Multiplying 2-digit by 2-digit: 23x44

compute 23 times 44 and maybe the hardest part of this problem or maybe the first hard part is to recognize that that dot even means multiplication this could have also been written as 23 times 44 or they could have written it as 23 in parentheses times 44 so you just put the two parentheses next to each other that also implies multiplication so now that we know we're multiplying let's actually do the problem so we're going to multiply 23 I'll write it bigger we're going to multiply 23 by 44 I'll write the traditional multiplication sign there just so that we know we're multiplying it's not when you write it vertically like this you very seldomly we very seldom put a dot there so let's do some multiplication so we start off let's start off multiplying this four in the ones place times 23 so you have three times four is 12 we can write two in the ones place but then we want to carry the 1 or we want to regroup that one in the tens place so it's 12 so you put the one over here and now you have 4 times 2 is 8 plus 1 is 9 is 9 so you can think about it is 4 this fort right here times 23 is 92 that's what we just solved for now we want to figure out what this 4 times 23 is now what we do here is when you just do it mechanically when you just learn the process you stick a zero here but the whole reason why you're putting a zero here is because you're now dealing with a four in the tens place if you get another I don't know a three or four or whatever digit you're dealing with the hundreds place you'd put a Z more zeroes here because we're going to find out the 4 times 23 is 92 we just figure that out if we just multiply this 4 times 23 again we would get 92 again but this 4 is actually a 40 so it actually should be 920 and that's why we're putting that 0 now you're going to see it in a second so we have let me put this in a different color so this 4 now we're multiplying 4 times 3 is 12 let's put the 2 right here it should be in the tens place because this is really a 40 times the 3 just think about it but or you could just think over process is the next space that's free 4 times 3 is 12 carry the 1 this blue one is from last time you ignore it now you don't want to mess that up make that mess it up that's when we multiplied this 4 so now we have 4 times 2 is 8 plus 1 is 9 is 9 so what we've figured out so far is 4 times 23 is 92 and this green 4 times 23 is 920 and that's because this green 4 actually represents 40 it's in the tens place so when you multiply 44 times 23 it's going to be 4 times 23 which is 92 plus 40 times 23 which is 920 I just want to make sure we understand what we're doing here and so we can take their sum now let's add them up 2 Plus 0 is 2 9 plus 2 is 11 carry the 1 1 plus 9 is 10 put a comma here just so it's easy to read every third digit so 23 times 44 is 1012