Fractions (from Latin: fractus, "broken") are numbers expressed as the ratio of two numbers, and are used
primarily to express a comparison between parts and a whole.
The earliest
fractions were reciprocals of integers: ancient symbols representing one part of two, one part
of three, one part of four, and so on.^{ }A much later development were
the common or "vulgar" fractions which are still used today (½,
⅝, ¾, etc.) and which consist of a numerator and a denominator, the numerator representing a
number of equal parts and the denominator telling how many of those parts make
up a whole. An example is 3/4, in which the numerator, 3, tells us that the
fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts
make up a whole.
A still later development was the decimal fraction, now called
simply a decimal, in which the
denominator is a power of ten,
determined by the number of digits to the right of a decimal separator, the appearance of
which (e.g., a period, a raised period (•), a comma) depends on the locale (for
examples, see decimal separator).
Thus for 0.75 the numerator is 75 and the denominator is 10 to the
second power, viz. 100, because there are two
digits to the right of the decimal separator.
A third kind of fraction still in common use is the percentage, in which the denominator
is always 100. Thus 75% means 75/100.
Other uses for fractions are to represent ratios, and to represent division. Thus the fraction 3/4 is
also used to represent the ratio 3:4 (three to four) and the division 3 ÷ 4
(three divided by four).
Addition
The first rule of addition is that only
like quantities can be added (Our solved example in
mathguru.com uses this concept)
12:22 PM 8/5/2011Imagine a pocket containing two quarters,
and another pocket containing three quarters; in total, there are five
quarters. Since four quarters is equivalent to one (dollar), this can be
represented as follows:
.
If of a cake is to be added to of a cake, the pieces need to be converted
into comparable quantities, such as cake-eighths or cake-quarters.
Adding
unlike quantities
To add fractions containing unlike
quantities (e.g. quarters and thirds), it is necessary to convert all amounts
to like quantities. It is easy to work out the chosen type of fraction to convert
to; simply multiply together the two denominators (bottom number) of each
fraction.
For adding quarters to thirds, both types
of fraction are converted to (twelfths).
Consider adding the following two
quantities:
First, convert into twelfths by multiplying both the
numerator and denominator by three:
.
Note that is equivalent to 1, which shows that, is
equivalent to the resulting.
Secondly, convert into twelfths by multiplying both the
numerator and denominator by four: . Note that is
equivalent to 1, which shows that, is equivalent to the resulting.
Now it can be seen that:
is equivalent to:
(Our solved example in mathguru.com uses
this concept)
This method can be expressed algebraically:
And for expressions consisting of the
addition of three fractions:
Subtraction
The process for subtracting fractions is,
in essence, the same as that of adding them: find a common denominator, and
change each fraction to an equivalent fraction with the chosen common
denominator. The resulting fraction will have that denominator, and its
numerator will be the result of subtracting the numerators of the original
fractions. For instance,
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Fraction_(mathematics)
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative
Commons Attribution- ShareAlike 3.0 Unported License.