Multiply with partial products
Let's multiply 7 times 253 and see what we get. So just like in the last example, what I like to do is I like to rewrite the largest number first. So that's 253. And then write the smaller number below it and align the place value, the 7. It only has a ones place, so I'll put the 7 right over here below the ones place in 253. And then put the multiplication symbol right over here. So you could read this as 253 times 7, which we know is the same thing as 7 times 253. And now we are ready to compute. And there are many ways of doing this, but this one you could call the standard way. So what I do is I start with my 7. And I multiply it times each of the numbers up here, and I carry appropriately. So first I start with 7 times 3. Well, 7 times 3 we know is 21. Let me write that down. 7 times 3 is equal to 21. You could do this part in your head, but I just want to make it clear where I'm getting these numbers from. What I would do in the standard method is I would write the 1 into 21 down here, but then carry the 2 to the tens place. Now I want to figure out what 7 times 5 is. We know from our multiplication tables that 7 times 5 is equal to 35. Now, we can't just somehow put the 35 down here. We still have to deal with this 2 that we carried. So we compute 7 times 5 is 35, but then we also add that 2. So it's 35 plus 2 is 37. Now, we write the 7 right over here in the tens place and carry the 3. Now we need to compute what 7 times 2 is. We know that 7 times 2 is 14 from our multiplication tables. We can't just put a 14 down here. We have this 3 to add. So 7 times 2 is 14, plus 3 is 17. So now we can write the 17 down here, because 2 is the last number that we had to deal with. And so we have our answer. 7 times 253 is 1,771.