### Video Transcript

Calculate 4175 multiplied by 81.

Here, we’re multiplying a four-digit number, 4175, by a two-digit number, 81. This isn’t the sort of calculation that we can do in our heads. So let’s use a written method, long multiplication, to help us find the answer. First of all, we’re going to write out both numbers vertically. 4175 multiplied by 81. Notice how we’ve made sure that each digit is lined up in the correct columns. Now, to work out the answer, what we’d normally do is to take each digit, one by one, in the first number and multiply them by the ones digit in the second number.

In this calculation, this would give us the answer to 4175 times one. There’s a one in the ones place. But rather than work out the answer digit by digit, we can look at this calculation and think to ourselves. We know what it’s going to be. 4175 multiplied by one is 4175. We’ve saved ourselves some time there because we already knew what the answer was going to be. Any number multiplied by one stays the same. Now, our second step requires a little bit more thought. We need to multiply 4175 by the number in the tens place, which is eight. Now, it would be a mistake to multiply 4175 by eight. The eight is actually worth eight tens. So we need to multiply it by 80. Now, we know that 80 is the same as 10 times eight. So really, what we’re working out is 4175 times 10 times eight.

To multiply any number by 10, we simply shift the digits one place to the left. So if we write a zero as a placeholder in the ones place, all our digits in the answer now are going to be shifted one place to the left. It’s as if we’ve multiplied them by 10. We’ve already done the times 10 part of the calculation. We now just need to multiply each digit by eight. And this will be the same as if we’d multiplied by 80. Firstly, we’ll look at the ones digit. What is five times eight? Let’s start with a fact we already know. We know that 10 times eight equals 80, and five is half of 10. So five times eight will be half of 80. And half of 80 we know is 40. Five times eight equals 40.

Now, the tens digit is seven. What is seven times eight? Well, we know five times eight is 40. And seven is two more than five. So we need to add another two lots of eight to 40. Two times eight equals 16. So from this we can work out that seven times eight is the same as 40 plus 16. The answer’s 56. Now, we already have four that we’ve exchanged. So we need to add that four to 56 to give us an answer 60.

Time to multiply the hundreds. One times eight we know is eight. We’ve already exchanged six. So we need to add that to eight to give us an answer of 14. And finally, what is four times eight? As we’ve already said, five eights are 40. So four eights must be one lot of eight less than 40. 40 take away eight equals 32. We’ve already got one that we’ve exchanged that we need to add. So that takes us to 33. So we’ve found the answer to 4175 times one and also times 80. And now, we just need to put the two parts back together to find out the answer to 4175 times 81.

Five ones plus zero ones equals five ones. Seven tens plus zero tens equals seven tens. 100 plus zero equals 100. Look how the hundreds, tens, and ones in our answer are the same as one of the numbers that we’ve multiplied. Four thousands plus four thousands equals eight thousands. Then we’ve got nothing to add to our three lots of ten thousand and also our three hundred thousands. We’ve used long multiplication to find the answer. 4175 multiplied by 81 equals 338175.