Transcript 2.7 – Division of Real Numbers

Chapter 2 – Properties of
Real Numbers
2.7 – Division of Real Numbers
2.7 – Division of Real Numbers
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Today we will learn how to:
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Divide real numbers
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Use division to simplify algebraic expressions
2.7 – Division of Real Numbers
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Suppose you owe a friend $50.00. You and
your friend decide to come up with a payment
schedule. You decide on 4 equal monthly
payments. We can determine the monthly
payment using division of real numbers.
2.7 – Division of Real Numbers
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Every real number (except zero) has a
RECIPROCAL
The product of a number and its reciprocal is 1
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Example: 2 · ½ = 1
This property is referred to as the inverse property
of multiplication.
2.7 – Division of Real Numbers
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The reciprocal of a is 1 , when a ≠ 0
a
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Example: -8 and 
1
8
a
b
The reciprocal of
is , when a ≠ 0 and b ≠ 0
b
a
2 and 5
 Example: 

5
2
2.7 – Division of Real Numbers
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Zero is the only real number that has no
reciprocal. There is no number that when
multiplied by zero gives a product of 1.
Because zero does not have a reciprocal, you
cannot divide by zero.
2.7 – Division of Real Numbers
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You can use a reciprocal to write a division as a
product.
DIVISION RULE
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To divide a number a by a nonzero number b, multiply a
by the reciprocal of b.
1
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a b  a
b
2.7 – Division of Real Numbers
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Example 1
1. 15  (5)
5
2.  45 
6
1
2
3
3.
3
1
4.
2
3
2.7 – Division of Real Numbers
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THE SIGN OF A QUOTIENT
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The quotient of two numbers with the same sign is
positive
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-a  -b = a/b
-20  (-4) = 5
The quotient of two numbers with opposite signs is
negative
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-a b = - a/b
-20  4 = -5
2.7 – Division of Real Numbers
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Example 2
Simplify the expression 9  27 x
3
2.7 – Division of Real Numbers
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Example 3
A mountain climber descends 300 feet in 50 minutes.
What is her velocity?
2.7 – Division of Real Numbers
HOMEWORK
Page 111
#24 – 31, 32 – 46 even, 48 – 51, 62 – 63