# Introduction to fractions

Suppose you have a loaf that has been divided to be shared equally among eight people, yet only one of them takes a piece. In this case, the denominator represents the parts into which the bread was divided and the numerator, the part that was taken after dividing it. The above, we can represent it in the following way:

1/8 = part taken by the person / part into which the bread was divided

This expression represents a fraction (or broken), which is defined as each of the parts into which the unit is divided.

## Definition

A fraction is each of the parts into which the unit has been divided. They express the division of a whole into parts; it is also known as broken. To be clear about this concept, we must first know the parts of it, such as the denominator and the numerator:

• Denominator: indicates the number of equal parts into which the unit is divided.
• Numerator: indicates the number of parts that are taken after the unit is divided.

## Notation

To write a fraction, write the numerator at the top separated by an oblique or horizontal line of the denominator. Thus, three-fourths is written  or 3/4.

## Nomenclature

To read a fraction, the number that is in the numerator is stated first and then the denominator, however, the number in it does not read the same:

• If it is 2 it is read Medium or Half.
• If it is 3 it is read Third or Third part).
• If it is 4 it is read Quarter or Fourth part).
• If it is 5 it is read Fifth or Fifth part).
• If it is 6 it is read Sixth or Sixth (part).
• If it is 7 it is read Seventh or Seventh).
• If it is 8 it is read Eighth or Eighth (part).
• If it is 9 it is read Nineth or Ninth).
• If it is 10 it is read Tenth or Tenth).

When the denominator is greater than 10, the denominator is read by adding the ending Avo to the name of the number (eleventh or eleventh (part), sixteenths, fifty-sixth).

## Meaning

Every fraction is considered as the quotient of two algebraic expressions, in which the numerator represents the dividend and the denominator the divisor. Thus 7/8 represents the quotient of a division in which the numerator 7 is the dividend and 8 the divisor.

## Fraction types

• Own fractions: in them the numerator is less than the denominator. For example: 2/3, 7/9, 15/19.
• Improper fractions: in them the numerator is greater than or equal to the denominator. For example: 4/3, 9/9, 21/19.
• Mixed fractions: they are those that consist of an integer part and a fractional part. For example: 5 ⅜, a + x / y.