Table of Contents
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.
Example: $ 3\frac{1}{2} $, $ 5\frac{3}{4} $, $ 7\frac{5}{6} $
Writing repeating numbers as fractions
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}
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 |