### Video Transcript

54 multiplied by 23 equals what?

We can tell by the way that this calculation has been written out that we need to use long multiplication to find the answer. We could find the answer mentally. But to start with, let’s use a written method. Long multiplication will help us to keep track of all the different numbers.

First, we can multiply 54 by the three digit. Four times three equals 12 and five multiplied by three equals 15 plus the one that we’ve exchanged equals 16. Now, we need to multiply 54 by the two digit, which of course is worth two tens or 20. We don’t need to do this digit by digit. This is the sort of calculation we could work out quite quickly in our heads.

If we know that 54 times two or 54 doubled is 108, then we know that 54 times 20 will be 10 times this amount, 1080. So that’s how to find the answer mentally. Let’s go through and carry on using long multiplication. We know that multiplying by 20 is the same as multiplying by 10 and then by two. We know that when a number is multiplied by 10, the digits move one place to the left. So if we put a placeholder zero in the ones place, we’ve shifted all the digits one place to the left. We’ve multiplied by 10.

Now we just need to multiply by two as normal. Four times two equals eight and five times two equals 10. And there that answer of 1080 that we predicted. Now what we need to do is to add our totals of 54 times three and 54 times 20 to find the overall total: 54 times 23.

Two ones plus zero ones equals two ones. Six tens plus eight tens equals 14 tens. And we can exchange 10 of those 14 tens for 100. 100 plus zero hundreds equals 100. Don’t forget the 100 underneath equals two hundreds. And finally, we got nothing to add to the 1000. And so, the answer is 1242.

The way the multiplication was written we knew that we should use long multiplication to find the answer. But we did say we could have used a mental method. How could we have found the same answer mentally? Although it’s not the method we should have used, let’s go through it now, just as a check.

The first thing we could do is to swap the numbers around and think of the calculation as 23 multiplied by 54. 54 can be partitioned into 50 and four. And both of these numbers are fairly easy to multiply by. First, let’s multiply by 50. We know that 23 times 100 equals 2300. And so, 23 times 50 will be half of this, which is 1150.

Now we just need to work out 23 multiplied by four. Multiplying a number by four is the same as doubling it and then doubling it again. 23 doubled is 46 and then doubled again is 92. So we know 23 times four equals 92. Now we know what 23 times 50 and 23 times four are, we just need to add them together to find the answer. And the answer is 1242. Although we weren’t expected to use this method, it’s always interesting to spot different ways that we could use mental methods to find the answer.

54 multiplied by 23 equals 1242.