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Algebra 1Ch 2.5 Multiplication of Real Numbers
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Objective Students will multiply real numbers
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Rules for Multiplying
The rules for multiplying real numbers are: If the signs are the same the answer is positive
If the signs are different the answer is negative.
Lets look at some examples
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Example #1 Same Signs Multiply 3 3
In this instance both factors are positive so your answer will
be positive
3 3 = 9
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Example #2 Same Signs Multiply - 3 (- 5)
In this instance both factors are negative so your answer will
be positive
- 3 (- 5) = 15
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Example #3 Different Signs Multiply 5 (- 8)
In this instance the factors have different signs. The 5 is
positive and the 8 is negative your answer will be negative
5 (- 8) = - 40
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Example #4 Different Signs Multiply - 6 3
In this instance the factors have different signs. The 6 is
negative and the 3 is positive your answer will be negative
- 6 3 = - 18
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Comment Of course the examples that were used were
pretty simple and you could do the math in
your head A strategy that you can use here to make you
life easy is to chunk the problemthat is
1. Multiply the numbers first2. Then evaluate for the sign
Lets look at an example of what I mean
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Chunking Multiply - 10 4
In this instance the factors have different signs.
10 4 = 401. Multiply 10 4 first to get the total of 40
2. Then evaluate for the signs in this instance the signs are
different so your answer will be negative- + = -
The solution to the problem is: -10 4 = -
40
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Comment Make no mistake about itwe will use this
concept throughout this course
It is expected that you master the rules ofmultiplying real numbers
If the sign is wrongthe whole problem is
wrong.As a rule I do not give partialcredit
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Properties of Multiplication There are 5 properties of multiplication Commutative Property
Associative Property
Identity Property Property of Zero
Property of Opposites
You are probably already familiar with some of
these propertiesHowever, in this lesson we willgive you the appropriate mathematical name for the
property and show you what it looks like
Lets look at each one individually
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Commutative Property The commutative property states:
The order in which two numbers are
multiplied does not change the productThis property can be expressed as follows:
Algebraically: a b = b a
Example: 3 (-2) = (-2) 3
-6 = -6
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Associative Property The associative property states:
The way you group three numbers when
multiplying does not change the productThis property can be expressed as follows:
Algebraically: (a b) c = a (b c)
Example: (-6 2) 3 = -6 (2 3)-12 3 = -6 6
- 36 = - 36
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Identity Property The identity property states:
The product of a number and 1 is that
numberThis property can be expressed as follows:
Algebraically: a 1 = a
Example: - 4 1 = -4
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Property of Zero The property of zero states:
The product of a number zero is zero
This property can be expressed as follows:
Algebraically: a 0 = 0
Example: 5 0 = 0
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Property of Opposites The property of opposites states:
The product of a number and 1 is the
opposite of the numberThis property can be expressed as follows:
Algebraically: a (-1) = -a
Example: -1 (-3) = 3
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Using the rules of multiplication The purpose for reviewing the rules and properties
of multiplication is so that you know how to use
them when solving problems
When solving problems you will use the process that
we learned in an earlier lesson
That is
Write the problem Substitute
Simplify
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Example Evaluate the expression when x = -3
5(x 4)
1. Write the problem 5(x 4)
2. Substitute5(-3 4)
3. Simplify 5(-7)
-35
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Analysis
In the previous example you should have
analyzed the problem first to know what to do
to solve it Lets take a look at what you were expected
to know
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Analysis
Evaluate the expression when x = -3
5(x 4)
In this problem you were expected to know:
To substitute -3 for x to get 5(-3 4)
The order of operations tells you to evaluate the parenthesis first
The rules for subtracting real numbers states that you add the opposite and
follow the rules for adding
In this case, since the signs are the same you add and keep the signs
After simplifying the parenthesis you were to multiply
The rules for multiplying state that if the signs are different the answer is
negative
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Comments
As you can see in the previous example, solving the
problem involved more then the concepts that we
just reviewed
Often it is not explicitly stated what you need to
dothroughout this course you will be expected to
analyze problems and then solve them based upon
what you have learned That is why I require that you show your workso
that we can go back and problem solve when you
dont get the correct solution
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Comments
On the next couple of slides are some practice
problemsThe answers are on the last slide
Do the practice and then check your answersIfyou do not get the same answer you must
question what you didgo back and problem
solve to find the error
If you cannot find the error bring your work to
me and I will help
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Your Turn
Find the product
2. (-8)(3)
3. (20)(-65)4. (-15)
Simplify the variable expression7. (-3)(-y)
8. 5(-a)(-a)(-a)
3
5HGJ
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Your Turn
Evaluate the expression:
-8x when x = 6
3x2 when x = -2 -4(|y 12|) when y = 5
-2x2 + 3x 7 when x = 4
9r3 (- 2r) when r = 2
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Your Turn Solutions
-24
-1300
-9 3y
-5a3
1. -48
2. 12
3. -284. -27
5. 76
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Summary
A key tool in making learning effective is beingable to summarize what you learned in a lesson inyour own words
In this lesson we talked about multiplying realnumbers and the properties of multiplicationTherefore, in your own words summarize thislessonbe sure to include key concepts that thelesson covered as well as any points that are stillnot clear to you
I will give you credit for doing this lessonpleasesee the next slide
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Credit
I will add 25 points as an assignment grade for you working on
this lesson
To receive the full 25 points you must do the following:
Have your name, date and period as well a lesson numberas a heading.
Do each of the your turn problems showing allwork
Have a 1 paragraph summary of the lesson in your own
words
Please be advised I will not give any credit for work submitted:
Without a complete heading
Without showing work for the your turn problems
Without a summary in your own words