Category : 4th Class
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\[\frac{22}{23}>\frac{21}{22}\]
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