3-Digit Multiplication: A Step-By-Step Review | Multiplying by a 3-Digit Number | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to go through a quick review of three digit multiplication if it's been a while and you need a quick refresher this should be helpful whether you're in high school college continuing your education as an adult helping with an assignment or maybe you just learned this recently and need a quick refresher really no matter where you're at here are a couple of examples to help you out let's jump into number one where we have 325 times 281 now the first thing that we're going to do we're going to line this up vertically so we're going to rewrite it up and down 325 times 281 now we're ready to go through our multiplication process so we start by multiplying the top number by the ones digit of the bottom number so the ones digit of the bottom number is the one in 281 so we need to take that one to the five the two and the three we can forget about the two and the eight in 281 right now we're only concerned about the ones digit we'll get to those other digits later so we'll start with one times five which is five then we have one times two which is two and then one times three which is three so now we're done with the ones digit of our bottom number so i'm going to cross it off i'm going to cross things off as we finish up with them that way we avoid confusion moving forward through our process now we move to the tens digit where we have an eight now the value of that eight is eighty we're moving over one place to the left to the tens digit so we need a zero right here as we start with our tens digit now we can multiply so eight times five is forty so we have another zero here and carry the 4. then we do 8 times 2 which is 16 plus 4 is 20. so another 0 and carry the 2. and then we have 8 times 3 which is 24 plus the carry 2 is 26. so we'll write our 6 and there aren't any more places to the left to multiply by so we can bring that 2 straight down here and we have twenty six thousand i'll put our comma in and we're done with this eight and we're done with the four and two that we carried so i'm crossing all that off that way we know we are done with it now we move to the hundreds digit we have a 2 there that 2 has a value of 200 so we need two zeros once we move over to the hundreds place now we multiply two times five is ten so we'll put our zero carry the one two times two is four plus one is five and then we have two times three which is 6. 65 000 so we can put our comma in and once we get to this point we add these numbers to get our final product or answer we'll start with the ones place five plus zero plus zero is five two plus zero plus zero is two three plus zero plus zero is three six plus five is eleven so we'll put our one and then carry the other one and then one plus two is three plus six is nine we will put in our comma and this is our final answer 91 325 now i do want to mention one more thing before moving on to number two and this is going to help our overall understanding of this process let's take a look at these three numbers right here the three numbers we added together to get our final answer those are called partial products they are part of the final product the product is the answer to a multiplication problem so again the three numbers we added together are called partial products they're part of that final product now 325 well that came from the ones place where we had a one so we did one times the top number which is 325 one times 325 equals 325 so that was our first partial product then we moved to the tens digit where we had an eight the value of that eight is eighty so we had eighty times our top number of three hundred twenty-five and that gave us an answer of 26 000 so that was our second partial product and then lastly we had a 2 in the hundreds place that 2 has a value of 200 so we did 200 times 325 and that gave us 65 000 so that was our last partial product and at that point we add the partial products to get our final answer which was 91 325 so something to keep in mind as you're going through the process let's move on to number two where we have 6724 times 549 so let's line this up vertically and then go through our process so we'll start with the ones where we have a nine so nine times four 36 carry the three then we have nine times two which is 18 plus that three is 21 then we have 9 times 7 which is 63 plus that 2 is 65 and then we have 9 times 6 which is 54 plus that carried six that gives us 60 so we can put our zero there are no more places to the left to multiply by so we can bring that six straight down so we have sixty thousand five hundred sixteen we can put our comma in and then we are done with the ones and then these carried numbers now we'll move to the tens place and multiply by that tens digit which is a four so that four has a value of forty we are moving over to the tens so we need a zero there then we do four times four which is sixteen carry the one four times two is eight plus one is nine then we have four times seven which is twenty-eight so we'll put our eight and carry the two and then we have four times six which is 24 plus 2 is 26 no more places to the left so we can bring that 2 straight down put our comma in and we have 268 hundred sixty we're done with the four this carried one and then this carried two lastly we're moving over to the hundreds place where we have a five now that five has a value of five hundred so we need our two zeros there again because we're moving over to the hundreds place and now we can multiply start with five times four which is twenty so we have another zero carry the 2. then we have 5 times 2 which is 10 plus the carried 2 that gives us 12. then we have 5 times 7 which is 35 plus the carried 1 is 36 carry the 3 and then we have 5 times 6 which is 30 plus that carried 3 is 33 we will put a 3 here and then the carried 3 there are no more places to the left so we can bring it straight down we can put a comma here and then another comma here and now we are ready to add start with the ones place so six plus zero plus zero gives us six one plus six is seven five plus nine is fourteen carry the one one plus zero is one plus eight is nine plus two is eleven carry the one one plus six is seven plus six is thirteen plus six is nineteen carry the one one plus two is three plus three is six and then we have a three in the millions place we can put a comma here and a comma here and this is our final answer three million six hundred ninety one thousand four hundred seventy six so there you have it there's a quick review of three digit multiplication i hope that helped thanks so much for watching until next time peace