Question

Divide the product of $3\frac{1}{2}$ and $4\frac{1}{5}$ by the product of $2\frac{1}{2}$ and $5\frac{2}{3}$ .

Answer 1

Step 1 : Find the products

$$\begin{gathered} 3\frac{1}{2}\times 4\frac{1}{5}=\frac{7}{2}\times \frac{21}{5} \\ =\frac{147}{10} \end{gathered}$$

And ,

$$\begin{gathered} 2\frac{1}{2}\times 5\frac{2}{3}=\frac{5}{2}\times \frac{17}{3} \\ =\frac{85}{6} \end{gathered}$$

Step 2 : Divide the products

$\begin{array}{rcl}\frac{147}{10}÷\frac{85}{6}& =& \frac{147}{10}\times \frac{6}{85}\\ & =& \frac{882}{850}\\ & =& \frac{2\times 441}{2\times 425}\\ & =& \frac{441}{425}\end{array}$

Hence, the required answer is $\frac{441}{425}$.