Transcript Ch 2.2 Adding Real Numbers

Algebra 1
Ch 2.2 – Addition of Real Numbers
Objective
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Students will add real numbers
Before we begin…
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In this lesson we will look at the rules for
adding real numbers
Additionally, we will look at 4 properties of
addition
We will be working with the properties and
adding real numbers throughout this
course…You will make your life easy if you
can master these concepts…
Properties of Addition
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The properties of addition are:
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Commutative Property
Associative Property
Identity Property
Property of Zero (Inverse Property)
You should already be familiar with these
properties and may have use them informally
in the past…In this lesson we will give them a
name and we will look at each one
individually…
Commutative Property
The commutative property states
“ The order in which two numbers are added
does not change the sum”
This property can be expressed as follows:
Algebraically:
a+b=b+a
Example:
3+2=2+3
5=5
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Associative Property
The associative property states
“The way you group three numbers when
adding does not change the sum”
This property can be expressed as follows:
Algebraically:
(a + b) + c = a + (b + c)
Example:
(-5 + 6) + 2 = -5 + (6 + 2)
1 + 2 = -5 + 8
3=3
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Identity Property
The identity property states:
“The sum of a number and zero is that
number”
This property can be expressed as follows:
Algebraically:
a+0=a
Example:
- 4 + 0 = -4
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Property of Zero
The property of zero is also known as the
inverse property. It states:
“The sum of a number and its opposite is
zero”
This property can be expressed as follows:
Algebraically:
a + (-a) = 0
Example:
5 + (-5) = 0
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Adding Real Numbers
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The rules for adding real numbers are the same as
for adding integers…
You learned these rules in 6th and 7th grade…
In this course you will be expected to know these
rules by rote memory…
Make no mistake about it….if the sign is wrong
the whole problem will be marked wrong…The
reason for that is later on in the course you will be
transforming and interpreting equations…If you do
not master the rules of integers you will not be
successful working with equations…
Rules for Adding
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1.
2.
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There are a number of ways to add
integers…however, the basic two rules are:
If the signs are the same you add and keep
the sign.
If the signs are different you subtract and
keep the sign of the larger number
Let’s see what they look like…
Adding – with the same sign
Add: 15 + 25
Since both numbers are positive simply add. The
final answer will be positive and look like this:
15
+ 25
40
Adding – with the same sign
Add: -10 + (-12)
Since both numbers are negative simply add. The
final answer will be negative and look like this:
(-10)
+ (-12)
-22
Adding – with the different signs
Add: -10 + 8
The signs of both numbers are different. 10 is negative and
8 is positive. To get you answer subtract 8 from 10 to get
2. Since 10 is the larger number and negative your answer
will be negative and look like this:
-10
+
8
-2
Adding – with the different signs
Add: 12 + (-5)
The signs of both numbers are different. 12 is positive and
5 is negative. To get you answer subtract 5 from 12 to get
7. Since 12 is the larger number and positive your answer
will be positive and look like this:
12
+ (-5)
7
Strategy
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When working with integers a strategy that
you can use to make it easier for you is to
chunk the problem…
That is…do the numbers first and then
evaluate for the signs.
Thought Process…
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When adding integers the thought process that you
should be going through is listed below
The first question you should be asking your self is
“are the signs the same or different?”
If you decide that the signs
are the same.
If you decide that the signs
are different.
Then add the numbers
Then subtract the numbers
Your answer will be the same
sign as the numbers
Figure out what the sign of
the larger number is and give
that sign to the answer
Comments
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On the next couple of slides are some practice
problems…The answers are on the last slide…
Do the practice and then check your answers…If
you do not get the same answer you must
question what you did…go back and problem
solve to find the error…
If you cannot find the error bring your work to
me and I will help…
Your Turn
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Identify the properties
1.
-8+0=-8
2 + (-3) = -3 + 2
-2 + 2 = 0
(-4 + 3) + 1 = -4 + (3 + 1)
2.
3.
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Your Turn
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Find the sum
5.
17 + 35 =
14 + (-11) =
0 + (-5) =
2 + (-9) + 3 =
-4 + 10 + (-6) =
6.8 + 3.3 + (-4.1) =
6.
7.
8.
9.
10.
Your Turn Solutions
1.
2.
3.
4.
Identity Property
Commutative Property
Property of Zero
Associative Property
5.
6.
7.
8.
9.
10.
52
3
-5
-4
0
6.0
Summary
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A key tool in making learning effective is being able to
summarize what you learned in a lesson in your own
words…
In this lesson we talked about adding real numbers
and the properties of addition… Therefore, in your
own words summarize this lesson…be sure to include
key concepts that the lesson covered as well as any
points that are still not clear to you…
I will give you credit for doing this lesson…please see
the next slide…
Credit
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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:
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Have your name, date and period as well a lesson number as a
heading.
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Do each of the your turn problems showing all work
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Have a 1 paragraph summary of the lesson in your own words
Please be advised – I will not give any credit for work submitted:
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Without a complete heading
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Without showing work for the your turn problems
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Without a summary in your own words…