This
was the question:
I
need to find out more about math vocabulary, such as multiplicand,
multpiler,known value,and algebraic expression.Could you please send
me the defintions!!!!!!!!
thank you sooooo much.
Professor
Homunculus' answer:
First of all, thanks
for asking so politely, and for showing appreciation for the answer.
But what's up with the grammar and spelling? I'm not mentioning it
because I want to hassle you, but because you are going to find out
that math and logic are a lot like grammar, and the better you are
at them, the less misunderstandings you will cause.
This is only going
to answer the simplest of your questions, but it may be of help because
of the way it is explained. It gives you a good reason as to "why" certain
words are used.
multiplicand * multiplier
= product
addend + augend = sum
dividend / divisor = quotient
minuend - subtrahend = difference
The multiplier is
the number you are multiplying by. It is the number which is doing
the action. That is why it has the er at
the end of the word. A multiplier does something, like other words
which end in er, like writer, catcher, builder,
etc. When you say, "Seven
times five," you are "times-ing" the seven by the five,
so the seven is sitting there, minding it's own business, not doing anything,
and along comes the five, and the five "times-es" (multiplies)
the seven. The five is doing the multiplying. It is the multiplier. (By
the way, please don’t say “times-ing,” I just used
it here because it’s a word some people understand better. But
it’s good to get out of that habit.)
The multiplicand is the other number, the one which is being multiplied.
In the above case, it is the seven. It is being multiplied; it is not
doing the multiplying.
It is true that if
you reverse the numbers, each one switches it's role.
That means that
in:
7 x 5
the seven is the multiplicand and the five is
the multiplier.
and in:
5 x 7
the five is the multiplicand and the seven is
the multiplier.
Of course you know
that it doesn't matter which order you put the numbers in
when multiplying (or adding), because of the commutative properties
of multiplication and addition. Just remember that when they change
positions, they change names.
I know this may sound
confusing, so let me give you a little example of why it's done like
this:
Multiplication (of
whole numbers) is about "groups of..." What I mean by this, is that
you can say, "groups of" instead of "multiplied by."
In the real world,
if you have three nickels (the name for U.S. five-cent pieces, for
our non-U.S. readers), you'd probably represent that as 3*5= 15 cents. You'd have 3 "groups
of" five-cent coins .
Naturally, you could
do it the other way, and imagine five groups of three pennies (5*3).
It would give you the same answer, but it wouldn't be as neat.
You could imagine
5*3 as "a nickel, three times," and that could work as well. It's your
choice. But now you see that the order that you write the numbers in
is determined by the way you think about the problem.
(By the way, that
is another proof that math is not "just one way with no room for imagination."
Math is like a language, and there are rules of grammar, but you can
say anything you want with it. It doesn't control what you think, just
how you represent it. Amazing, nicht wahr?)
The multiplier and
the multiplicand are about being and doing, and the way we represent
which number is doing which is by its position. The number that comes
behind the word "by" when
you say "Something
multiplied by something else" is the multiplier.
Knowing that, can
you figure out which number in a problem written like this is the multiplier?
You would say, "Three
multiplied by four." The four is doing
the work, so the four is the multiplier. The three is the multiplicand.
If you are like I
was in school, you probably wonder why they each have separate
names, even though it doesn't matter which order you multiply numbers
by. Good question.
Here is the answer:
it is simply a way to keep track of them when you are talking about
multiplication, or teaching people how to multiply. It is simpler than
saying, "the
number on the left," "the number on the right," "the
top number," or "the
bottom number."
The answer to a multiplication
problem is called the product. Why do we have a special name for it?
Because if you hear someone say, "what
is the product of six and two?" you automatically know that they
are talking about multiplication, not division, addition, or anything
else. Learning the basic terms just makes explaining things easier, that's
all.
Along the same line
of reasoning, the divisor is the one doing the dividing (the or at
the end is like the er at the end of multiplier). The dividend is
like the multiplicand - it is the passive element. (See how
the -end is like the -and?) The
answer to a division problem is the quotient.
In addition, both
are called addends. Actually, there is a word for the first
element, and it is called the augend, but no one uses that
term anymore, although I think we should. The answer in addition is
called the sum.
In subtraction, the
minuend is the number being subtracted from, and the subtrahend is
the number being subtracted. The answer is the difference.
Hope this was a beginning
to understanding,
Professor Homunculus
I've written some
more about this at The Math Mojo Chronicles (Math Mojo's official blog.
You can read about it in the post called "Augends,
Addends and Commutative Property of Addition" |
