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Multiplying Fractions

Multiplying Fractions. Warm UP!. Vocabulary. Polynomial – The sum or difference of monomials. Rational expression – A fraction whose numerator and denominator are polynomials. Domain of a rational expression – the set of all real numbers except those for which the denominator is zero.

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Multiplying Fractions

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  1. Multiplying Fractions Warm UP!

  2. Vocabulary • Polynomial – The sum or difference of monomials. • Rational expression – A fraction whose numerator and denominator are polynomials. • Domain of a rational expression – the set of all real numbers except those for which the denominator is zero. • Reduced form – a rational expression in which the numerator and denominator have no factors in common.

  3. A rational number is expressed as a quotient of two integers. (a fraction!) A rational expression is expressed as a quotient of two polynomials.

  4. Simplifying Rational Expressions • Factor the numerator and denominator and then divide the common factors • Divide out the common factors

  5. Dividing Out Common Factors Step 1 – Identify any factors which are common to both the numerator and the denominator. • The numerator and denominator have a common factor. • The common factor is the five.

  6. Step 2 – Divide out the common factors. • The fives can be divided since 5 5 = 1 • The x remains in the numerator. • The (x-7) remains in the denominator Dividing Out Common Factors

  7. Step 1: Factor the numerator and the denominator completely looking for common factors.

  8. What is the common factor? Step 2: Divide the numerator and denominator by the common factor.

  9. Simplify:

  10. Fractions are UNDEFINED when the denominator is zero How do I find the values that make an expression undefined? Completely factor the original denominator.

  11. Excluded values of the denominator… The denominator of a fraction can never be zero, because dividing by zero is impossible. What values of x would make the denominator of this expression equal to 0? -2x = 0 or x = 0 EXCLUDED VALUE When x = 0, the expression is UNDEFINED.

  12. Find the excluded values of the expression: 1. 2. Set the denominator equal to 0 and solve for x The excluded value is 3 because the expression is undefined when x = 3 3x – 9 = 0 3( x – 3) = 0 3 = 0 ( x – 3) = 0 x = 3 On your own... Find the excluded values:

  13. Is x = 5 a solution of the equation below? Why or why not? Can you name another excluded value of the equation?

  14. Restrictions on Rational Expressions For what value of x is undefined? It is undefined for any value of “x” which makes the denominator zero. The restriction is that x cannot equal 5.

  15. Now try to do some on your own. Also find the values that make each expression undefined?

  16. Factor. Reduce. Multiply your remaining factors. Check to see if you can reduce again. Multiplying Rational Expressions

  17. Multiply. Simplify the Product. 1st Reduction: 2nd Reduction: Multiply Out

  18. Multiply. Simplify the Product. 1st Reduction: 2nd Reduction: Multiply Out

  19. Multiply. Simplify the Product. Factor 1st Reduction: 2nd Reduction: Multiply Out

  20. Let’s do another one. Step #1: Factor the numerator and the denominator.

  21. 1 1 1 1 1 1 Step #2: Divide the numerator and denominator by the common factors.

  22. Step #3: Multiply the numerator and the denominator.

  23. Multiply

  24. 1 5 1 4 Remember how to divide fractions? Multiply by the reciprocal of the divisor.

  25. Dividing rational expressions uses the same procedure. Ex: Simplify It turns into MULTIPLICATION!

  26. 1 1 1 1

  27. Now you try to simplify the expression:

  28. Now try these on your own.

  29. Here are the answers:

  30. Home Work • Pg 163 1 – 15 odd • Pg 167 1 – 15 odd

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