3(a + b) = 3a + 3b is an example of which algebraic property?
Distributive Property
Associative Property of Addition
Commutative Property of Addition
Symmetric Property
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jimthompson5910 (jim_thompson5910):
what did you get?
OpenStudy (caitlinnr14):
im confused
jimthompson5910 (jim_thompson5910):
so you're completely stuck and haven't gotten anywhere?
OpenStudy (caitlinnr14):
nope
jimthompson5910 (jim_thompson5910):
the Symmetric Property is the idea that
if x = y, then y = x
so that answer choice is eliminated since this isn't what we want
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jimthompson5910 (jim_thompson5910):
what is the Commutative Property of Addition ?
OpenStudy (caitlinnr14):
addends can be added in any order and the sum is always the same.
jimthompson5910 (jim_thompson5910):
good
jimthompson5910 (jim_thompson5910):
basically the idea that
x+y = y+x
for any real numbers x and y
jimthompson5910 (jim_thompson5910):
so that's out too
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jimthompson5910 (jim_thompson5910):
how about the Associative Property of Addition
what does that say?
OpenStudy (caitlinnr14):
it doesn't matter how you add them, the totals are always same.
jimthompson5910 (jim_thompson5910):
close, more like how the grouping doesn't affect the answer
OpenStudy (caitlinnr14):
ok
jimthompson5910 (jim_thompson5910):
so
a+(b+c) = (a+b)+c
for any real numbers a, b, c
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jimthompson5910 (jim_thompson5910):
so that choice is out
jimthompson5910 (jim_thompson5910):
the only thing left is the distributive property
jimthompson5910 (jim_thompson5910):
and it turns out that the distributive property is
x(y+z) = x*y + x*z
which is exactly what is used in the original problem