Video: Estimating the Sum of Two Three-Digit Numbers by Rounding to the Nearest Ten

Look at how Amelia estimated this sum. Estimate 273 + 146. Estimate the sum of 615 + 209 by rounding both numbers to the nearest ten. Estimate the sum of 262 + 147 by rounding both numbers to the nearest ten.

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Video Transcript

Look at how Amelia estimated this sum. Estimate 273 plus 146.

Now this problem asked Amelia to estimate the answer, not calculate it exactly. A good way to estimate a problem is to round the numbers so they become a lot easier for us to work with. So the first thing that Amelia decides to do is to take each of the numbers from that addition and to round them to the nearest ten.

Now we know that the number 273 comes between the tens 270 and 280, and the nearest ten is 270. So we round the number 273 downwards to 270. Next, Amelia looks at the second number. 146 comes in between the tens 140 and 150. And if we look close to our number line, we can see that it’s slightly nearer to 150. So Amelia needs to round that number up this time to 150.

Now by rounding those numbers, what Amelia’s done is she’s made that calculation a lot easier. It won’t give her an exact answer, but it’ll give her a quick answer and an answer that’s about right. So we can see that Amelia now adds those numbers together. 270 plus 150 equals an estimate of 420. So the first thing Amelia did was to round both numbers to the nearest ten. The second thing that she did was to calculate using those rounded numbers. So Amelia can now say, “I don’t know the exact answer to the question, but I do know that it’s going to be about 420.”

Let’s use the same method now to solve a different problem. Estimate the sum of 615 plus 209 by rounding both numbers to the nearest ten. Now 615 is a really interesting number because it’s exactly halfway between two tens numbers, 610 and 620. So what should we do?

Now some people might think, because it’s half way, I’m gonna choose to round it down, and others might think they ought to round it upwards. And this could get really confusing. So to avoid this happening, we have a convention or a rule in maths which says any number that ends in a five always rounds upwards to the nearest ten. The number 615 ends in a five. It’s one of these in-the-middle numbers, and so we’re gonna follow that rule and round it upwards to the nearest ten. We’re going to round it upwards to 620. And if we round our second number, we can see that 209 also rounds upwards to 210. So we’ve changed our numbers into 620 and 210.

Step two is to calculate using our rounded numbers. And we can see that our calculation looks a lot easier now. We can work out the answer mentally. 620 plus 210 equals 830, and so our estimate to the sum of 615 plus 209 is 830.

Let’s try one more example. This time, we’ll remove the rules from the side to see whether we can remember them. Estimate the sum of 262 plus 147 by rounding both numbers to the nearest ten.

Step one: let’s round our numbers. 262 is nearer to 260, so we’re going to round that number downwards. 147 is nearer to 150, so we’re gonna round 147 upwards. Step two: we can add our rounded numbers together. 260 plus 150 equals 410, and so our estimated sum of 262 plus 147 is 410.

Interestingly, if you added those two numbers together, the actual answer that we get is 409. So you can see that using this estimation method where we round both the numbers to the nearest ten is quite an accurate way of getting a good idea of what the answer is going to be.

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