Fraction

**Category : **4th Class

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.

*play_arrow*Introduction*play_arrow*Fraction*play_arrow*Conversion of mixed Fraction into Improper Fraction*play_arrow*Comparison of Fraction*play_arrow*Operation on the Fractions*play_arrow*Decimals*play_arrow*Comparison of Decimals*play_arrow*Addition of Decimals*play_arrow*Subtraction of Decimals*play_arrow*Multiplication of Decimals*play_arrow*Division of a Decimal by the Power of 10*play_arrow*Fractions and Decimals*play_arrow*Fractions and Decimals

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