Question

Find the product: $20\frac{1}{2}\times 19\frac{1}{2}$

Answer 1

State and simplify the given expression:

The given expression is $20\frac{1}{2}\times 19\frac{1}{2}$.

It can be simplified as follows,

$20\frac{1}{2}\times 19\frac{1}{2}=\frac{\left(20\times 2\right)+1}{2}\times \frac{\left(19\times 2\right)+1}{2}$ $\left[\because a\frac{b}{c}=\frac{\left(a\times c\right)+b}{c}\right]$

$$\begin{gathered} \Rightarrow 20\frac{1}{2}\times 19\frac{1}{2}=\frac{40+1}{2}\times \frac{38+1}{2} \\ \Rightarrow 20\frac{1}{2}\times 19\frac{1}{2}=\frac{41}{2}\times \frac{39}{2} \end{gathered}$$

$\Rightarrow 20\frac{1}{2}\times 19\frac{1}{2}=\frac{41\times 39}{2\times 2}$ $\left[\because \frac{a}{b}\times \frac{c}{d}=\frac{a\times c}{b\times d}\right]$

$$\begin{gathered} \Rightarrow 20\frac{1}{2}\times 19\frac{1}{2}=\frac{1599}{4} \\ \Rightarrow 20\frac{1}{2}\times 19\frac{1}{2}=399\frac{3}{4} \end{gathered}$$

Hence, the value of the product $20\frac{1}{2}\times 19\frac{1}{2}$ is $399\frac{3}{4}$.