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## Proper Fractions:

Observe the fractions \(\frac{1}{3}\), \(\frac{2}{5}\), \(\frac{3}{10}\), \(\frac{4}{17}\), \(\frac{21}{22}\), \(\frac{101}{120}\)

All these fractions have the numerator less than the denominator. Such fractions are called **proper fractions**.

Fractions whose numerators are less than the denominators are called proper fractions.

### Proper, Improper and Mixed fractions Example1:

When we represent a proper fraction on a number line it always lies to the left of 1.

## Improper Fractions:

Observe the fractions \(\frac{10}{9}\), \(\frac{6}{5}\), \(\frac{22}{19}\), \(\frac{101}{89}\), \(\frac{20}{20}\), \(\frac{198}{120}\)

All these fractions have the numerator greater than the denominator. Such fractions are called **improper fractions**.

Fractions with the numerator either equal to or greater than the denominator are called improper fractions.

Fractions like \(\frac{5}{4} \), \(\frac{7}{2} \), \(\frac{9}{4} \) etc., are not proper fractions.These are improper fractions.

The mixed number 2 2 3 as an improper fraction.

## Mixed Fraction:

Consider \(2\frac{3}{4}\). It is a combination of the whole number 2 and the proper fraction \(\frac{3}{4}\). So, \(2\frac{3}{4}\) is a mixed number. Similarly, \(3\frac{15}{16}\), \(4\frac{1}{5}\), \(6\frac{8}{9}\), \(13\frac{1}{2}\) etc. are **mixed numbers**.

A combination of a whole number(except 0) and a proper fraction is called a mixed fraction.

Mixed Fractions are also called as Mixed Numbers.

Mixed Fractions are used when you need to count whole things and parts of things at the same time.

There are 1 whole circle and \(\frac{3}{4} \) of another circle.

We write as \(1\frac{3}{4}\) and read it as ‘**one and three-fourth**‘

We don’t put ‘+’ sign in between the numbers, this is why we say ‘and’.

There are 2 whole triangles and \(\frac{2}{3} \) of another triangle. This is \(2 + \frac{2}{3} \) and is written as **\(2\frac{2}{3} \)**.