# 3rd Class Mathematics Fractions Fractions and Its Type

## Fractions and Its Type

Category : 3rd Class

### Types of Fractions

The fraction whose numerator is smaller than the denominator is called proper fraction. The fractions  are proper fractions The fractions whose numeratoris greater than the denominator is called improper fractions. The fractions,are improper. A mixed Fraction has both whole and fractional parts. The fraction is a mixed fraction. 3 is the whole part and  is the fractional part of the mixed fraction

Express the shaded parts of the following figures in its equivalent mixed fractions.

(a)

(b)

(c)

(d) All of these

(e) None of these

Explanation:

A whole figure is completely shaded and represented by 1and another same figure is divided into four parts and its three parts areshaded. Hence theshaded parts is represented by  Thus, their sum

Half of a whole

When a whole number or object is divided into two equal parts, each part is called half of the whole part. The half of a whole number is obtained by multiplying the number by  and the half of a figure is obtained by dividing the figure into two equal parts. In the figure given below, the shaded part of the figure is same as theunshaded part of the figure. Therefore, the shaded part of the figure is exactly half of unshaded part of the figure. One half of a figure covers completely to the otherhalf of the same figure.

Quarter of a Whole

When a number or figure is divided into four equal parts each one part is called quarter of the number and it is written as The quarter part of a number 56 is obtained by multiplying the number by  Therefore, the quarter of In the figure given below there are four same figures made by cutting a paper. One of them is shaded therefore, one of 4 figures is shaded and written as the shaded part of the figure is

Three Quarter or Three - Fourths

If a number or a figure is divided into four equal parts then three parts out of fourhree quarter of the number or figure. Three quarter of a number is obtained by multiplying the number by Therefore, the three quarter of the number In the figure given below, one figure is divided into four equal parts, three parts are shaded and one part is unshaded therefore/the shaded parts of the figure are three quarter or three - fourth of whole parts of the figure and written as  part of the figure is shaded. Out of four equal parts one is unshaded. Therefore, the unshaded part of the figure is written as

The figure given below is made by cutting a plain paper. The shaded part of the figure is:

(a)

(b)

(c)

(d)

(e) None of these

Explanation Given figure is divided into four equal parts and its three parts are shaded.

Like and Unlike Fractions

The fractions having same denominator is called like fraction. andare like fractions because every fraction has equal denominators. Fractions and  are not like fractions because both the fractions have unequal denominators. The fractions are like fractions:  They all have equal denominators, i. e. 4, but the fractions  are not like fractions: because they all have unequaled nominators and therefore, they are called unlike fractions.

Equivalent. Fraction

If numerator and denominator of a fraction is multiplied or divided by the same number, the resulting fraction is called its equivalent fraction. The equivalent Factions of  are and the equivalent fractions of  are Therefore, the equivalent fraction of a given fraction is obtained by multiplying both the numerators and denominators of the fraction by the same number.

Sum of like fractions

In the addition of like fractions, the sum of numerators is the numerator and the common denominator is the denominator of the resulting fraction for example,

(a)

(b)

(c)

(d) All of these

(e) None of these

Explanation :

The sum of the like fractions

Subtraction of Like Fractions

Difference between two like fractions

In the subtraction of two like fractions, the difference of the numerators is the numerator and the common denominator is the denominator of the resulting fraction.

For example,

Subtract the fractions:

(a)

(b)

(c)

(d) All of these

(e) None of these