Video: Estimating the Difference between Two Three-Digit Numbers

Look at this calculation. 715 − 326 = _. Estimate the answer by rounding both numbers to the nearest hundred. Estimate the answer by rounding both numbers to the nearest ten. Calculate the exact answer. Tip: Use the estimates to see if your answer is sensible.

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Video Transcript

Look at this calculation, 715 subtract 326. Estimate the answer by rounding both numbers to the nearest 100. Estimate the answer by rounding both numbers to the nearest 10. Calculate the exact answer. Tip: use the estimates to see if your answer is sensible.

In this problem, we’ve been given a calculation. It’s a subtraction that involves two three-digit numbers, 715 subtract 326. And we can see, to start with, that the numbers have been set out vertically. This is a vertical subtraction. But instead of just calculating the exact answer straight away, this problem asks us to estimate. And we can estimate the answer to this subtraction by using rounding to help. It’s a quick way of giving us an indication of around about what the answer is going to be. It won’t give us the exact answer. But it will give us an idea.

So the first step of our problem, we’re asked to estimate the answer by rounding both numbers to the nearest 100. Let’s start with the first number in our subtraction, 715. Now, the two multiples of 100 that this number is in between is 700 and 800. We know that halfway point between these multiples of 100 is 750. If we look at the tens digit in 715, we can see that the number has one ten. If a number has one, two, three, or four tens, then we always round it downwards. And we can see from the number line why this is. The nearest 100 to 715 is 700. So instead of 715, we’ll write the first number in our subtraction as 700. And we could do exactly the same with the second number in our subtraction, 326. The two multiples of 100 that this number is in between are 300 and 400. And halfway between is 350. If we look at the tens digit again in 326, we can see that it has two tens. And as we’ve said already, this means that we need to round the number down to the nearest 100.

And so, in the first part of our problem, the calculation becomes 700 subtract 300. Seven take away three is four. And so by rounding both numbers to the nearest 100, we can estimate that the answer to our subtraction is going to be about 400. 700 subtract 300 equals 400. But we don’t just have to estimate the answer by rounding to the nearest 100. In the second part of the question, we’re asked to estimate the answer by rounding both numbers to the nearest 10. To begin with, let’s write out our original calculation. 715 subtract 326. Now, when rounding to the nearest 10, the tens digit is important. But equally important is the ones digit to the right of it. This will tell us whether to round up or down. In the number 715, we have five ones. As we’ve said already, if a digit is one, two, three, or four, we round down. So this means that if a digit is five, six, seven, eight, or nine, we round up. So we’ll cross out the five and replace it with a zero. And let’s round our tens digit up to 720.

Looking at our second number, 326, we can see again that we have a digit. That means we need to round up. The digit in the ones place is six. So once again, we’ll erase the six and replace it with a zero. And because the digits five, six, seven, eight, and nine round up and this digit was a six, we’re going to round up to 330. Our calculation has become 720 subtract 330. Perhaps, a quick way to subtract 330 is to partition it. First, subtract 300 and then subtract the 30. 720 take away 300 equals 420. And then, if we take away 30 from 420, we’re left with 390. So by rounding both numbers to the nearest ten, we now have an answer of 390.

Finally, we’re asked to calculate the exact answer. And we can use our original vertical subtraction to do this. But notice that we’re given a tip. We’re told to use our estimates to see if our answer is sensible. For example, if our answer was 239, we might think to ourselves that we worked it out wrongly. Both our estimates seem to be around about 400. And so we’re expecting the exact answer to be perhaps slightly less than 400. Let’s find out.

First, subtract the ones. Now, we can’t take six ones away from five ones. So we’re going to have to do some exchanging. We’ll take one ten. Now, we have zero tens in the tens place. And we’ll exchange it for 10 ones. So now, we’ve got 15 ones. 15 ones take away six ones leaves us with nine ones. Now, we can’t take two tens away from zero tens. So again, we’re going to have to exchange. We’ll take one of our hundreds. So we now have six hundreds left. And we’ll exchange it for 10 tens. Now, the subtraction in the tens column is 10 tens take away two tens, which leaves us with eight tens. And finally, six hundreds take away three hundreds leaves us with three hundreds. The exact answer to the subtraction is 389. Looking at our estimates, we would say this is a sensible answer. It’s just less than 400, which is what we expected.

We estimated the answer to 715 take away 326, firstly by rounding both numbers to the nearest 100. And the answer was 400. Then, we rounded both numbers to the nearest 10. And our estimate this time was 390. Finally, we calculated the exact answer. And we found that the difference between 715 and 326 was 389.

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