Fraction : If any unit be divided into any number of equal parts, one o more of these parts is called a fraction of the unit.
The fractions one-fifth two-fifths, three-fifths are written as $\frac{1}{5}, \frac{2}{5}$ and $\frac{3}{5}$ respectively.
- Numerator : The upper number, which indicates the number of parts taken to form the fraction, is called the numerator.
- Denominator : The lower number, which indicates the number of equal parts into which the unit is divided, is called the denominator.
- Terms : The numerator and the denominator of a fraction are called its terms.
Note—
1. A fraction is also called a rational number.
2. A fraction is equal to zero when its numerator alone is zero. The denominator of a fraction is always assumed to be non-zero.
3. A fraction is unity when its numerator and denominator are equal.
4. The value of a fraction is not altered by multiplying or dividing the numerator and the denominator by the same number.
Example : $\frac{2}{5}=\frac{2 \times 5}{5 \times 5}=\frac{2 \div 6}{5 \div 6}$
5. When the numerator and the denominator of a fraction have no commor factor other than 1 , the fraction is said to be in its lowest terms.
Example : $\frac{12}{15}=\frac{3 \times 4}{3 \times 5}=\frac{4}{5}$
6. When the fraction is reduced to its lowest terms, its numerator and denominator are prime to each other i.e., they have no common factor.
7. An integer can be expressed as a fraction with any denominator we want. Example : If we want to express 19 as a fraction whose denominator is 17 , the process will be as follows :
$19=\frac{19 \times 17}{17}=\frac{323}{17}$
