Question

Arrange the following fractions in ascending order:
$\frac{1}{2},\frac{3}{4},\frac{5}{6}\mathrm{and}\frac{7}{8}$

Answer 1

The given fractions are $\frac{1}{2},\frac{3}{4},\frac{5}{6}\mathrm{and}\frac{7}{8}$.
L.C.M. of 2, 4, 6 and 8 = (2 $\times$ 2 $\times$ 2 $\times$ 3) = 24
We convert each of the given fractions into an equivalent fraction with denominator 24.
Now, we have:
$$\begin{gathered} \frac{1}{2}=\frac{1\times 12}{2\times 12}=\frac{12}{24};\frac{3}{4}=\frac{3\times 6}{4\times 6}=\frac{18}{24} \\ \frac{5}{6}=\frac{5\times 4}{6\times 4}=\frac{20}{24};\frac{7}{8}=\frac{7\times 3}{8\times 3}=\frac{21}{24} \end{gathered}$$

Clearly, $\frac{12}{24}<\frac{18}{24}<\frac{20}{24}<\frac{21}{24}$

∴ ​$\frac{1}{2}<\frac{3}{4}<\frac{5}{6}<\frac{7}{8}$
Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{1}{2},\frac{3}{4},\frac{5}{6},\frac{7}{8}$​