Transcript Document 7426444

Multiplying
and Dividing
Real Numbers
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Warm Up
Add or subtract:
1) 12 - 18
2) -6 + 14
3) 3 - (-5)
4) 11 + (-8)
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Multiplying and Dividing Real Numbers
When you multiply two numbers, the signs of the numbers
you are multiplying determine whether the product is
positive or negative.
This is true for division also.
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Multiplying and Dividing Signed
Numbers
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Multiplying and Dividing Signed Numbers
Find the value of each expression.
A) -12 · 5
= -60
The product of two numbers with
different signs is negative.
B) 8x for x = -5
4
8x = 8 x -5
4
= 8(-5)
4
= -40 = -10
4
First substitute - 5 for x.
4
Multiply.
The quotient of two numbers with
different signs is negative.
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Now you try!
Find the value of each expression.
1a) 35 ÷ (-5)
1b) -11 (-4)
1c) -6x for x = 7
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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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Dividing by Fractions
Divide.
To divide by - 8 , multiply by -15 .
15
8
Multiply the numerators and multiply
the denominators.
- 4 , multiply by -8 have the same sign,
5
15
so the quotient is positive.
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Write 4 as a fraction with a denominator
of 1. Write 9 1 as an improper fraction.
4
To divide by 37 , multiply by 4 .
4
37
- 4 and 9 1 have different signs,
4
so the quotient is negative.
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Now you try!
Divide.
2a)
2b)
2c)
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No number can be multiplied by 0 to give a
product of 1, so 0 has no reciprocal.
Because of this, division by 0 is not possible.
We say that division by 0 is undefined.
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Properties of Zero
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Multiplying and Dividing with Zero
Multiply or divide if possible.
A) 0 ÷ 16.568
=0
B) 63 7 ÷ 0
8
= undefined
C) 1 · 0
=0
Zero is divided by a nonzero number.
The quotient of zero and any nonzero number is 0.
A number is divided by zero.
Division by zero is undefined.
A number is multiplied by zero.
The product of any number and 0 is 0.
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Now you try!
Multiply or divide.
3a)
3b)
3c)
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Recreation Application
A hot-air balloon is taken for a 2.5-hour trip. The wind speed
(and the speed of the balloon) is 4.75 mi/h. The balloon travels
in a straight line. How many miles away from the liftoff
site will the balloon land?
Find the distance traveled at a rate of 4.75 mi/h for 2.5
hours. To find distance, multiply rate by time.
rate times time
4.75 · 2.5
= 11.875
The hot-air balloon will land 11.875 miles from
the liftoff site.
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Now you try!
4) 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?
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Assessment
Find the value of each expression.
1) -72 ÷ (-9)
2) 11 (-11)
3) -7.2 ÷ x for x = 3.6
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Divide:
4)
5)
6)
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Multiply or divide if possible.
7) 3.8 ÷ 0
8) 0 (-27)
9) 0 ÷ 2
3
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10) It is estimated that 7 million people
saw off-Broadway shows in 2002. Assume
that the average price of a ticket was $30.
How much money was spent on tickets for
off-Broadway shows in 2002?
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Let’s review
Multiplying and Dividing Real Numbers
When you multiply two numbers, the signs of the numbers
you are multiplying determine whether the product is
positive or negative.
This is true for division also.
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Multiplying and Dividing Signed
Numbers
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Multiplying and Dividing Signed Numbers
Find the value of each expression.
A) -12 · 5
= -60
The product of two numbers with
different signs is negative.
B) 8x for x = -5
4
8x = 8 x -5
4
= 8(-5)
4
= -40 = -10
4
First substitute - 5 for x.
4
Multiply.
The quotient of two numbers with
different signs is negative.
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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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Dividing by Fractions
Divide.
To divide by - 8 , multiply by -15 .
15
8
Multiply the numerators and multiply
the denominators.
- 4 , multiply by -8 have the same sign,
5
15
so the quotient is positive.
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Properties of Zero
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Multiplying and Dividing with Zero
Multiply or divide if possible.
A) 0 ÷ 16.568
=0
B) 63 7 ÷ 0
8
= undefined
C) 1 · 0
=0
Zero is divided by a nonzero number.
The quotient of zero and any nonzero number is 0.
A number is divided by zero.
Division by zero is undefined.
A number is multiplied by zero.
The product of any number and 0 is 0.
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Recreation Application
A hot-air balloon is taken for a 2.5-hour trip. The wind speed
(and the speed of the balloon) is 4.75 mi/h. The balloon travels
in a straight line. How many miles away from the liftoff
site will the balloon land?
Find the distance traveled at a rate of 4.75 mi/h for 2.5
hours. To find distance, multiply rate by time.
rate times time
4.75 · 2.5
= 11.875
The hot-air balloon will land 11.875 miles from
the liftoff site.
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You did a great job
today!
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