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Fractions - Fractional Units as Parts of a Whole

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A fraction is a number representing a part of a whole. This 'whole' can be a single object (like a pizza) or a group/collection of objects (like a box of pens).

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A fraction is written in the form ab\frac{a}{b}, where aa is the numerator and bb is the denominator.

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The denominator (bb) represents the total number of equal parts into which the whole has been divided. It must be noted that b≠0b \neq 0.

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The numerator (aa) represents the number of equal parts that have been taken or considered.

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For a fraction to be valid, the whole must be divided into equal parts. If the parts are not of equal size, they cannot be represented as a standard fraction.

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Fractions can be represented on a number line. For example, to represent 47\frac{4}{7}, the distance between 00 and 11 is divided into 77 equal divisions, and the 4th4^{th} mark from 00 represents 47\frac{4}{7}.

📐Formulae

Fraction=NumeratorDenominator\text{Fraction} = \frac{\text{Numerator}}{\text{Denominator}}

Fraction=Number of parts being consideredTotal number of equal parts in the whole\text{Fraction} = \frac{\text{Number of parts being considered}}{\text{Total number of equal parts in the whole}}

Fraction of a Collection=Number of specific itemsTotal number of items in the collection\text{Fraction of a Collection} = \frac{\text{Number of specific items}}{\text{Total number of items in the collection}}

💡Examples

Problem 1:

Identify the fraction represented by the shaded portion if a circle is divided into 88 equal sectors and 55 of them are shaded.

Solution:

58\frac{5}{8}

Explanation:

The total number of equal parts is 88, which becomes the denominator. The number of shaded parts is 55, which becomes the numerator. Thus, the fraction is 58\frac{5}{8}.

Problem 2:

What fraction of a day is 88 hours?

Solution:

824=13\frac{8}{24} = \frac{1}{3}

Explanation:

We know that 1 day=24 hours1 \text{ day} = 24 \text{ hours}. Here, the whole is 2424 hours (denominator) and the part taken is 88 hours (numerator). The fraction is 824\frac{8}{24}, which can be simplified to 13\frac{1}{3} by dividing both parts by 88.

Problem 3:

Express the following scenario as a fraction: Out of 1515 bulbs in a room, 77 are fused. What fraction of bulbs are working?

Solution:

815\frac{8}{15}

Explanation:

Total number of bulbs = 1515. Number of fused bulbs = 77. Number of working bulbs = 15−7=815 - 7 = 8. The fraction of working bulbs is working bulbstotal bulbs=815\frac{\text{working bulbs}}{\text{total bulbs}} = \frac{8}{15}.