Write the following in ascending order:$\frac{1}{2},\ \frac{4}{5},\ \frac{-2}{3},\ \frac{-1}{2},\ \frac{-5}{7}$.

Given: Fractions: $\frac{1}{2},\ \frac{4}{5},\ \frac{-2}{3},\ \frac{-1}{2},\ \frac{-5}{7}$.

To do: To write the given fractions in the ascending order.

Solution: 
 

Given fractions: $\frac{1}{2},\ \frac{4}{5},\ \frac{-2}{3},\ \frac{-1}{2},\ \frac{-5}{7}$.

L.C.M. of the denominators $2,\ 5,\ 3,\ 2,\ 7=210$

$\frac{1}{2}=\frac{1}{2}\times\frac{55}{55}=\frac{55}{210}$

$\frac{4}{5}=\frac{4}{5}\times\frac{42}{42}=\frac{168}{210}$

$\frac{-2}{3}=\frac{-2}{3}\times\frac{70}{70}=\frac{-140}{210}$

$\frac{-1}{2}=\frac{-1}{2}\times\frac{105}{105}=\frac{-105}{210}$

$\frac{-5}{7}=\frac{-5}{7}\times\frac{30}{30}=\frac{-150}{210}$

On arranging the given fractions in ascending order:

$\frac{-150}{210}<\frac{-140}{210}<\frac{-105}{210}<\frac{55}{210}<\frac{168}{210}$.

Therefore, $\frac{-5}{7}<\frac{-2}{3}<\frac{-1}{2}<\frac{1}{2}<\frac{4}{5}$.

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Updated on: 10-Oct-2022

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