4th Class Mathematics Decimals and Fractions Fraction

   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.