When you were about two years old you probably learned to hold up
two fingers when you were asked how old you were. Two fingers are
real and in this case represented two years of time. From the very
beginning of civilization numbers were meant to count real things,
like the number of sheep when sheep were being sold or traded. Then
zero meant none, no sheep. In today's mathematics numbers that are
greater than zero are called positive numbers.
Let's think about subtraction for a minute where we "take away" a
number. Pretend you want to buy some music CDs from your friend who
has 8 CDs for sale. While there are 8 CDs for sale you want to buy
just 6 of them. You "take away" 2 CDs and the math is 8 - 2 = 6.
Another way to look at your CD trading transaction is -2 or negative
2. Is the negative number real? Your friend who was selling CDs still
has 2 CDs so it's okay to decide that the negative number is real.
The idea of negative numbers has been around for a long time. The
ancient Chinese people used negative numbers in the marketplace. In
fact they used red counting rods for positive numbers and black counting
rods for negative numbers. It wasn't until centuries later, in the
16th century, that mathematicians outside of China started using negative
Are you familiar with the term sea level? The location of sea level
is determined by scientists. Picture yourself standing on a high cliff
looking out over the ocean and feeling the nice ocean breezes. How
far is it down to the water? If it's 30 feet to the water you are
30 feet above sea level. But the exact science of sea level is a bit
more complicated than this simple example.
The tallest mountain in the world, Mount Everest, is 29,035 feet
above sea level. Flat areas in the middle of the United States sometimes
are only 600 feet above sea level! The lowest point in the United
States is Death Valley which is located in both California and Nevada.
Death Valley is 282 feet below sea level or -282 feet in relation
to sea level.
Based on the examples of selling CD's and sea level, you know that
negative integers make sense. But does it make sense to have a negative
decimal number like -17.56? It certainly does!
Negative numbers are used a lot in banking and finance. It's easy
to think of positive numbers as plus or addition and negative numbers
as minus or subtraction. Do your parents use an ATM machine? Money
doesn't flow from an ATM machine by magic, does it? Your parents deposit
money in the bank and when they withdraw money from the bank at the
ATM machine, the amount is subtracted from their account. Basically
any withdrawal from a bank account is a negative number. Since dollars
and cents are shown as decimal numbers, it's easy to see that negative
decimal numbers make sense.
In fact, all electronic banking transactions are based upon
the idea of positive and negative numbers. Banks really don't transfer
actual dollar bills very often. Banks send computer messages to each
other that credit an account with a positive number or debit an account
with a negative number. But when banks or other financial companies
prepare printed statements, they use the opposite color scheme from
the ancient Chinese. Today black is used for positive numbers and
red is used for negative numbers.
So, negative numbers are extremely important in you and your family's
everyday life. Now you know that negative numbers exist for sure.