4th Class Mathematics Decimals and Fractions Comparison of Fraction

  Comparison of Fraction  

    Comparison of Like Fractions

Let\[\frac{p}{q}\]and\[\frac{r}{q}\]are like fractions.

If p is greater than \[q,\frac{p}{q}>\frac{r}{q}\]        

Compare between\[\frac{\mathbf{7}}{\mathbf{9}}\]and\[\frac{5}{\mathbf{9}}\].Which is greater?

Solution:

\[7>5\] \[\frac{7}{9}>\frac{5}{9}\]  

 Comparison of Fractions Having Same Numerator

If the two fractions have same numerator, the fraction which has smaller denominator is greater. Like\[\frac{P}{Q}\]is greater than\[\frac{P}{R}\]if\[\text{Q}<\text{R}\].  

Find the greatest fraction out of the given fractions:

\[\frac{18}{23},\frac{18}{17},\frac{18}{19},\frac{18}{20},\frac{18}{12}\]

Solution:

\[\frac{18}{12}\]is the greatest fraction among the given fractions. As it has smallest denominator.  

 Comparison of Unlike Fractions

Compare between\[\frac{7}{13}\]and\[\frac{6}{9}\]  

Step 1:  Convert the fractions into like fractions.

\[\frac{7\times 9}{13\times 9}=\frac{63}{117}\]

And\[\frac{6\times 13}{9\times 13}=\frac{78}{117}\]  

Step 2: The fraction having greater numerator is greater.

\[\because \]\[78>63\]

\[\therefore \]\[\frac{78}{117}>\frac{63}{117}\]or\[\frac{6}{9}>\frac{7}{13}\]  

Compare between\[\frac{21}{22}\]and\[\frac{22}{23}\], which is greater?

Solution: \[\frac{21}{22}=\frac{21\times 23}{22\times 23}=\frac{483}{506}\]

\[\frac{22}{23}=\frac{22\times 22}{23\times 22}=\frac{484}{506}\]

\[\because \]\[484>483\]

\[\therefore \]\[\frac{484}{506}>\frac{483}{506}\]or\[\frac{22}{23}>\frac{21}{22}\]