Question

Arrange the following fractions in increasing order, and select the correct option.
$\frac{4}{3},\frac{6}{5}$ and $\frac{4}{3}\times \frac{6}{5}$

• A. $\frac{4}{3}\times \frac{6}{5},\frac{4}{3}$ and $\frac{6}{5}$
• B. $\frac{4}{3},\frac{6}{5}$ and $\frac{4}{3}\times \frac{6}{5}$
• C. $\frac{6}{5},\frac{4}{3}$ and $\frac{4}{3}\times \frac{6}{5}$
• D. $\frac{4}{3}\times \frac{6}{5},\frac{6}{5}$ and $\frac{4}{3}$

Answer 1

The correct option is C $\frac{6}{5},\frac{4}{3}$ and $\frac{4}{3}\times \frac{6}{5}$

We need to arrange $\frac{4}{3},\frac{6}{5}$ and $\frac{4}{3}\times \frac{6}{5}$ in an ascending order.

Now, $\frac{4}{3}\times \frac{6}{5}=\frac{4\times 6}{3\times 5}=\frac{8}{5}$
$\underset{–}{\text{Note:}}$ The product of improper fractions is always greater than each of the improper fractions.

$\frac{4}{3},\frac{6}{5}$ and $\frac{4}{3}\times \frac{6}{5}$, i.e., $\frac{4}{3},\frac{6}{5}$ and $\frac{8}{5}$ have to be arranged in an increasing order.

Converting $\frac{4}{3},\frac{6}{5}$ and $\frac{8}{5}$ as like fractions (making denominator same as LCM of (3, 5, 5) = 15):
$\frac{4}{3}=\frac{4}{3}\times \frac{5}{5}=\frac{20}{15}\cdots \left(1\right)$
$\frac{6}{5}=\frac{6}{5}\times \frac{3}{3}=\frac{18}{15}\cdots \left(2\right)$
$\frac{8}{5}=\frac{8}{5}\times \frac{3}{3}=\frac{24}{15}\cdots \left(3\right)$

From $\left(1\right),\left(2\right),\left(3\right)$, it is very clear
$\frac{18}{15}<\frac{20}{15}<\frac{24}{15}$
$\Rightarrow \frac{6}{5}<\frac{4}{3}<\frac{8}{5}$
$\Rightarrow \frac{6}{5}<\frac{4}{3}<\frac{4}{3}\times \frac{6}{5}$
Hence, $\frac{6}{5},\frac{4}{3}$ and $\frac{4}{3}\times \frac{6}{5}$ are in increasing order, i.e., option (c.) is the correct one.