Question Video: Multiplying Two-Digit Numbers Mathematics • 4th Grade

Calculate the following: 29 × 64 = _

04:40

Video Transcript

Calculate the following: 29 multiplied by 64 equals what.

In this question, we’re given a pair of two-digit numbers to multiply together, and we’re given a really big clue as to how to do this because the way that this calculation is being set out is by writing both numbers on top of each other. This means that digits are in columns. One way of describing this is as the column method. And by writing the numbers like this, it helps us to split them up into their tens and ones. Both parts of the number 29 need to be multiplied by both parts in the number 64. Let’s make a plan of all the multiplications we’re going to need to do.

So to begin with, we’re going to need to multiply every part of the number 29 by the four ones in 64, so that’s nine times four and then 20 times four. That way, we’ve multiplied 29 by four altogether, haven’t we? Then we need to multiply every part of the number 29 by the six 10s in 64. So we’ll start off by working out nine times 60 and then, finally, 20 times 60. Then we’ll have also multiplied all the parts of 29 by 60. And if we then can combine all our parts together, we can find the answer. So to begin with, let’s multiply by our four ones. Now we know multiplying by four is the same as doubling and then doubling again. So finding out nine times four is the same as doubling nine to get 18 and then doubling 18. 18 doubled is 36, so we know nine times four is 36.

Next, we need to multiply 20 by four. Remember, this digit two doesn’t have a value of two. It’s in the tens place. It’s worth 20. Again, we can use doubling to help us. 20 doubled is 40, and then 40 doubled is 80. So we know that 20 times four is 80. Now we need to multiply everything by the six 10s in 64. So what’s nine times 60? Well, we can use our knowledge of place value to help us here. Nine sixes are 54. So nine lots of six 10s equals 54 10s, which is the same as 540. Finally then, we need to multiply 20 by 60. Now, to help us, we can recall what two 60s are, and that’s 120. So by trying to find out what 20 lots of 60 are, our first factor has increased 10 times. Instead of two times 60, we’re actually looking for 20 times 60.

Our answer then is going to be 10 times larger. And we know that to find a number that’s 10 times larger than another one, we just shift the digit one place to the left, so 120 becomes 1200. So now we’ve multiplied each part of the number 29 by the ones and then the tens of the number 64. To find our overall answer then, we just need to add these partial products together. So to start with, if we add our ones, we can see the digit is six and all the other digits are zero. So we’ve got six ones. In the tens column, we got a few more to think about. We’ve got three 10s plus eight 10s plus another four 10s.

Now, how would you add these quickly? Perhaps we could put the three and the four together to make seven 10s. And we know that eight 10s plus eight 10s will be 16 10s. So if we add eight 10s to seven 10s, it’s going to be 15 10s. So we’re going to need to exchange 10 of our 15 10s for 100 and then five 10s. Adding the hundreds then, we’ve got five 100s plus another two 100s. That’s seven 100s. Not forgetting the one that we’ve just exchanged, that’s eight 100s altogether. And there’s just the 1000 in our thousands column. So in this question, we’ve multiplied together a pair of two-digit numbers using the column method. This helps us to make sure that every part of the number 29 is multiplied by every part of the number 64. 29 multiplied by 64 equals 1,856.

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