3rd Class Mathematics Fractions

                                                                  Fractions

Introduction

The Latin name of fraction is fractus. It means broken. It has two parts, upper and lower part. The upper part is called numerator and lower part is denominator.

Fractions in Its Lowest Term

The lowest term of a fraction is obtained by dividing numerator and denominator with common divisor. The lowest form of the fraction \[\frac{6}{9}\] is\[\frac{2}{3}\]. The lowest term of the fraction g is obtained by dividing the numerator and denominator with a common divisor 3.

• Example

What is lowest term of the fraction\[\frac{45}{65}\]?

(a) \[\frac{9}{13}\]                     (b) \[\frac{2}{3}\]

(c) \[\frac{5}{9}\]                      (d) All the above

(e) None of these

Answer (a)

Explanation: Common divisor of 45 and 65 is 5. Therefore, dividing 45 and 65 by 5, we get\[\frac{9}{13}\].

• Example

Find the simplest form of the shaded parts of the figure in fraction given below:

(a) \[\frac{3}{8}\]                                   (b) \[\frac{1}{2}\]

(c) \[\frac{1}{5}\]                                   (d) All the above

(e) None of these

Answer (b)

Explanation: Total number of divisions is 8 and number of shaded parts is 4.

Therefore, shaded parts\[=\frac{4}{8}=\frac{1}{2}\].

Proper, Improper and Mixed Fractions

The fraction whose numerator is smaller than the denominator is called proper fraction. The fractions whose numerator is greater than the denominator is called improper fractions. A mixed fraction has both whole and fractional parts. The fraction \[3\frac{7}{3}\]is a mixed fraction.

• Example

Which one of the following fractions is correct about the shaded parts of the given figure?

(a) \[1\frac{3}{4}\]                                 (b) \[1\frac{5}{3}\]

(c) \[5\frac{3}{4}\]                     (d) All the above

(e) None of these

Answer (a)

Explanation: Total number of parts in each figure = 4 number of shaded parts in are 4 and 3 respectively.

Therefore, shaded parts \[=\frac{4}{4}+\frac{3}{4}=1+\frac{3}{4}=1\frac{3}{4}\]

Fraction Represented on the Number Line

We can represent a fraction on a number line. In order to represent \[\frac{3}{4}\] on a number line, draw a line and mark a point A to represent 1. Now divide the gap between O and A into four equal parts. Let X, Y and Z by the points of division.

In the figure given above, the line OZ represents the fraction\[\frac{3}{4}\].

Unit Fraction

A fraction, whose numerator is 1 is called a unit fraction. For example, \[\frac{1}{5},\] \[\frac{1}{3},\] \[\frac{1}{10}\] \[\frac{1}{9},\] are unit fractions. Here denominators of all fractions are different but numerators are 1.