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Fractions

Category : 4th Class

Fractions

Synopsis

Fraction:

A fraction represents a part of a whole.
In a fraction, two numerals are written one below the other separated by a line. The written above the line is called the numerator and the numeral below the line is denominator.

e.g.,

In a fraction, the denominator tells us how many equal parts the whole has been divided into and the numerator tells us how many parts of the whole are being considered.

Like fractions: Fractions which have a common denominator are called like fraction

e.g., \[\frac{2}{9},\frac{4}{9},\frac{5}{9}\]etc.,

Unlike fractions: Fractions with different denominators are called unlike fraction;

e.g., \[\frac{2}{3},\frac{4}{5}\]

Proper fraction: In a fraction, if the numerator is less than the denominator, it I called a proper fraction.

e.g., \[\frac{2}{5},\frac{7}{11}\]etc.,

Improper fraction: In a fraction, if the numerator is greater than or equal to the denominator it is called an improper fraction.

Note: if the numerator is equal to the denominator, the fraction represents a whole number, i.e., 1

Unit fractions: Fractions with 1 or unity as the numerator are called unit fractions

e.g., \[\frac{1}{3},\frac{1}{5}\]etc.,

Mixed fraction: A fraction which is a combination of a whole number and a fraction is called a mixed fraction or mixed number

e.g., \[1\frac{3}{4},7\frac{1}{11}\]

Equivalent fractions: The fractions that represent the same part are called equivalent fractions.

Both \[\frac{2}{8}\] and \[\frac{1}{4}\] represent the same part of a whole. So \[\frac{2}{8}=\frac{1}{4}\].

Comparing fractions:

(a) Fractions with the same numerators: Of two fractions with a common numerator, the fraction that has a smaller denominator is greater.

e.g., \[\frac{3}{5}\]and \[\frac{3}{7}\]

Since, the numerators are the same, comparing their denominators, we get \[\text{5}<\text{7}\].

\[\therefore \] \[\frac{3}{5}>\frac{3}{7}\]

(b) Fractions with the same denominators: Of two fractions with a common denominator, the fraction that has a larger numerator is greater

e.g., \[\frac{2}{9}\]and \[\frac{7}{9}\]

Since the denominators are the same, comparing their numerators, we get \[7>2\].

\[\therefore \] \[\frac{7}{9}>\frac{2}{9}\]

(c) Fractions with different numerators and denominators: To compare fractions with different numerators and denominators, first convert them to get the same denominator by writing their equivalent fractions and then compare.

e.g., \[\frac{3}{4}\] and \[\frac{5}{6}\]

Step 1: Check if numerators or denominators are the same. The given fractions do not have the same numerators or denominators.

Step 2: Find equivalent fractions with common denominators. \[\frac{3\times 3}{4\times 3}=\frac{9}{12}\] and \[\frac{5\times 2}{6\times 2}=\frac{10}{12}\]

Step 3: Compare the numerators. \[\text{9}<\text{1}0\]

\[\therefore \]\[\frac{3}{4}<\frac{5}{6}\]

Ordering fractions: Writing fractions in ascending or descending orders is called ordering fractions.

e.g., 1: The fractions\[\frac{1}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7}\]and \[\frac{6}{7}\]are in ascending order since\[\text{1}<\text{3}<\text{4}<\text{5}<\text{ 6}\].

e.g., 2: The fractions \[\frac{8}{9},\frac{7}{9},\frac{6}{9},\frac{5}{9}\]and\[\frac{2}{9}\]are in descending order since\[\text{8}>\text{7}>\text{6}>\text{5}>\text{2}\].

Addition of fractions: To add two like fractions,

(a) Add the numerators,

(b) Write the sum over the same denominator.

Subtraction of fractions: To subtract two like fractions,

(a) Subtract the numerators,

(b) Write their difference over the same denominator.

e.g., \[\frac{8}{9}-\frac{3}{9}=\frac{8-3}{9}=\frac{5}{9}\]

Fraction of a number: To find the fraction of a number,

(a) Divide the number by the denominator.

(b) Multiply the quotient obtained by the numerator.

e.g., \[\frac{3}{4}\]of \[60.\]\[60\div 4=15\]and \[3\times 15=45\Rightarrow \frac{3}{4}\]of \[60=45\]

Conversions: