Question Number 84740 by Rio Michael last updated on 15/Mar/20
$$\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:−\mathrm{18}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{4} \\ $$
Commented by mr W last updated on 15/Mar/20
$$−\mathrm{18}=\left(−\mathrm{5}\right)×\mathrm{4}+\mathrm{2} \\ $$$$\Rightarrow{remainder}\:=\:\mathrm{2} \\ $$
Commented by Rio Michael last updated on 15/Mar/20
$$\mathrm{sir}\:\mathrm{can}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{be}\:\mathrm{negative}? \\ $$
Commented by mr W last updated on 15/Mar/20
Commented by Rio Michael last updated on 15/Mar/20
$$\mathrm{thanks}\:\mathrm{so}\:\mathrm{much}\:\mathrm{sir} \\ $$
Commented by MJS last updated on 16/Mar/20
$$\mathrm{some}\:\mathrm{define}\:\mathrm{negative}\:\mathrm{remainders} \\ $$$$−\mathrm{18}\boldsymbol{\div}\mathrm{4}=−\left(\mathrm{18}\boldsymbol{\div}\mathrm{4}\right)=−\mathrm{4}\:\mathrm{remainder}\:−\mathrm{2} \\ $$$$\Leftrightarrow \\ $$$$\left(−\mathrm{4}\right)×\mathrm{4}+\left(−\mathrm{2}\right)=−\mathrm{16}−\mathrm{2}=−\mathrm{18} \\ $$$$\mathrm{but}\:\mathrm{I}\:\mathrm{think}\:\mathrm{it}'\mathrm{s}\:\mathrm{more}\:\mathrm{common}\:\mathrm{to}\:\mathrm{keep}\:\mathrm{remainders} \\ $$$$\mathrm{positive} \\ $$
Answered by jairodejesusestradaA last updated on 15/Mar/20
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