Whole
Numbers (Integers):
The Natural
numbers are those
numbers with which we first became aware, "I have 1 marble, 2
jacks, 9 pennies..." We then had to add the place holding
number "0" in order to systematically talk about numbers larger than
9. In particular, what distinguishes 9 from 90 is the 0. The
0 holds the ones place and pushes the 9 up to the tens place, meaning that
we have no ones but we have 9 tens, and 9 tens is 90.
When we start talking about
money matters then we have phrases such as "I have $20, I owe you
$5." In this case, assuming I pay my debts, I only have $15
that I can actually spend. The "-" symbol written in front of
the amount of money represents the amount "owed," that is, my debt.
So a list of these numbers would represent all of the amounts I have to
spend as a credit (with no "-" symbol ) and the amounts I owed,
those listed with the "-" symbol.
$30
(credit)
$10
(credit)
-$5
(debt)
$15 (credit)
-$2 (debt)
So, in this case I have $45 credit and $7 debt, so if I pay my
debt I'd have $38 credit.
As a last example, what does it mean if I have a $20 credit and
a $20 debt? Assuming, again that I pay my debit, then I'd
have to use all of my $20 credit and I'd be left with no money to spend.
The only number that could represent this case is the number 0, so $0 would
mean I have no debits and no credits.
If we include the "-" symbol and the place holder
number "0" with the Natural numbers we have the set of Integers. But
we must understand that the "-" symbol means something special and when written
in front of a number, must "become part" of
that number. This symbol directly affects the number following
and cannot be separated from it!
To distinguish these numbers, we'll call the numbers with
the "-" in front of them the "negative" numbers, and the others
we'll call "positive" numbers. The special number 0, we'll just
call "zero."
In the example above the positive numbers are: 20, 10, and
15; the negative numbers are -5 and -2. We'll use the "-"
even though we called these numbers "negative numbers" to distinguish them from
the positive numbers 5 and 2.
This is another FREE ALGEBRA PRINTABLE presented to you from the
Algebra section of
K12math.com