Video: Estimating Products of Three-Digit by One-Digit Numbers and Using Estimates to Check Reasonableness

We can estimate to check our work. Estimate 269 × 6 by rounding 269 to the nearest hundred. Find the product. Check that your answer is reasonable using your estimate. 269 × 6 = _

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Video Transcript

We can estimate to check our work. Estimate 269 multiplied by six by rounding 269 to the nearest hundred. And then find the product. Check that your answer is reasonable using your estimate. 269 multiplied by six equals what.

In this problem, we’re going to use estimation to help us get a rough idea of what the answer to a multiplication is going to be. After we’ve estimated the value of 269 multiplied by six, we’re then going to work out the actual answer and use our estimate to check back and to see whether our answers look like it might be right. So to begin with, we are asked to estimate 269 multiplied by six by rounding 269 to the nearest hundred. 269 is in between 200 and 300. But which of these hundreds is it nearest to?

Halfway between 200 and 300 is 250. And we know 269 is greater than this. It’s perhaps about here on the number line. And so we can see that 269 is nearest to 300. When rounding to the nearest hundred, we need to round this number up. And so if we’re estimating the answer to 269 multiplied by six, we can use the nearest hundred instead. Our calculation becomes 300 multiplied by six. This is a lot quicker and a lot easier to do. We know that three sixes are 18. And so 300 multiplied by six is 18 hundred or 1800. This is an estimate for the answer to 269 multiplied by six. We can use this to check our work and to see that it looks about right.

In the second part of the problem, we are asked to find the product. We know which method we’re supposed to use because the numbers have been written out already for us. Nine ones multiplied by six equals 45 ones. So we can write a four in the ones place and then exchange 50 of our ones for five tens. Six tens multiplied by six equals 36 tens. We’ve got five tens that we’ve exchanged. So that’s 41 tens. We write a one in the tens place and then exchange 40 of our tens for 4 hundreds. Finally, 200 multiplied by six equals 12 hundreds plus the four hundreds that we’ve exchanged equals 16 hundreds or 1600. And so the product of 269 and six is 1614.

So we can now check that our answers reasonable using our estimate. Does our answer look like it’s about right? Remember, our estimate was 1800. This is not far off 1614. So it looks like our answer is reasonable. We estimated 269 multiplied by six by rounding 269 to 300. We then multiplied 300 by six to find the estimate 1800. We then found the actual answer by multiplying 269 by six which was 1614. And we used our estimate to check that our answer was reasonable.

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