Question

Arrange the following fractions in ascending order:
$\frac{3}{4},\frac{7}{8},\frac{11}{16}\mathrm{and}\frac{23}{32}$

Answer 1

The given fractions are $\frac{3}{4},\frac{7}{8},\frac{11}{16}\mathrm{and}\frac{23}{32}.$
L.C.M. of 4, 8, 16 and 32 = (2 ⨯ 2 ⨯ 2 ⨯ 2 ⨯ 2) = 32


So, we convert each of the fractions whose denominator is not equal to 32 into an equivalent fraction with denominator 32.
Now, we have:
$\frac{3}{4}=\frac{3\times 8}{4\times 8}=\frac{24}{32};\frac{7}{8}=\frac{7\times 4}{8\times 4}=\frac{28}{32};\frac{11}{16}=\frac{11\times 2}{16\times 2}=\frac{22}{32}$
Clearly, $\frac{22}{32}<\frac{23}{32}<\frac{24}{32}<\frac{28}{32}$
∴ ​$\frac{11}{16}<\frac{23}{32}<\frac{3}{4}<\frac{7}{8}$

Hence, the given fractions can be arranged in the ascending order as follows:
$\frac{11}{16},\frac{23}{32},\frac{3}{4},\frac{7}{8}$