Subtracting Real Numbers

Algebra 1

Ch 2.3 – Subtraction of Real Numbers

Objective  Students will subtract real numbers

Before we begin…  In elementary school you learned how to subtract

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numbers…in those instances the number you were subtracting was never bigger than the original number… In today’s lesson we will look at subtracting real numbers…recall that real numbers are positive and negative numbers… Student’s have a hard time with this concept because they are not used to working with negative numbers… So there is a rule to help you…. Let’s look at that rule…

Subtracting Real Numbers  To subtract real numbers you: 2. Add the opposite 3. Then follow the rules for adding

Example: Algebraically: Example:

a – b = a + (-b) 3 – 5 = 3 + (-5) -2= -2

Example #1  Find the difference 1.

-4-3

Change the problem to an addition problem by adding the opposite of 3, which is – 3.

-4 -

3

- 4 + (- 3) 1.

Then follow the rules for adding. In this case both signs are the same so you add and keep the sign…

-4 + (- 3) -7

Example #2  Find the difference 1.

10 - 11

Change the problem to an addition problem by adding the opposite of 11, which is – 11.

10 -

11

10 + (- 11) 1.

Then follow the rules for adding. In this case the signs are different so you subtract and keep the sign of the larger number

10 + (- 11) -1

Example #3  Find the difference 1.

11 - 10

Change the problem to an addition problem by adding the opposite of 10, which is – 10.

11 -

10

11 + (- 10) 1.

Then follow the rules for adding. In this case the signs are different so you subtract and keep the sign of the larger number

11 + (- 10) 1

Example #4  Find the difference 1.

- 3 – (-6)

Change the problem to an addition problem by adding the opposite of (-6), which is 6.

-3 - (-6) -3 + 6

1.

Then follow the rules for adding. In this case the signs are different so you subtract and keep the sign of the larger number

+

-3 6 3

Comment  In the previous example you will notice that

you subtracted a negative

- 3 – (-6) Double negative gets changed to a positive

 Whenever you see the double negative

sign…a bell should go off in your head that you need to do something…and that is change the double negative to a positive

Comment  It is really important that you are

comfortable working with positive and negative numbers…  Later on in this course when we work with linear and quadratic equations you will find out that the sign of a number means something…  You will make your life easy if you are able to master these concepts up front….

Comments  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  2. 3. 4. 5. 6.

Find the difference 4–9 8 – (-5) -2 – (-7) 12.5 – 9.8 5.4 – (-3.8)

1. -6.6 – (-16.1) 2. 6 - |-2| 3. 15 - | - 6| 4. |5| - 7.9 5. 34.1 - |-57.2|

Your Turn Solutions 1. -5

1. 9.5

2. 13

2. 4

3. 5

3. 9

4. 2.7

4. -2.9

5. 9.2

5. -23.1

Summary  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 subtracting real numbers … 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  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. Do each of the your turn problems showing all work 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…