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Further Musings on "Multiplicand" and "Multiplier"

Date: 06/09/2011 at 22:12:56
From: Carter
Subject: clarification of math terms of multiplicand and multiplier

I have seen Dr. Math's answer to the definition of multiplicand and
multiplier, and would like to share my thoughts.

Consider the possible multiplicand and multiplier in

   (9 x 4) = 36

I believe these designations become clearer when the objective is written
or spoken, such as "What is your age times 4?" If your age is 4, then four
is the multiplicand and the multiplier is 9. If on the other hand your age
is 9, then the multiplicand is nine and the factor is 4.

The distinction between multiplicand and multiplier is less clear with
questions about the total of contributions if, to continue the example,
four individuals each gives nine dollars. In my opinion, the multiplicand
is the number that has the same units as the product. For example, I would
say that the multiplicand is the dollar amount, because it is a four
dollar contribution that is magnified by the number of contributors.

Date: 06/09/2011 at 22:56:07
From: Doctor Peterson
Subject: Re: clarification of math terms of multiplicand and multiplier

Hi, Carter.

I'm not sure which page you are responding to; I'll suppose it's this:

  Multiplicand, Multiplier

But you might also have seen this:

  Defining Multiplication

Or this:

  Groups in Multiplication

In any APPLICATION of multiplication, the multiplicand is the number to be
multiplied (or scaled up, or repeated, or whatever), and the multiplier is
the number by which it is to be multiplied (aka, the scale factor, repeat
count, etc.). As you say, that is really unrelated to the way it happens
to be written.

The equation 9 x 4 = 36 need not represent "What is your age times 4?" It
might just as well be what you'd write for "What is 9 times your age?" In
either case, it is clear that the age (9 or 4 years, respectively) is the
multiplicand, because it is the number you start with and modify. But it
is written as the first number in one case, and the second in the other.

I agree with you that dollar amounts (unit prices) are multiplicands,
while numbers or quantities are multipliers. But I would not consider it a
good general principle to say that the multiplicand has the same units as
the product. In the case of 9 pounds at 4 dollars per pound, the product
is in dollars; no two numbers have the same unit! What you say would apply
only when the multiplier is a dimensionless quantity (a mere number of
times, or items).

So in simple problems that require multiplication, it's fairly easy to
identify the multiplier and multiplicand based on the application. The
distinction, however, becomes less and less meaningful as you do more
complex things. (For example, when calculating the force of gravity using 
F = GMm/d^2, which of the two masses is the multiplicand?) In the
abstract, however, just given as A x B with no connection to an
application, they are both just "factors" and play an equal role.

- Doctor Peterson, The Math Forum
Associated Topics:
Elementary Definitions
Elementary Multiplication

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