Warm Up

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Warm Up
Lesson Presentation
Lesson Quiz
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Warm Up Multiply or divide. 1. 6(7)

42
3.
42 7

6
4
4.
2.
5. Write as a mixed number.
6.
Write as an improper fraction.
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Objectives
Multiply real numbers. Divide real numbers.
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Vocabulary
reciprocal multiplicative inverse
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When you multiply two numbers, the signs of
the numbers you are multiplying determine
whether the product is positive or negative.
Factors Product

3(5) Both positive
15 Positive
3(5) One negative
15 Negative
3(5) Both negative
15 Positive
This is true for division also.
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Multiplying and Dividing Signed Numbers
WORDS Multiplying and Dividing Numbers with the Same Sign If two numbers have the same sign, their product or quotient is positive.
NUMBERS 4 ? 5 20 15 (3) 5
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Multiplying and Dividing Signed Numbers
WORDS Multiplying and Dividing Numbers with Different Signs If two numbers have different signs, their product or quotient is negative.
NUMBERS 6(3) 18
18 2 9
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Example 1 Multiplying and Dividing Signed Numbers
Find the value of each expression.
A.
The product of two numbers with different signs
is negative.
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B.
The quotient of two numbers with the same sign is
positive.
12
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Example 1C Multiplying and Dividing Signed
Numbers
Find the value of the expression.
The quotient of two numbers with different signs
is negative.
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Check It Out! Example 1a and 1b
Find the value of each expression.
1a. 35 ? (5)
The quotient of two numbers with different signs
is negative.
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1b. 11(4)
The product of two numbers with the same sign is
positive.
44
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Check It Out! Example 1c
Find the value of each expression.
1c. 6x for x 7
6x 6(7)
First substitute 7 for x.
The product of two numbers with different signs
is negative.
42
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Two numbers are reciprocals if their product is
1. A number and its reciprocal are called
multiplicative inverses. To divide by a number,
you can multiply by its multiplicative inverse.
Dividing by a nonzero number is the same as
Multiplying by the reciprocal of the number.
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Multiplicative inverses
1
10
10 5 2
10 2
5
5
Dividing by 5 is the same as multiplying by
the reciprocal of 5, .
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(No Transcript)
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Example 2A Dividing by Fractions
Example 2 Dividing by Fractions
Divide.
To divide by , multiply by .
Multiply the numerators and multiply the
denominators.
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Example 2B Dividing by Fractions
Divide.
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Check It Out! Example 2a
Divide.
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Check It Out! Example 2b
Divide.
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Check It Out! Example 2c
Divide.
The signs are different so the quotient is
negative.
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No number can be multiplied by 0 to give a
product of 1, so 0 has no reciprocal. Because 0
has no reciprocal, division by 0 is not possible.
We say that division by zero is undefined.
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Properties of Zero
Multiplication by Zero
The product of any number and 0 is 0.
WORDS
0(17) 0
NUMBERS
ALGEBRA
a 0 0
0 a 0
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Properties of Zero
Zero Divided by a Number
The quotient of 0 and any nonzero number is 0.
WORDS
NUMBERS
ALGEBRA
0 a 0
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Properties of Zero
Division by Zero
WORDS
Division by 0 is undefined.
12 0
NUMBERS
Undefined
ALGEBRA
a 0
Undefined
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Example 3 Multiplying and Dividing with Zero
Multiply or divide.
0
15
A.
Zero is divided by a nonzero number.
The quotient of zero and any nonzero number is 0.
0
B. 22 ? 0
A number is divided by zero.
undefined
Division by zero is undefined.
C. 8.45(0)
A number is multiplied by zero.
0
The product of an number and 0 is 0.
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Check It Out! Example 3a
Divide
Multiply by the reciprocal.
Any number multiplied by 0 equals 0.
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Check It Out! Example 3b and 3c
Divide
3b. 0 0
Any number divided by 0 is undefined.
0 0 undefined
3c. (12.350)(0)
The product of any number and 0 is 0.
(12.350)(0) 0
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Example 4 Recreation Application
rate
times
time
1 3
3 4
1
?
3
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Example 4 Recreation Application
Multiply the numerators and multiply the
denominators.
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The hot-air balloon lands 5 miles from the
liftoff site.
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Check It Out! Example 4
What if? On another hot-air balloon trip, the
wind speed is 5.25 mi/h. The trip is planned for
1.5 hours. The balloon travels in a straight
line. How many miles away from the liftoff site
will the balloon land?
5.25(1.5)
Speed times time equals distance.
Distance traveled.
7.875 mi
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Lesson Quiz
Find the value of each expression.
35 7
1.
2. 2x for x 6
5
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Multiply or divide if possible.
undefined
0
15 miles