If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
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 the parentheses and then we want 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 parenthesis 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 times 10 and we know the trick whenever we multiply something times a power of 10 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 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 want left-to-right that would 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 let's see we're going to get the exact same answer as if we multiply the 12 times the 3 and then the 10 so let's just let's just verify it for ourselves so 3 times 10 3 times 10 is 30 and we still want to multiply the 12 times that it was 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 could do the 12 times 3 first or you could do the 3 times 10 first either way they both evaluate it 160