8.10 Tuesday/Wed • Chapter 8 Review Wed/Thur • Chapter 8 Test Friday

  4. Assignment • Pgs. 336-337 #3-29 all

  5. Introduction • Algebraic expressions such as are called mixed expressions. Changing mixed expressions to rational expression is similar to changing mixed numbers to improper fractions.

  6. Mixed number to Improper Fraction

  7. Mixed expression to Rational Expression

  8. Ex. 1: Find ← Multiply by x2 + y2 representation of 1. ← Combine both 1st and 2nd terms over the common denominator x2 + y2. ← Distribute the 8 using distributive property. ← Combine like terms and simplify.

  9. What if it has more than one fraction? • If a fraction has one or more fractions in the numerator or denominator, it is called a complex fraction. Some complex fractions are shown below:

  10. Consider the complex fraction. To simplify this fraction, rewrite it as: and proceed as follows: Recall that to find the quotient, you multiply by 8/7, the reciprocal of 7/8.

  11. Consider the complex fraction. To simplify this fraction, rewrite it as: and proceed as follows: Recall that to find the quotient, you multiply by d/c, the reciprocal of c/d.

  12. Simplifying Complex Fractions Rule • Any complex fraction Where b ≠ 0, c ≠ 0, and d ≠ 0, may be expressed as:

  13. Ex. 2: Simplify ← The LCD is xy for both the numerator and the denominator. ← Add to simplify the numerator and subtract to simplify the denominator. ← Multiply the numerator by the reciprocal of the denominator.

  14. Ex. 2: Simplify ← Eliminate common factors.

  15. Ex. 3: Simplify ← The LCD of the numerator is x + 4, and the LCD of the denominator is x – 3.

  16. Ex. 3: Simplify ← FOIL the top and don’t forget to subtract the 1 and add the 48 on the bottom.

  17. Ex. 3: Simplify ← Simplify by subtracting the 1 in the numerator and adding the 48 in the denominator.

  18. Ex. 3: Simplify ← Multiply by the reciprocal. x2 + 8x +15 is a common factor that can be eliminated.

  19. Ex. 3: Simplify ← Simplify

  20. Ex. 4: Simplify ← The LCD of the numerator is x + 1, and the LCD of the denominator is x – 2.

  21. Ex. 4: Simplify ← Distribute and subtract to simplify the numerator.

  22. Ex. 4: Simplify ← Simplify

  23. Ex. 4: Simplify ← Multiply by the reciprocal. ← x – 2 is the common factor which can be eliminated.

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