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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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mathsFractionsTypes of fractions

Proper, Improper, and Mixed fractions

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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proper fraction 1 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`.

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

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

The picture represents the fraction `6/4`. improper 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`. improper 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` improper fraction 6/4 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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