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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