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54 multiplied by 23 equals what?
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We can tell by the way that this calculation has been written out that we need to use long multiplication to find the answer.
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We could find the answer mentally.
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But to start with, let’s use a written method.
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Long multiplication will help us to keep track of all the different numbers.
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First, we can multiply 54 by the three digit.
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Four times three equals 12 and five multiplied by three equals 15 plus the one that we’ve exchanged equals 16.
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Now, we need to multiply 54 by the two digit, which of course is worth two tens or 20.
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We don’t need to do this digit by digit.
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This is the sort of calculation we could work out quite quickly in our heads.
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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.
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So that’s how to find the answer mentally.
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Let’s go through and carry on using long multiplication.
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We know that multiplying by 20 is the same as multiplying by 10 and then by two.
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We know that when a number is multiplied by 10, the digits move one place to the left.
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So if we put a placeholder zero in the ones place, we’ve shifted all the digits one place to the left.
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We’ve multiplied by 10.
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Now we just need to multiply by two as normal.
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Four times two equals eight and five times two equals 10.
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And there that answer of 1080 that we predicted.
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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.
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Two ones plus zero ones equals two ones.
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Six tens plus eight tens equals 14 tens.
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And we can exchange 10 of those 14 tens for 100.
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100 plus zero hundreds equals 100.
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Don’t forget the 100 underneath equals two hundreds.
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And finally, we got nothing to add to the 1000.
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And so, the answer is 1242.
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The way the multiplication was written we knew that we should use long multiplication to find the answer.
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But we did say we could have used a mental method.
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How could we have found the same answer mentally?
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Although it’s not the method we should have used, let’s go through it now, just as a check.
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The first thing we could do is to swap the numbers around and think of the calculation as 23 multiplied by 54.
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54 can be partitioned into 50 and four.
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And both of these numbers are fairly easy to multiply by.
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First, let’s multiply by 50.
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We know that 23 times 100 equals 2300.
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And so, 23 times 50 will be half of this, which is 1150.
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Now we just need to work out 23 multiplied by four.
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Multiplying a number by four is the same as doubling it and then doubling it again.
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23 doubled is 46 and then doubled again is 92.
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So we know 23 times four equals 92.
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Now we know what 23 times 50 and 23 times four are, we just need to add them together to find the answer.
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And the answer is 1242.
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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.
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54 multiplied by 23 equals 1242.