Multiplying Rational Numbers Examples

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Berniece Garrison
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1 Multiplying Rational Numbers Examples 1. To multiply rational numbers (fractions,) you multiply the numerators and multiply the denominators Multiplying Fractions This method can be generalized as follows: For all rational numbers b a and d c, where b 0 and d 0, a c ac. b d bd This same method can be used to multiply rational expressions.. Example: Find 5 b 5 b 5b a 7 a 7 7a 5 b and simplify. State any excluded values. a 7 Multiply the numerators. Multiply the denominators. Since 7a cannot equal zero, a 0. a d 9b c 3. Example: Find and simplify. State any excluded values. 3bc 16ad The GCF is 6abcd. a d 9b c 18a b cd 3ab Change the fraction to simplest form. 3bc 16ad 8abcd 8d Since bc and ad cannot equal 0, a 0, b 0, c 0, and d 0. "Multiplying Rational Numbers" www.beaconlearningcenter.com Rev

2 . Thought Provoker Find a value for b so that a + b b + c b 0 a c. 5. Thought Provoker Find values for b so that ab a. bc c b any real number except Review students of the Cross-Product rule: This same method can be used with rational expressions. 7. Example: Find x + 5 1x 3x x + 7x + 10 and simplify. x 0, -5, or - x + 5 1x 3x x + 7x + 10 x x x 3 x ( x + 5)( x + ) x x x 3 x ( x + 5)( x + ) Simplify stress that each polynomial must be written in factored form and then simplified. x x + A common error that students make in simplifying is show here. 1 x x + 1 "Multiplying Rational Numbers" www.beaconlearningcenter.com Rev

3 8. Example: Find a + 8 a 5 a 5 5a + 10 and simplify. a + 8 a 5 ( a + ) 1( a 5) a 5 5a + 10 ( a 5)( a + 5) 5( a + ) ( a + ) 1( a 5) ( a 5)( a + 5) 5( a + ) 5( a + 5) Simplify a 5, -5, or - 5a Example: Find x x 6 x + 7x x x + x + and simplify. x x 6 x + 7x + 1 ( x 3)( x + ) ( x + 3)( x + ) 9 x x + x + (3 x)(3 + x) ( x + )( x + ) 1 ( x 3)( x + ) ( x + 3)( x + ) 1( x 3)( x + 3) ( x + )( x + ) 1 x + Notice that 1( x + ) 3 x -1(x 3) ( x 3)( x + ) ( x + 3)( x + ) 1( x 3)( x + 3) ( x + )( x + ) x 3, -3, or - x + x + Simplify Caution students to write the negative sign before the fraction bar and not with the numerator. For example, x + x + is not the same as. x + x + "Multiplying Rational Numbers" www.beaconlearningcenter.com Rev

4 Name: Date: Class: Multiplying Rational Numbers Worksheet Find each product and simplify (Exclude values if necessary) ab c ac d 9. b + 0b + 99 b + 7 b + 9 b + 1b y y b + 19b + 8 b 9 b 3 b + 15b (a + 7c) c a 5. 3 ( x y) x y m 9 m x 16 x + 9 x 8. 3a 6 a + 3 a 9 a a "Multiplying Rational Numbers" www.beaconlearningcenter.com Rev

5 Multiplying Rational Numbers Worksheet Key Find each product and simplify ab c ac d ab c b ac d d a 0, c 0, and d 0 3. y y 3 1( y 3) 7 7 ( y 3) 1 y 3 c a 7. (a + 7c) c a 1 1(a + 7c) (7c + a) ( x y) x y ( x y)( x y) x y 1 ( x y) 3 x y "Multiplying Rational Numbers" www.beaconlearningcenter.com Rev

6 6. 9 m 9 m ( m 3)( m + 3) 1 ( m 3) 3 3 m + 9 m 3 7. x 16 x + 9 x 1 ( x + )( x ) x + x 9 1( x ) 1 + 8x x 8. 3a 6 a + 3 a 9 a a 3( a ) 1 ( a + 3) ( a + 3)( a 3) a( a ) 3 a 3a a 3, -3, 0, or 9. b + 0b + 99 b + 7 b + 9 b + 1b + 11 b -9, -1, or -11 ( b + 9)( b + 11) 1 ( b + 7) b ( b + 9) ( b + 11)( b + 1) b b + 19b + 8 b 9 b 3 b + 15b + 36 b 3, -3, or -1 1 ( b + 7)( b + 1) ( b 3)( b + 3) b ( b 3) ( b + 3)( b + 1) 1 "Multiplying Rational Numbers" www.beaconlearningcenter.com Rev

7 Student Name: Date: Multiplying Rational Numbers Checklist 1. On question 1, did the student find the product and simplify correctly?. On question, did the student find the product and simplify correctly? 3. On question 3, did the student find the product and simplify correctly?. On question, did the student find the product and simplify correctly? 5. On question 5, did the student find the product and simplify correctly? 6. On question 6, did the student find the product and simplify correctly? 7. On question 7, did the student find the product and simplify correctly? 8. On question 8, did the student find the product and simplify correctly? "Multiplying Rational Numbers" www.beaconlearningcenter.com Rev

8 9. On question 9, did the student find the product and simplify correctly? 10. On question 10, did the student find the product and simplify correctly? Total Number of Points A B C D F 90 points and above 80 points and above 70 points and above 60 points and above 59 points and below Any score below C needs remediation! "Multiplying Rational Numbers" www.beaconlearningcenter.com Rev

DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES

DOING BATTLE WITH RADICAL EQUATIONS EXAMPLES 1. Inverse Operations Operations that undo each other, such as multiplication and division.. Warm-up Activity Ask students to rewrite each of the following