Based on the value of the fraction in comparison with the whole, the fractions are classified as proper fractions, improper fractions and mixed fractions.

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Consider the given figure. The colored part is the representation of a fraction and the gray part is shown only as a representation of the whole.

The fraction is `1/4`.

The fraction represented by the colored part in the given figure is `2/4`

The fraction represented by the colored part in the given figure is `6/4`

The picture represents the fraction `6/4`. Number of parts in the given fraction: `6`

Number of parts making a whole: `4`

The number of parts in the given fraction is greater than the number of parts making a whole.

The picture represents the fraction `6/4`. The `4` parts of the given fraction is rearranged to make a whole and remaining `2` parts are shown nearby. So, `6/4` can be given as `1 2/4`.

The picture represents three fractions

• Fraction given by green part: `1/4`

• Fraction given by purple parts : `6/4`

• Fraction given by orange parts : `1 2/4` The word "fraction" means "part of a whole".

• In the three given fractions, only `1/4` is strictly part of whole. The value of the fraction is less than `1`, which is properly part of whole. Such fractions are called proper fractions.

• The fraction `6/4` is greater than `1`, and is represented as numerator by denominator. Such fractions are called improper fractions.

• The fraction `1 2/4` is greater than `1`, and is represented as a whole number along with a fraction. Such fractions are called mixed fractions.

The word "proper" means: required or correct type. Proper fractions are fractions that are smaller than a whole and properly a fraction of a whole.

The word "improper" means: not of correct type. Improper fractions are fractions that are larger than a whole.

The word "mixed" means: consisting of different quantities or elements. Mixed fractions are fraction that have an integer count of whole and a proper fraction.

*familiarize with the terminology *

proper fraction

*familiarize with the terminology *

improper fraction

*familiarize with the terminology *

mixed fraction

proper fraction: smaller than a whole and properly a fraction of a whole

improper fraction: larger than a whole in fraction form

mixed fraction: larger than a whole given as mix of a whole number and a fraction

**Proper Fraction: **number of parts in the fraction (numerator) is less than the number of parts making a whole(denominator) given as numerator divided by denominator. Proper fractions are less than 1.

**Improper Fraction: **number of parts in the fraction (numerator) is greater than the number of parts making a whole(denominator) given as numerator by denominator. Improper fractions are greater than 1 given as numerator by denominator.

**Mixed Fraction: ** Specified as number of wholes with a fraction. Mixed fractions are greater than 1 and given as whole number followed by a numerator by denominator.

*Solved Exercise Problem: *

What type of fraction is `7 (30)/(35)`?

- proper fraction
- improper fraction
- mixed fraction
- mixed fraction

The answer is 'mixed fraction'.

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