Question

Arrange the following mixed fractions in the increasing order.

• A. 2$\frac{3}{4}$
• B. 2$\frac{2}{5}$
• C. 2$\frac{3}{5}$
• D. 1$\frac{3}{4}$

Answer 1

First we convert the given mixed fractions into improper fractions. So, $2\frac{3}{4}=\frac{11}{4}$, $2\frac{2}{5}=\frac{12}{5}$, $2\frac{3}{5}=\frac{13}{5}$ and $1\frac{3}{4}=\frac{7}{4}$.
Now, we find the L.C.M. of the denominators (4 and 5), which is 20. Thus, we have $\frac{11}{4}=\frac{55}{20}$, $\frac{12}{5}=\frac{48}{20}$, $\frac{13}{5}=\frac{52}{20}$ and $\frac{7}{4}=\frac{35}{20}$.
Since 35$<$48$<$52$<$55, we have $\frac{7}{4}<\frac{12}{5}<\frac{13}{5}<\frac{11}{4}$.
$⟹1\frac{3}{4}<2\frac{2}{5}<2\frac{3}{5}<2\frac{3}{4}$