Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Multiply. 1. 2x2(x 3) 2. (x 5)(3x
7) 3. 3x(x2 2x 2) 4. Simplify
. Divide. Simplify your answer. 5. 6. 7.
8.
3x2 8x 35
2x3 6x2
3x3 6x2 6x
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The rules for multiplying rational expressions
are the same as the rules for multiplying
fractions. You multiply the numerators, and you
multiply the denominators.
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Additional Example 1A Multiplying Rational
Expressions
Multiply. Simplify your answer.
Multiply the numerators and denominators.
Factor.
Divide out the common factors.
Simplify.
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Additional Example 1B Multiplying Rational
Expressions
Multiply. Simplify your answer.
Multiply the numerators and the denominators.
Arrange the expression so like variables are
together.
Simplify.
Divide out common factors. Use properties of
exponents.
Simplify. Remember that z0 1.
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Additional Example 1C Multiplying Rational
Expressions
Multiply. Simplify your answer.
Multiply. There are no common factors, so the
product cannot be simplified.
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Check It Out! Example 1a
Multiply. Simplify your answer.
Multiply the numerators and the denominators.
Factor and arrange the expression so like
variables are together.
Simplify.
Divide out common factors. Use properties of
exponents.
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Check It Out! Example 1b
Multiply. Simplify your answer.
Multiply the numerators and the denominators.
Factor and arrange the expression so like
variables are together.
Simplify.
Divide out common factors. Use properties of
exponents.
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Additional Example 2 Multiplying a Rational
Expression by a Polynomial
Multiply .
Simplify your answer.
Write the polynomial over 1.
Factor the numerator and denominator.
Divide out common factors.
Multiply remaining factors.
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Check It Out! Example 2
Multiply
Simplify your answer.
Write the polynomial over 1.
Factor the numerator and denominator.
Divide out common factors.
Multiply remaining factors.
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There are two methods for simplifying rational
expressions. You can simplify first by dividing
out and then multiply the remaining factors. You
can also multiply first and then simplify. Using
either method will result in the same answer.
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Additional Example 3 Multiplying a Rational
Expression Containing Polynomial
Multiply . Simplify
your answer.
Method 1 Simplify first.
Factor.
Divide out common factors.
Simplify.
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Additional Example 3 Continued
Method 2 Multiply first.
Multiply.
Distribute.
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Additional Example 3 Continued
Then simplify.
Factor.
Divide out common factors.
Simplify.
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Check It Out! Example 3a
Multiply .
Simplify your answer.
Simplify first.
Factor.
Divide out common factors.
Simplify.
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Check It Out! Example 3b
Multiply .
Simplify your answer.
Simplify first.
Factor.
Divide out common factors.
Simplify.
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The rules for dividing rational expressions are
the same as the rules for dividing fractions. To
divide by a rational expression, multiply by its
reciprocal.
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Additional Example 4A Dividing by Rational
Expressions and Polynomials
Divide. Simplify your answer.
Write as multiplication by the reciprocal.
Multiply the numerators and the denominators.
Divide out common factors.
Simplify.
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Additional Example 4B Dividing by Rational
Expressions and Polynomials
Divide. Simplify your answer.
Write as multiplication by the reciprocal.
Factor. Rewrite one opposite binomial.
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Additional Example 4B Continued
Divide. Simplify your answer.
Divide out common factors.
Simplify.
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Additional Example 4C Dividing by Rational
Expressions and Polynomials
Divide. Simplify your answer.
Write the binomial over 1.
Write as multiplication by the reciprocal.
Multiply the numerators and the denominators.
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Additional Example 4C Continued
Divide. Simplify your answer.
Divide out common factors.
Simplify.
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Check It Out! Example 4a
Divide. Simplify your answer.
Write as multiplication by the reciprocal.
Multiply the numerators and the denominators.
Simplify. There are no common factors.
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Check It Out! Example 4b
Divide. Simplify your answer.
Write as multiplication by the reciprocal.
Multiply the numerators and the denominators and
cancel common factors.
Simplify.
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Check It Out! Example 4c
Divide. Simplify your answer.
Write the trinomial over 1.
Write as multiplication by the reciprocal.
Multiply.
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Check It Out! Example 4c Continued
Divide. Simplify your answer.
Factor. Divide out common factors.
Simplify.
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Additional Example 5 Application
Tanya is playing a carnival game. She needs to
pick 2 cards out of a deck without looking. The
deck has cards with numbers and cards with
letters. There are 6 more letter cards than
number cards.
a. Write and simplify an expression that
represents the probability that Tanya will pick 2
number cards.
Let x the number cards.
Write expressions for the number of each kind of
card and for the total number of items.
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Additional Example 5 Continued
The probability of picking a number card and then
another number card is the product of the
probabilities of the individual events.
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Additional Example 5 Continued
b. What is the probability that Tanya picks 2
number cards if there are 25 number cards in the
deck before her first pick? Round your answer to
the nearest hundredth.
Since x represents the number of number cards,
substitute 25 for x.
Substitute.
Use the order of operations to simplify.
The probability is approximately 0.19.
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Check It Out! Example 5
What if? There are 50 blue items in the bag
before Martys first pick. What is the
probability that Marty picks two blue items?
Round your answer to the nearest hundredth.
Use the probability of picking two blue items.
Since x represents the number of blue items,
substitute 50 for x.
Substitute.
Use the order of operations to simplify.
The probability is approximately 0.23.
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Lesson Quiz Part I
Multiply. Simplify your answer.
1.
2.
2
3.
Divide. Simplify your answer.
4.
5.
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Lesson Quiz Part II
6. A bag contains purple and green toy cars.
There are 9 more purple cars than green cars.
a. Write and simplify an expression to represent
the probability that someone will pick a purple
car and a green car.
b. What is the probability of someone picking a
purple car and a green car if there are 12 green
cars before the first pick? Round to the nearest
hundredth.
0.24