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Properties of Equality

Page history last edited by PBworks 16 years, 4 months ago
 

 

PROPERTIES OF EQUALITY!!

 

 

 

          Course Summary

 

 

 

The Properties of equality are  usually used in Algebra in the

 

solving of certain algebraic

 

equations. There are four types of properties, which  are the four operations you use in math

 

addition, subtraction, multiplication, and division. BUT, now they are called Addition property of

 

equality, Subtraction property of equality, Multiplication property of equality, and Division

 

property of equality.

 

 

Theory or how to use the properties of equality

 

       The properties are usually used in algebra to get rid of the nasty variables or

 

unknowns. In an equation, it has to be balanced, so when you do something to one

 

side of an equation you must do the same thing to the other therefore making it

 

equal. Understood?... good! That is what the Properties of Equality are based on EQUALITY=equal,

 

one side is the same as the other. Remember to be careful when you are using this

 

method because one little slip and our answer could be completely wrong. Now in

 

an equation to use the equalities you again have to be careful, you usually do the

 

inverse (opposite) operation to the other side of the equation which means across the

 

= sign. Ex: 7n=21 you probably already know the answer but translate it into

 

something we all understand which means: 7 times something (n) is 21 so you isolate

 

the variable which is "n" leaving 7 and 21 since it is n times seven you divide 21

 

with 7 equalling three which equals three. IF you don't believe me you can check

 

you work 7x3=21. Not so hard right?

 

     Subtraction property of Equality

 

                  In the subtraction property of equality we have to

 

use the inverse of subtraction to make the subtraction... in other

 

words it has to be an addition equation to use the subtraction

 

property of equality so the question has to be like this:

 

50+x=65 Here you would use the subtraction property by

 

subtracting 50 from both sides 50-50=0. That cancels each other

 

out then 65-50=15 so x=15 and you check 50+15=65. Simple!

 

Also for those smarties out there here is

 

the algebraic formula from mathwords:

 

"Subtraction: If a = b then a – c = b– c."

 

 

 

 

 

 

Addition property of equality

 

So if you still don't remember we use the inverse or opposite operation so in this

 

case it has to be subtraction to make it an addition property. Ex: n-653=254 so in

 

order to do this you must add 653 and 254=907 and that will find n. Check with 907-

 

653 and that should result with 254! Another Algebraic Formula from Mathwords on

 

the property of addition:" If a = b then a + c = b + c."

 

Multiplication  property of equality

 

           The inverse of multiplication is division right? So that means to use

 

 

the multiplication property it has to be a division operation. For example:

 

x/10=50, now we have the opposite of x/10 which is 10/1 we multiply 10/1with x/10 

 

it will cancel each other out, isolating the variable. Now we have 10(10/1 is the same thing as 10)

 

times 50 making 500 so, x=500. Finally we check the problem 500/10=50, 500 divided by 10 equals

 

50, that's how we use the multiplication property of equality! The Algebraic example again from math 

 

words (its a really helpful site the links on the bottom):"If a = b then ac = bc."

 

 

 

 

 

Division Property of Equality

 

        It is the opposite or inverse of the multiplication operation so you can only use it during a multiplication

 

problem such as: 5x=105. What we do to one side of the equation we do to the other so 5x/5 (5x divided by 5)

 

=105/5 (105 divided by 5). x is isolated leaving it by itself and now you have 105 divided by 5 which is 21. x=21

 

Now we check 5x21=105 when 21=x! Final Algebraic example:"If a = b and c ≠ 0 then a/c = b/c"

 

                                      X-Tra Practice!

 

 

Name the property or  properties illustrated by each statement

 

 

1.)n x 1=n     2.) 15/3+3=5=4     3.) 2/3 x 3/2=1    4.)3 x 0=0  

 

5.)11-2=11-2   6.) 0+n=n

 

 

 

 

 Here is some helpful links that I used to put this together:

 

Other Explanations for the properties

 

Other properties and helpful things

 

Equivalence Properties of Equality

 

Another perspective or explanation of the properties of equality

 

Other Related WIKI Pages:

 

 

Distributive Property

 

Properties of Addition and Multiplication

 

 

 

 

BY Reading this I hope you now know more about the properties of equality,

 

 

how to use them, and basic Algebra. Feel free to comment (contributors only) =)))

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Comments (15)

Anonymous said

at 2:38 pm on Oct 24, 2007

Looks a little crowded doesn't it???

Anonymous said

at 12:18 pm on Oct 27, 2007

i agree wit jennay...but nice work

Anonymous said

at 12:31 pm on Oct 29, 2007

niceeee its colorful haha

Anonymous said

at 9:26 pm on Oct 29, 2007

ha i finally found yours. I spent bout 10 minutes tryin to find it. Its very interesting. i only have on thing to say and that is that ur words kinda get cut off when " The properties of equality are used in..."
Its still cool! :)

Anonymous said

at 9:39 pm on Oct 31, 2007

the reason theres gaps in between is so it wouldn't be scrunched! i hope it looks better

Anonymous said

at 9:52 pm on Oct 31, 2007

yep it does. good job

Anonymous said

at 12:17 pm on Nov 3, 2007

It would look a little better if it was double-spaced, or at least spaced between paragraphs. Oh yea, you spelled "properties" wrong on the first line. =D

Anonymous said

at 12:18 pm on Nov 3, 2007

o wait, it is doubled spaced. nvr mind.

Anonymous said

at 1:16 pm on Nov 5, 2007

pretty kool!!! ^.^

Anonymous said

at 2:32 pm on Nov 5, 2007

colorful and good job

Anonymous said

at 5:17 pm on Nov 5, 2007

nick, scientifis notation is math!(replying from nathan's page)

Anonymous said

at 7:58 pm on Nov 5, 2007

Nice! <3

Anonymous said

at 7:13 pm on Nov 7, 2007

o nick, one more thing. Some of the colors hurt my eyes. U should try to fix those up. Ur page is almost done!

Anonymous said

at 6:27 pm on Nov 21, 2007

Painful use of color. The use of color is supposed to enhance the information on your page.
I worry about these explanations being your own. There are some spelling and grammar errors.
I would like to see more examples.

2.5 of 4 points
10.5 of 12 total project points

Anonymous said

at 6:46 pm on Apr 23, 2008

I agree with Jad and Mr. Martin. really, you should change the colors.

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