When you go to the store and something costs $3 and you hand the
clerk a $5 bill you will receive $2 in return. This is pretty easy
to keep account of as the two one dollar bills are whole numbers.
But what if 10% sales tax was added to the $2 purchase? Then, you
would have to pay an increase of 1/10 to your purchase. You change
would no longer be $3 but $2.80. Yes, simply making a slight change
to a whole number brings you right into the world of fractions, decimals
and percents. Fractions, decimals and percents are everywhere and
you simply can not avoid them even if you tried. One would believe
that the commonality of these three values would lead to people understanding
them better but many are still a little bit in the dark as to their
value. So, it becomes important to understand what they are and how
they differ from one another.
A fraction refers to "part" of a whole number. For example, 1 is a whole number
and if you were to cut it in half you would be left with the fraction
of 1/2 A fraction is made up of two separate whole numbers a numerator
and a common denominator. In 1/2, the number two is known as the common
denominator and the 1 is the numerator.
The relationship between fractions, decimals and percents is clear when you
look at the fraction 1/2. When you divide the numerator by the common
denominator you get a decimal. That is seen in the following: 1 divided
by 2 equals .5. This relates to a percentage in the sense that .5
is a half and half is represented in percents as 50%. So, if .5 =
50% and 1/2= .5 then 1/2= 50%. Making a fraction into a percent is
easy as you simply place the percentage over the whole number 100
and then reduce it. So, 50% becomes 50/100 which is reduced to 1/2.
50% becomes a decimal by then dividing the whole number by a common
denominator. 1/2 becomes 2 divided by 1 which equals .5 So, the relationship
between fractions, decimals and percents is that they are simply different
numerical expressions of the same value.
This is commonly known as a mixed number which is the result of an
improper fraction. Improper fractions (colloquially called a 'top
heavy' fraction) are fractions that have a numerator that is greater
than the common denominator. For example, 33 1/3 would appear as the
following fraction 10/3. When reducing the fraction the result is
the improper number .333 with the threes going on into infinity. Interestingly,
fractions never appear in decimals, however, as 33 1/3% would be reflected
But, once again, while they look different they simply express the
same values through different representations. For example, did you
know, however, that there is a method of telling time known as the
decimal method? When we look at the clock - even a digital clock -
we are looking at fractions based on 24 hours in the day. (Actually
12 hours but we realize that the same time slots are repeated during
AM or PM) The decimal system, however, bases its ability to tell time
on using decimals and the power of ten. This is commonly called military
time and is ranges from 0000 to 2400 hours. Both methods are designed
to express the passage of 24 hours and both do so accurately. They
simply do it in a different representational method.
So, you can say that fractions, percents and decimals are two sides
of the proverbial same coin with each having their own unique traits.