Multiplication of Real Numbers

8/14/2019 Multiplication of Real Numbers

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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

Multiplication of Real Numbers

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