### Video Transcript

3468 multiplied by 62 equals what?

We can tell by the way that this calculation has been set out vertically that we need to use long multiplication to find the answer. And long multiplication is understanding that if we need to multiply by 62, we’re going to have to partition 62. 62 is the same as 60 and two. So if we’re looking to multiply 3468 by 62, we can multiply the number by two then by 60. And if we add these two amounts together, we’ll find the overall total of 3468 multiplied by 62.

So let’s begin with the first step. We need to multiply 3468 by two. And we can do this column by column from right to left. Eight multiplied by two equals 16, which is six ones. And we can exchange 10 ones for one 10. Six multiplied by two equals 12 plus the one that we’ve already exchanged gives us 13. And again, we can exchange 10 tens for 100. Four hundreds multiplied by two equals eight hundreds plus the one that we’ve exchanged equals 900. And then, finally, three thousands multiplied by two gives us six thousands. And so we know that 3468 multiplied by the two part of 62 is 6936.

Now we need to multiply the top number by the six digit in 62. But we can’t just multiply this number by six because the six is worth 60. It would be much easier if we could just multiply by six. But we can’t because that six is worth six tens. Multiplying by 60 is the same as multiplying by 10 and then by six. And we know that when we multiply a number by 10, the digits shift one place to the left. So if we write a zero in the ones place, all of our digits now that we write down have shifted one place to the left. We’ve multiplied them by 10. So now, we can multiply each digit by six.

Eight sixes are 48. Six sixes are 36 plus the four we’ve exchanged equals 40. That is how each of our answers is one more place to the left and it would be normally. This shows that we’re not really multiplying by six. We’re actually multiplying by 60. Four sixes are 24 plus the four we’ve exchanged equals 28. And finally, three sixes are 18 plus the two that we’ve exchanged takes us to 20. And so we can say 3468 multiplied by the 60 part of 62 equals 208080.

Now, all we need to do is to combine the two answers to find the total. If we add zero ones to six ones, we’re still left with six ones. Now, we can add the tens. This is why it’s such a good idea to cross through any digits that we’ve exchanged and we’ve dealt with. On this video, we are using an orange color for them so they’re easy to spot and to ignore now when we’re adding up. If you’re using a pencil, sometimes it’s easy to see them and to include them as part of the overall total. So to avoid doing this, it makes sense just to cross them through when they’re dealt with.

Three tens plus eight tens equals 11 tens. And we can exchange 10 tens for 100. Although nine hundreds plus zero hundreds equals nine hundreds, we’ve still got that 100 underneath to consider. So the total of this column is ten hundreds, which we can exchange for 1000. Six thousands plus eight thousands equals fourteen thousands. But we exchange one as well. That takes us to fifteen thousands. And ten of those thousands are the same as one lot of 10000. Although we’ve got nothing in this column, we’ve still got that one lot of 10000 underneath that we exchanged. And finally, we only have two hundred thousands in a hundred thousands place.

And so we found the answer using long multiplication. We multiplied by two and then by 60. And then we combined those two answers together to find what multiplying by 62 will be worth.

3468 multiplied by 62 equals 215016.