Expert: Josh - 9/13/2004

Question
how do I Identify each property shown?


(8.7 + 6.3) + 3.7 = 8.7 + (6.3 + 3.7)



Thanks It Would Help Me Out!

Answer
Hi Cody,

This property is called the "associative law of addition".
In plain terms, it means, that if we have to add up three or more numbers, the order in which you carry out the additions (likewise, for subtractions), doe NOT matter.

So, in general, if we have
a + b + c
You can group this expression like this,
(a + b) + c  ...[#1]
or this,
a + (b + c). ...[#2]

[#1] means that you work out what (a+b) is, then, add this onto c. Whereas, [#2] means that you first work out what (b+c) is, then, you add "a" to the result of (b+c).

To spell this out,
if we let a=8.7, b=6.3 c=3.7,
then,
8.7 + 6.3 + 3.7
=(8.7 + 6.3) + 3.7
=15.0 +3.7
=18.7

which of course, as we can verify here, is equivalent to
=8.7 + (6.3 + 3.7)
=8.7 + 10.0
=18.7

One more thing, you may or may not have heard of this, there's also a rule called the "commutative law of addition", which in plain term, means that you can re-arrange the terms (like "a","b","c" in the example shown earlier) and add them in any order.

Example,
a+b+c and b+c+a and c+a+b etc. all amount to the same thing. If you prefer to look at numbers, for example,
1 + 2 + 4
= 1 + 4 + 2 ...here, we swapped b=2 and c=4.
= 7 eventually, they add up to seven.

Cheers,
Josh