Why Decimal Division Works
Date: 04/24/2001 at 03:14:31 From: Marc Subject: WHY division by decimals For my college math education class I have to write a paper on why (not how) the procedure of division with decimals works. The question is, "All elementary school students learn how to divide with decimals such as in the problem 551.2/1.06. Explain as if talking to 5th and 6th graders why this procedure works." If you could help me it would help very much! Thanks, Marc
Date: 04/24/2001 at 08:51:51 From: Doctor Peterson Subject: Re: WHY division by decimals Hi, Marc. If you'd like to look over our shoulders as we actually explain division of decimals to a 5th or 6th grader, visit our archives: Fractions and Decimals - Elementary School Level http://mathforum.org/dr.math/tocs/fractions.elem.html Division - Elementary School Level http://mathforum.org/dr.math/tocs/division.elem.html Here's a sample: How to Divide Decimals by Decimals http://mathforum.org/dr.math/problems/wright3.7.98.html That should give you some good ideas for your own explanation. The basic idea is that we first learn a method for dividing whole numbers. When we introduce decimals, we find that the work can be divided into two parts, just as in multiplication: we can first ignore the decimal point entirely, and get the DIGITS of the answer using the methods we've already learned; then we can determine where in that answer to put the decimal point. This is because, for example, we can rewrite a division of decimals as a division of whole numbers times a division of powers of ten: 1.95 195 * 0.01 195 0.01 195 ---- = ---------- = --- * ---- = --- * 0.01 * 10 = 3 * 0.01 * 10 6.5 65 * 0.1 65 0.1 65 This says that, after dividing 195 by 65, we put the decimal point in the same place it was in the dividend, 1.95 (multiplying 3 by 0.01 to get 0.03), and then shift it one place to the right (multiplying by 10, which is the same as dividing by 1/10, to get 0.3). The traditional way to make this memorable is to first move the decimal points in the divisor and dividend until the dividend is whole, and then put the decimal point in the quotient directly above the new position in the dividend. This effectively shifts the decimal point in the quotient first to the left, accounting for the decimal in the dividend, and then the to right, accounting for the divisor. So you see, it's not that we MUST divide only by a whole number; rather, this is just one easily remembered way to decide where to put the decimal point in the quotient. It's not much different from what we do in multiplication of decimals, where we first ignore the decimal point, and then add the number of decimal places in the two numbers. In division, we are really SUBTRACTING the number of decimal places in the two numbers; but explaining it in terms of moving the decimal point ensures that we won't accidentally subtract in the wrong order. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.