This is the video for lesson 40 on my web site, Multiplying Two Digits by One Digit.
Many students use a calculator to do all of their computations but it's important to be able to do multiplication by hand and more importantly to understand why it works the way that it does. Let’s take a look at some examples from the lesson on my web site.
First, I'm going to multiply 34 times two. Now, notice that I have my places lined up. I have the ones place on top of the 1’s place and the 10’s place on top of the 10’s place. In case, there is nothing in the 10’s place for the second number but still, the places are lined up appropriately which is very important otherwise, we’ll do the entire problem incorrectly.
Now in multiplying, we always start by multiplying the ones digit of the second number times the ones digit of the first number so we basically just do two times four which is eight. And in this particular problem, there is nothing else to do for that. We just write the eight and the one’s place of our answer. Now, I'm going to multiply the ones place of my second number times the 10’s place of the first number.
Now according to the procedure from multiplication, we’ll just do two times three which is six and then write the six here. It's important to understand what’s really going on. This three in the first number represents 30. It’s three 10’s which is 30. So, what we’re actually doing is 30 times 2 which is 60. 60 is six 10’s and that’s why we have a six in the 10’s place in our answer. Make sure that you understand that. It's really important to understand that multiplication is not just as magical procedure that works. We really are working with place of value.
Okay. Let’s take a look at the next example, 76 times 4. Again, I have my places lined up correctly. Just like we did before, first I'll do four times six. Now, that equals 24. Now we have a problem because 24 is a two-digit number. Here’s what we do. We’re going to put the four in the 1 place of our answer because in 24 we have four 1’s and we have two 10’s. We’re going to write a little tiny two above the 10’s place. And what that tells us is that when we work with 10’s which we’ll do in a moment; we have to add in those two 10’s that we still have to account for.
Okay. Now, I’ll do four times seven. And again, remember that the seven is really seven 10’s which represents 70. Okay. So 7 times 4 is 28. But since we’re dealing with 10’s, it's not 28. It's really 280. Now stated in other way though, it is 28 10’s which means I'll write 28 in the 10’s column or ending in the 10’s column which is here. Before I do that though, I have to add in the two 10’s from my previous calculation so it's actually 28 10’s plus two 10’s which is 30 10’s and I'll write that like this, 30 in the 10’s place. Keep in my mind that 30 10’s is really the same as 300. Make sure you see how that works.
Let’s take a look at another example, 99 times nine. Again, starting on the right, we have 9 times nine which is 81. I have to write the 1’s, the one, one in my one’s place and I'm going to carry the eight over here. All these means is we have to remember to add in eight 10’s after the next computation. Nine times nine is 81. Adding in the eight, the eight 10’s that we carried gives us 89 so we have 89 10’s which gets written like this and remember that 89 10’s equals 890.
I know that many students are thinking that they could easily do these problems on a calculator so why bother to know all these. It's just important to understand why the multiplication works the way it does and it's very important to have a solid understanding of place value and understand what it is that we’re really doing when we multiply in these problems.
Make sure you fully understand this. In later lessons, we’ll take this skill to the next level.
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