Question

Can someone explain the transitive property of equality to me? I don't understand it. :)

Answer 1

Transitive Property of Equality

The following property: If a = b and b = c, then a = c. One of the equivalence properties of equality.

Note: This is a property of equality and inequalities. One must be cautious, however, when attempting to develop arguments using the transitive property in other settings.

Here is an example of an unsound application of the transitive property: "Team A defeated team B, and team B defeated team C. Therefore, team A will defeat team C."

Answer 2

Why is it the property for this though? O____O

If AB + BC = AC, and AB + BC = 40, then AC = 40?

The B is cancelled out? O_____O

Answer 3

Correct

Answer 4

Would it also apply if you multiplied or divided them? O_____O

Answer 5

I believe so...

Answer 6

Really, Sweden? O____O

Answer 7

no no. AB is a representation of a number.
BC is a representation of another number. you could call BC CD and still get the same answer if that makes sense to you.
its like you are giving the numbers names.
suppose AB = 25. This means that we are calling the number 25 AB. You can call 25 as Jessica if you want. This way we can use the abstract form of numbers instead of using 25.
suppose you are adding the ages of your family members.
It makes more sense for the person reading your calculation if you say
myAge+GrannysAge+Mom'sAge+ dad'sAge = 200
instead of 25+75+50+50 = 200
get it?

Answer 8

we assign names to numbers because it makes more sense in the real world.
at the end of the day, you can always say granny'sAge even though the value of her age changes every year. The numbers are not really important. What is important is what we mean by those numbers.

Answer 9

Yes really..

Answer 10

so AB+BC = 40 means that
the value of AB added to the value of BC gives 40
AC = 40 means that the value of AC is 40.
since we know that AB + BC also equals 40, this must mean that AB+BC = AC
now replace AB, BC and AC with say jessica, mrbonez and dhatraditya.
that means
jessica + mrbonez = 40.
dhatraditya = 40.
therefore jessica + mrbonez = dhatraditya.
get it?

Answer 11

So Sweden + me = you because....um..? O____O ????

Answer 12

because the values of adding you and sweden is the same as my value.

Answer 13

Cuz of your level? O___O

Answer 14

36+32=56?

Answer 15

no no lol.
let me explain with an example.
suppose my age is 40. suppose your age is 15 and suppose mrbonez's age is 25.
that means that when you add your age and mrbonez's age, you get a total of 40 years, because
15+25 = 40.
instead of writing the above equation that way, you can say
jessica's age + mrbonez's age = 40 years
dhatraditya's age = 40 years.
that means
jessica's age + mrbonez's age = dhatraditya's age

Answer 16

see what happened there? the number 40 is not really important. the information you got out of that was that your age added to sweden's age gives my age.

Answer 17

in the real world, we look for what the numbers mean. we are not really concerned with the actual numbers. it could be ages or length of our shadows at 5 pm in the evening or whatever.

Answer 18

:D Ok, I see. So they cancel out the B because it is the common um...number(?) and adding them together is the equivalent of AC? O__O

Answer 19

no. you are not canceling out B. B is just part of a name.
suppose my name was Adam Bing
and your name was Betty Crocker.
for keeping it short, we just use our initials
lets say our ages add up to 40.
lets say there is another guy called adam corolla whose age is 40.
that means
Adam Bing + Betty crocker = 40
adam corolla = 40
adam bing + betty crocker = adam corolla.

now lets just use the initials of our names and see what happens.
AB+BC = 40
AC = 40
AB+BC = AC.
this doesnt mean that you canceled out B.
It just means you added two seperate numbers to get another number.

Answer 20

O____O So, it just tells you that AB+BC=AC..... :D Ok, I think I get it now.

Answer 21

the names AB, BC and AC are just representations of numbers. they have nothing in common. it just so happens that one name was called AB and another BC leading to the confusion you have

Answer 22

it would be like saying 15+50 = 10 because 5 cancels out. that doesnt make any sense.

Answer 23

Hmmm...ok.... O_____O

Answer 24

Thanks for your help though. ^___^b

Answer 25

np