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Which of the following is greater?$\frac{-1}{5}$ or $\frac{-1}{2}$
Given :
The given numbers are $\frac{-1}{5}$ and $\frac{-1}{2}$.
To do :
We have to find the greater among the given numbers.
Solution :
To find the greater number among $\frac{-1}{5}$ and $\frac{-1}{2}$, first, find the greater number among $\frac{1}{5}$ and $\frac{1}{2}$.
To compare, $\frac{1}{5}$ and $\frac{1}{2}$, find the LCM of the denominators.
LCM of 5, 2 is $5\times 2=10$.
Divide 10 by 5, 2, and note down the quotients.
$\frac{10}{5} = 2, \frac{10}{2} = 5$
Multiply both numerator and the denominator of every fraction by the corresponding quotients.
$\frac{1}{5} = \frac{1\times 2}{5 \times 2} =\frac{2}{10}$
$\frac{1}{2} = \frac{1\times 5}{2 \times 5} =\frac{5}{10}$
On comparing the numerator, we get,
$5 > 2$.
Therefore, $\frac{1}{2} >\frac{1}{5}$
So, $\frac{-1}{2} <\frac{-1}{5}$
Therefore, $\frac{-1}{5}$ is greater than $\frac{-1}{2}$.