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### Estimate the Sums

```Date: 07/24/2003 at 19:48:47
From: Johnny

My assignment has this question:

Use front-end estimation to estimate each sum.

428 + 219
374 + 425

This is just summer practice and I forgot how to do it. Do I turn 428
into a 400, turn 2 into 20, and the eight is in the ones place. Then
you do the same to 219 and then add them up to get the answer.
```

```
Date: 07/27/2003 at 11:42:02
From: Doctor Ian

Hi Johnny,

Well, 428 is kind of a long way from 400, so that might not be the
best estimate to use.

I look at problems like these as like fitting together pieces of a
puzzle. 28 is close to 30, and 19 is close to 20, and I know 30 and 20
add up to 50. So I'd probably do the first one this way:

428 + 219 = about 430 + 220

= 400 + 200 + 30 + 20

= 650

428 + 277 = ?

In this case, I'd be thinking about 25 and 75, instead of 30 and 20.
So I'd estimate the first number a little differently:

428 + 219 = about 425 + 275

= 400 + 200 + 25 + 75

= 600 + 100

= 700

This is kind of interesting. In each case, I started with the same
number, 428, but in one case I estimated it as 430, while in the other
case I estimated it as 425.

To understand why, it's important to keep in mind what the _point_ of
this kind of estimation is: it's to reduce the amount of work we have
to do. So when I'm thinking about using estimation to help me add two
numbers, usually what I'm doing is comparing them to pairs of numbers
that I can add easily: 30 and 20, 25 and 75, and so on.  That's what
tells me whether to estimate up or down.

Does that make sense?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Place Value

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