Box Multiplication

Welcome to math with mister J in this video, I'm going to cover how to multiply using the box method. Now the box method is a different type of strategy for multiplying larger numbers. This method is similar to the traditional standard logarithm, but you'll notice that the setup is different, but what we're doing is essentially the same. The box method actually helps break down what is happening through the traditional standard logarithm, and it will show how and why things work. It will give a better overall understanding of multiplying larger numbers. In this video, I'm specifically going to cover how to multiply a three digit number by a two digit number. So let's jump into number one where we have 368 times 43, and the steps that we're going to use in order to solve this with the box method are at the top of the screen. And our first step, we need to draw our box. So I'll come down here and we will take a look at this box. So the top side length there is a little longer than the sides. And that's because the top is going to be where we write this three digit number, and the side is where we are going to have the two digit number. So we're going to need more room for that three digit number there. So like I said, the top is going to be the three digit number, so we need three sections going vertically or up and down. Now the side is going to be the two digit number. So we need to split this in two sections. So that's what our box is going to look like. And the more you do of these, your spacing and how you make your boxes, you're going to get better at that, the more you do. So now we move to expand our factors. And the factors are the numbers that were multiplying in order to get our product, which is an answer to a multiplication problem. So for number one, the factors are 368 and 43. So we need to expand those out to show the value of each digit. So for example, let's start with this three here. So the value of that three is 300. So we're going to expand to show the value of each digit. The 6 has a value of 60. And the 8 has a value of 8. So that's why we have those three sections going up and down for that three digit number. Now let's do 43. So we'll start with the four, which has a value of 40. And the three has a value of three. So we drew our box. We expanded the factors. Now we multiply. So we can use mental math to multiply these numbers like this. So let's do 40 times 301st. So we'll do four times three, which is 12. And now we place our one, two, three, zeros. On the end of that 12, in order to push the one and the two to the correct place value and give us our correct answer. So 40 times 300 is 12,000. Now we can do 40 times 60. So four times 6 is 24. Put our two zeros here. Back on the end, that way it pushes everything to the correct place value. And we get 2400. Then we have 40 times 8. So four times 8, 32. One, zero on the end. 320. Now we're going to go to this three, so we'll start with three times 300. So three times three is 9, and then we need one, two, zeros on the end. And we have 900. Three times 60. Well, three times 6 is 18. And we have this one zero here. So we get 180. And we end with three times 8, which is 24. So we're done with the multiply step. Now we need to wrap things up with the add step. So we add all of these numbers here. And these are called our partial products. So they are part of that final product or answer. And I like to add them greatest to least. So what I mean by that, we would start with 12,000. Then we would go to 2400 and notice I'm lining all my places up and then we would have 900. 320 180 and 24. And now we are ready to add, so we have four two plus 8 is ten plus two is 12. One plus four is 5 plus 9 is 14 plus three is 17 plus one is 18. One plus two is three plus two is 5. And then we have one in the 10,000s place so we get 15,000 824. So on to number two, where we have 692 times 95. So let's draw our box and we want that top side there to be a little longer since that's going to be where the three digit number is. So let's break into three sections. And then the 95 is going to be on the side so we can break into two sections. Now we expand our factors. So we'll start with 6, which has a value of 600. A 9 value of 90. And a two with a value of two. 9 with a value of 90. And 5 with a value of 5. So now we're ready to multiply. 9 times 6, 54. And one, two, three, zeros. Try to squeeze this in here. So 54,000 there. I'll put my comma. Now we have 90 times 90, so 9 times 9 is 81. Two zeros. 8100. And then 90 times two. So 9 times two is 18. And one zero. So now we move to the 5, 5 times 6 is 30. Plus our we need our two zeros on the end there to push the three to the correct place value, and we get 3000. 5 times 90, 5 times 9 is 45. One, zero there. And we end with 5 times two, which is ten. So there are all of our partial products, and we are ready to add. So we'll start greatest to least. So 54 thousand, then we have 8000 100. Then we have 3000, then we have 450. Then we have 180, and we end with ten. It's always a good idea to double check that you have all of your partial products there in your addition problem. So we see that we have one, two, three, four, 5, 6, and we have one, two, three, four, 5, and 6. So we're good to go and ready to add. So we have a zero in the ones place. Then we have 5 plus 8, which is 13. Plus one is 14. Then we have one plus one is two plus four is 6 plus one is 7. Four plus 8 is 12 plus three is 15. And one plus 5 is 6. So we get 65,000 740. So there you have it. There's how you use the box method in order to solve a multiplication problem. I hope that helped. Thanks so much for watching. Until next time, peace.