# Vulgar (simple) fractions

*Vulgar fraction (denominator, numerator).*

Proper fraction. Improper fraction.

Mixed number (integer and fractional parts).

Converting of a mixed number into a vulgar

improper fraction and back. Reciprocal fractions.

Proper fraction. Improper fraction.

Mixed number (integer and fractional parts).

Converting of a mixed number into a vulgar

improper fraction and back. Reciprocal fractions.

*
A part of a unit or some equal parts of a unit
*
is called a
**
vulgar (simple) fraction
**
. A number of equal parts into which a
unit has been divided, is called a

*denominator*; a number of these taken parts, is called a

*numerator*. A fraction record:

Here 3 – a numerator, 7 – a denominator.

If a numerator is less than a denominator, then the fraction is less than 1 and called a
*
proper
*
fraction. If a numerator
is equal to a denominator, the fraction is equal to 1. If a numerator is greater than a denominator, the fraction is greater than 1. In both
last cases the fraction is called an
*
improper
*
fraction. If a numerator is divisible by a denominator, then this fraction is
equal to a quotient: 63 / 7 = 9. If a division is executed with a remainder, then this improper fraction can be presented as a
*
mixed number:
*

Here 9 – an incomplete quotient ( an integer part of the mixed number ), 2 – a remainder ( a numerator of the fractional part ),
7 – a denominator .

It is often necessary to solve a reverse problem – to convert a mixed number into a fraction. For this purpose, multiply
an integer part of a mixed number by a denominator and add a numerator of a fractional part. It will be a numerator of a vulgar
fraction, and its denominator is saved the same.

*
Reciprocal fractions
*
are two fractions whose product is 1. For
example, 3 / 7 and 7 / 3 ; 15 / 1 and 1 / 15 and so on.