Video: Estimating Products of Three-Digit and One-Digit Numbers

Look how Lily estimated the product by rounding the three-digit number to the nearest hundred. 562 × 6 is close to 600 × 6. 6 hundreds × 6 = 36 hundreds. I estimate that 562 × 6 will be close to 3600. Use her method to estimate 792 × 5. Use her method to estimate 253 × 9.

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Video Transcript

Look how Lily estimated the product by rounding the three-digit number to the nearest hundred. 562 times six is close to 600 times six. Six hundreds multiplied by six equals 36 hundreds. I estimate that 562 times six will be close to 3600. Use her method to estimate 792 multiplied by five, and then use her method to estimate 253 multiplied by nine.

Lily is multiplying a three-digit number by a single digit. And, if you notice, that’s what the two calculations that we’ve been asked to estimate have in common. They’re also a three-digit number multiplied by a single digit. We’re told that Lily doesn’t work out the answer exactly. But, what she does is to estimate the product. And, what she does is to round the three-digit number to the nearest hundred. She knows that 562 is close to 600. And so, she round it up to 600. Then we can see, because she knows that six times six equals 36, she also knows that six hundreds times six equals 36 hundreds. So, her estimation for the answer to 562 multiplied by six is close to 36 hundreds or 3600. So, let’s use her method now to estimate the answer to our two calculations.

Firstly, 792 multiplied by five. Firstly, we need to round 792 to the nearest hundred. We know that the two multiples of 100 that it’s between are 700 and 800. The halfway point between these two numbers is 750. And, we know that 792 is a lot nearer 800 than this point, probably about here. In fact, it’s only eight away from 800. So, we can say, just like Lily, 792 multiplied by five is close to 800 multiplied by five.

Now, we can use our knowledge of times tables to help. We know 10 times five is 50. So, eight times five is two lots of five less than 50 or 10 less than 50, which is 40. So, eight hundreds multiplied by five equals 40 hundreds. And, we know that 40 hundreds are the same as 4000. So, we can estimate that 792 multiplied by five will be close to 4000.

Now, let’s use her method again this time to estimate 253 multiplied by nine. We know that the two multiples of 100 that 253 lies between are 200 and 300. And again, it’s useful to think about where the halfway point is, which is 250. 253 is very close to the halfway point, but we can see that it’s slightly more than it, perhaps about there. So, even though it’s not as close to the larger 100 as before, it’s still closer to 300 than to 200. And so, we can say that 253 multiplied by nine is close to 300 multiplied by nine.

Which times tables factor we’re going to use to help us here? Well, if we know what three times nine is, we can use it to help us find out what three hundreds times nine is. Again, knowing what a number times 10 is will help us here. Three times 10 is 30. So, three times nine is three less than 30. The answer is 27. So, three hundreds times nine equals 27 hundreds. We know 27 hundreds is another way of saying 2700. So, we can say that 253 multiplied by nine will be close to 2700.

We used Lily’s method to estimate the answer to both of our calculations. First, we rounded each number to the nearest hundred. This gave us a new calculation that was a lot easier to work out. By writing each calculation as a number of hundreds multiplied by a single digit, we could just use the times tables fact to help. And so, we can estimate that 792 multiplied by five will be close to 4000, and 253 multiplied by nine will be close to 2700.

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