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Fractions - Fractional Units and Equal Shares

Grade 6CBSE

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

🔑Concepts

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A fraction is a number representing part of a whole. The whole may be a single object or a group of objects.

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For a fraction to be valid, the whole must be divided into equal parts. Each of these equal parts is known as a fractional unit.

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In a fraction ab\frac{a}{b}, the top number aa is the numerator (parts being referred to) and the bottom number bb is the denominator (total number of equal parts).

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If a whole is divided into nn equal shares, each share represents the unit fraction 1n\frac{1}{n}.

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Fractions can also represent a division of a collection. For example, 12\frac{1}{2} of 1010 items is 55 items.

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On a number line, the distance between 00 and 11 is divided into bb equal parts to represent fractions with denominator bb.

📐Formulae

Fraction=Number of equal parts selectedTotal number of equal parts in the whole\text{Fraction} = \frac{\text{Number of equal parts selected}}{\text{Total number of equal parts in the whole}}

Value of one share=Total QuantityTotal number of equal shares\text{Value of one share} = \frac{\text{Total Quantity}}{\text{Total number of equal shares}}

Unit Fraction=1n\text{Unit Fraction} = \frac{1}{n}

Improper Fraction=(Whole Number×Denominator)+NumeratorDenominator\text{Improper Fraction} = \frac{(\text{Whole Number} \times \text{Denominator}) + \text{Numerator}}{\text{Denominator}}

💡Examples

Problem 1:

A chocolate bar is divided into 1212 equal pieces. If Rahul eats 55 pieces, what fraction of the chocolate did he eat, and what fraction is left?

Solution:

Fraction eaten = 512\frac{5}{12}, Fraction left = 712\frac{7}{12}.

Explanation:

The total number of equal parts (denominator) is 1212. Rahul took 55 parts, so the fraction eaten is 512\frac{5}{12}. The remaining parts are 12−5=712 - 5 = 7, so the fraction left is 712\frac{7}{12}.

Problem 2:

Divide a collection of 4848 marbles into 44 equal shares. How many marbles are in each share, and what fractional unit does one share represent?

Solution:

Each share contains 1212 marbles and represents the fractional unit 14\frac{1}{4}.

Explanation:

To find the number of marbles in each share, we divide the total by the number of shares: 48÷4=1248 \div 4 = 12. Since the total is divided into 44 equal parts, each part is 14\frac{1}{4} of the whole.

Problem 3:

If you have 150150 pages in a book and you have read 4545 pages, subtract the read pages from the total to find the remaining pages. Show the calculation vertically.

Solution:

Remaining pages = 105105.

Explanation:

The total pages are 150150 and read pages are 4545. The subtraction is: 150−45105\begin{array}{r} 150 \\ -45 \\ \hline 105 \end{array} This represents that 105150\frac{105}{150} of the book is left to be read.

Fractional Units and Equal Shares Class 6 Notes & Examples