Question

Arrange the following fractions in increasing order.

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

Answer 1

$\text{Given}$: To arrange $\frac{1}{2},\frac{2}{3}$ and $\frac{1}{2}\times \frac{2}{3}$ in increasing/ascending order.

First, we are going to make the given fractions as like fractions (same denominator of fractions).

$\frac{1}{2}=\frac{1}{2}\times \frac{3}{3}=\frac{3}{6}\cdots \left(1\right)$

$\frac{2}{3}=\frac{2}{3}\times \frac{2}{2}=\frac{4}{6}\cdots \left(2\right)$

$\frac{1}{2}\times \frac{2}{3}=\frac{1\times 2}{2\times 3}=\frac{2}{6}\cdots \left(3\right)$

From $\left(1\right),\left(2\right),\left(3\right)$, it is very clear

$\frac{1}{2}\times \frac{2}{3}<\frac{1}{2}<\frac{2}{3}$

or $\frac{1}{2}\times \frac{2}{3},\frac{1}{2}$ and $\frac{2}{3}$ are in the ascending order.