Question $1$: In each case, calculate the appropriate ratio to show that the information given is consistent with the law of multiple proportions.

$($a$)$ Both ammonia $($NH$3)$ and hydrazine $($N$2$H$4)$ are composed of nitrogen and hydrogen. Ammonia contains $0\mathrm{.}2158$ g hydrogen for every gram of nitrogen. Hydrazine contains $0\mathrm{.}1439$ g hydrogen for every gram of nitrogen.

b$)$ Two of the compounds that consist of nitrogen and oxygen anitric oxide, also known as nitrogen monoxide $($NO$)$ and nitrous oxide $($N$2$O$),$ which is also known as dinitrogen monoxide. Nitric oxide contains $1\mathrm{.}142$ g oxygen for every gram of nitrogen. Nitrous oxide contains $0\mathrm{.}571$ g oxygen for every gram of nitrogen.