# 4th Class Mathematics Fractions and Decimals Fraction

## Fraction

Category : 4th Class

### Fraction

Fraction is used to indicate a part of a whole. It is represented as $\frac{a}{b}$ where, a is called numerator and b is called denominator of the fraction. It may be explained as - If a whole is divided into some equal parts, each part is called fraction of the whole and the number which is used to represent the part is called fractional number. Let 4 kg flour is divided into five equal parts. The amount each part will contain is represented as $\frac{4}{5}$ kg here $\frac{4}{5}$ is a number which is known as fraction. Thus fraction is a mathematical term which represents part of a whole. Shaded part in the following figures has been represented by fractions.

1 kg corn is divided into five equal parts. Represent the amount contained by each part as a fraction.

Solution:

1 kg corn is divided into five equal parts. Thus each part will contain $\frac{1}{5}$ kg  corn.

Like Fraction

The fractions having same denominator are called like fractions.

$\frac{1}{4},\frac{6}{4},\frac{7}{4}$ are like fractions.

Choose the like fractions from the following:

$\frac{2}{5},\frac{7}{8},\frac{4}{15},\frac{3}{8}$

Solution:  $\frac{7}{8}$and$\frac{3}{8}$are like fractions because they have same denominator.

Unlike Fraction

The fractions having different denominators are called unlike fractions.

$\frac{4}{5},\frac{5}{9},\frac{6}{3}$are unlike fractions because they have different denominators.

Are$\frac{4}{9}$and$\frac{5}{7}$unlike fractions?

Solution: Yes, because$\frac{4}{9}$and$\frac{5}{7}$have different denominators.

Conversion of Unlike Fraction into Like Fraction

Let$\frac{p}{q}$and$\frac{r}{s}$are two unlike fractions. To convert them into like fractions first multiply p and q by s then multiply r and s by q.

Thu $\frac{p\times s}{q\times s}$ and$\frac{r\times q}{s\times q}$are like fractions.

Convert$\frac{7}{11}$and$\frac{6}{9}$.into like fractions.

Solution:$\frac{7}{11}=\frac{7\times 9}{11\times 9}=\frac{63}{99}$

$\frac{6}{9}=\frac{6\times 11}{9\times 11}=\frac{66}{99}$

$\frac{63}{99}$and$\frac{66}{99}$are like fractions

Equivalent Fraction

The fractions which have same value are called equivalent fractions. Like$\frac{5}{21}$and$\frac{10}{42}$ are equivalent fractions.

Finding an Equivalent Fraction of a given Fraction

To find an equivalent fraction of a given fraction, numerator and denominator of the fraction is multiplied or divided by a same number.

Find an equivalent fraction of$\frac{\mathbf{16}}{\mathbf{21}}$.

Solution: Multiply both 16 and 21 by a same natural number.

$\frac{16\times 2}{21\times 2}=\frac{32}{42}$

Thus$\frac{16}{21}$ and$\frac{32}{42}$ are equivalent fractions.

Unit Fraction

The fractions in the form$\frac{p}{q}$ (when p = 1 and $q\ne 0$) are called unit fractions.

$\frac{1}{4},\frac{1}{5},\frac{1}{6}$are unit fractions.

$\frac{p}{14}$is a unit fraction. Find the value of P.

Solution:

$\frac{p}{14}$is a unit fraction and all the unit fractions have 1 as numerator. Therefore, P = 1.

Proper fraction

The fractions in which denominator is greater than the numerator are called proper fractions. Like$\frac{p}{q}$ is a proper fraction, if$\text{p}<\text{q}$.

Is$\frac{\mathbf{5}}{\mathbf{14}}$a proper fraction?

Solution: Yes, because in the fraction$\frac{5}{14}$ denominator 14 is greater than 5.

Improper Fraction

The fractions which has smaller nominator than the numerator called improper fractions. Like$\frac{p}{q}$is an improper fraction, if p > q.

Which one of the following is an improper fraction?

$\frac{5}{14},\frac{6}{10},\frac{19}{17},\frac{17}{19}$

Solution:$\frac{19}{17}$is an improper fraction because 19 > 17.

Mixed Fraction

Mixed fraction is a sum of a whole number and a proper fraction.

$p\frac{q}{r}$is a mixed fraction where p is whole number and$\frac{q}{r}$ is a proper fraction.

Write any two mixed fractions

Solution: $5\frac{2}{3},9\frac{4}{7}$ You may write other mixed fractions as well.

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