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## Arithmetic properties

Current time:0:00Total duration:2:15

# Associative law of multiplication

## Video transcript

Use the associative law of
multiplication to write-- and here they have 12 times 3 in
parentheses, and then they want us to multiply that times
10-- in a different way. Simplify both expressions
to show they have identical results. So the way that they wrote it
is-- let me just rewrite it. So they have 12 times 3 in
parentheses, and then they multiply that times 10. Now whenever something is in
parentheses, that means do that first. So this literally
says let's do the 12 times 3 first. Now, what
is 12 times 3? It's 36. So this evaluates to 36, and
then we still have that times 10 over there. And we know the trick. Whenever we multiply something
times a power of ten, we just add the number of zeroes that we
have at the back of it, so this is going to be 360. This is going to be
equal to 360. Now, the associative law of
multiplication, once again, it sounds like a very
fancy thing. All that means is it doesn't
matter how we associate the multiplication or it doesn't
matter how we put the parentheses, we're going to get
the same answer, so let me write it down again. If we were to do 12 times 3
times 10, if we just wrote it like this without parentheses,
if we just went left to right, that would essentially be
exactly what we just did here on the left. But the associative law
of multiplication says, you know what? We can multiply the 3 times 10
first and then multiply the 12, and we're going to get the
exact same answer as if we multiplied the 12 times
the 3 and then the 10. So let's just verify
it for ourselves. So 3 times 10 is 30, and we
still want to multiply the 12 times that. Now, what's 12 times 30? And we've seen this several
times before. You can view it as a 12 times
3, which is 36, but we still have this 0 here. So that is also equal to 360. So it didn't matter how we
associated the multiplication. You can do the 12 times 3 first
or you can do the 3 times 10 first. Either way, they
both evaluated to 360.