Question

A man on a diet is losing four-tenths of a kilogram each day. How many days will it take him to lose 3.2 kilograms?

Answer 1

so he's losing 4/10 of a Kg daily, how many times will that equal 3.2 Kgs? namely how many times does 4/10 go into 3.2?

well, let's firstly convert 3.2 to a fraction, and then divide.

$\bf \stackrel{\textit{1 decimal}}{3.\underline{2}}\implies \cfrac{32}{\underset{\textit{1 zero}}{1\underline{0}}}\implies \cfrac{16}{5} \\\\[-0.35em] ~\dotfill$

$\bf \cfrac{16}{5}\div \cfrac{4}{10}\implies \cfrac{16}{5}\div \cfrac{2}{5}\implies \cfrac{\stackrel{8}{~~\begin{matrix} 16 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 8$