====== Rational Numbers ======

===== Fractions =====

A fraction, or fractional number is used to represent a part of a whole number. Fractions consist of two numbers: **numerator** (above the line) and **denominator** (below the line).

The denominator tells you the number of equal parts into which something is divided.

The numerator tells you how many of these equal parts are being considered.


===== Proper and Improper Fractions =====

The numerator is smallar than the denominator in a proper fraction. In an improper fraction, the numerator is greater than or equal to the denominator.

  * Examples of proper fractions: $ 4/7 $, $ 2/9 $,
  * Examples of improper fractions: $ 3/2 $, $ 16/15 $,

===== Mixed Numbers =====

When a term contains both a whole number and a fraction, it is called a mixed number.

<WRAP center round box>
**Example:** $ 3\frac{1}{2} $, $ 5\frac{3}{4} $, $ 7\frac{5}{6} $
</WRAP>

===== Writing repeating numbers as fractions =====

<WRAP center round box>
**Example:** $ 0.\overline{7} $ sayısını kesirli olarak yazalım. 

\begin{align}

x = 0.\overline{7} & = 0.7777... \\
10x = 7.7777... & = 7 + 0.7777... = 7 + x \\
\end{align}

\begin{align}
10x = 7.\overline{7}& \\
\underline{-\quad x = 0.\overline{7} }& \\
9x = 7&
\end{align}

\begin{align}
9x = 7 \\
x = \frac{7}{9}
\end{align}
</WRAP>

===== Frequently used fractional numbers and their decimal equivalents =====

^ Fractional State ^ Decimal State ^ Percentage Status ^
| $ \frac{1}{100} $ | 0.01 | %1 |
| $ \frac{1}{8} $ | 0,125 | %12,5 |
| $ \frac{3}{8} $ | 0,375 | %37,5 |
| $ \frac{5}{8} $ | 0.625 | %62,5 |
| $ \frac{6}{8} = \frac{3}{4} $ | 0.75 | %75 |
| $ \frac{7}{8} $ | 0.875 | %87,5 |