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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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Note that the gray part is shown only as a representation of whole. What is the fraction represented by the colored part in the given figure? proper fraction 1

  • 5
  • `1/4`
  • `1/4`

The answer is '`1/4`'.

What is the fraction represented by the colored part in the given figure?proper fraction 2

  • 6
  • `2/4`
  • `2/4`

The answer is '`2/4`'.

What is the fraction represented by the colored part in the given figure?improper fraction 6/4

  • 6
  • `6/4`
  • `6/4`

The answer 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.

What does the word 'proper' mean?

  • of the required or correct type
  • of the required or correct type
  • in the wrong position

The answer is 'of the required or correct type'.

What does the word 'improper' mean?

  • not of the required or correct type
  • not of the required or correct type
  • in the wrong position

The answer is 'not of the required or correct type'.

What does the word 'mixed' mean?

  • being only one of its kind
  • consisting of different quantities or elements
  • consisting of different quantities or elements

The answer is 'consisting of different quantities or elements'.

What type of fraction is `3/7`?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is 'proper fraction'.

What type of fraction is `17/7`?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is 'improper fraction'.

What type of fraction is `2 3/7`?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is '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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