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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?

• 5
• 1/4
• 1/4

The answer is '1/4'.

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

• 6
• 2/4
• 2/4

The answer is '2/4'.

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

• 6
• 6/4
• 6/4

The answer 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.

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

What type of fraction is 17/7?

• Pronunciation : Say the answer once

What type of fraction is 2 3/7?

• Pronunciation : Say the answer once

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