Associative law of addition | Arithmetic properties | Pre-Algebra | Khan Academy


Use the associative law of
addition to write the expression. We have a 77 plus 2 in
parentheses, plus 3, in a different way. Simplify both expressions
to show they have identical results. So this associative law of
addition, which sounds very fancy and complicated, literally
means that you can associate these three numbers
in different ways or you can add them in different orders. Now let me just make
that clear. So the way they wrote it right
here, they wrote it 77 plus 2 in parentheses, and then
they wrote plus 3. These parentheses mean
do the 77 plus 2 before you add the 3. So if you were to evaluate
this, you would evaluate what’s in the parentheses first.
So you would say, well, 77 plus 2, that’s 79, so
everything in the parentheses just evaluates to 79. And then you still
have that plus 3. And 79 plus 3 is 82, so
this is equal to 82. That’s if you just evaluate
it the way that they gave it to us. Now, the associative law of
addition tells us it doesn’t matter whether we add 77 and 2
first or whether we add 2 and 3 first. We can associate
them differently. So this is going to be
the exact same thing. This is the exact same
thing as– we could write it this way. Let me write them all. 77 plus 2 plus 3. If we have no parentheses here,
this is actually the same thing as this over here,
because we’d go 77 plus 2 is 79 plus 3 is 82. But the associative law tells
as, well, you know what? I could do 77 plus 2 plus 3. I could add this first and then
add it to 77, and it’s going to be the exact same thing
as if I added these two guys first and then add the 3. Let’s verify that
for ourselves. So 2 plus 3 is 5, so this
evaluates to 77 plus 5. And 77 plus 5, once
again, is 82. So it doesn’t matter how you
associate the numbers. Either way, you get 82. And that’s the associative
law of addition.

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