Compatible Number Method for Estimating

Date: 09/10/2001 at 02:17:46
From: Salman
Subject: Word problem

We are supposed to estimate by using compatible numbers. What is a 
compatible number, and how does one estimate something like 574/8?

Date: 09/10/2001 at 12:25:30
From: Doctor Peterson
Subject: Re: Word problem

Hi, Salman.

I believe that the phrase "compatible number" in this context refers 
to a number you can use in place of the dividend to make the division 
easy, that is, a simple multiple of the divisor. In this case, I would 
look at the 57 and recognize that it is close to 56, a multiple of 8; 
therefore, 560/8 is an easy problem that gives a good estimate of 
574/8. What I did was essentially to round 574, not to the nearest 
ten, but to the nearest multiple of 8 by a number with only one 
non-zero digit.

To make an even better estimate, I could then notice that I have 
subtracted 14 from 574, so I will be subtracting 14/8 from the 
quotient; this is about 2, so a closer estimate would be 2 less than 
your answer from the first estimate. But that's not part of the 
compatible number method itself.

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