Estimate the Sums

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

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
Subject: Re: Addition

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

Now, suppose that I had this instead:

   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? 

With that in mind, how would you estimate your second addition?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/