Question Number 198036 by mathlove last updated on 08/Oct/23
$${if}\:{A}\boldsymbol{\div}\mathrm{6}\:{reminder}\:{is}\:\mathrm{4}\:{and}\:{B}\boldsymbol{\div}\mathrm{6} \\ $$$${reminder}\:{is}\:\mathrm{5}\:{then}\:\left({A}+{B}\right)\boldsymbol{\div}\mathrm{6} \\ $$$${reminder}\:{is}\:? \\ $$
Answered by AST last updated on 08/Oct/23
$${A}\overset{\mathrm{6}} {\equiv}\mathrm{4},{B}\overset{\mathrm{6}} {\equiv}\mathrm{5}\Rightarrow{A}+{B}\overset{\mathrm{6}} {\equiv}\mathrm{9}\overset{\mathrm{6}} {\equiv}\mathrm{3} \\ $$
Answered by Frix last updated on 08/Oct/23
$${a}=\mathrm{6}{m}+\mathrm{4} \\ $$$${b}=\mathrm{6}{n}+\mathrm{5} \\ $$$${a}+{b}=\mathrm{6}\left({m}+{n}\right)+\mathrm{9}= \\ $$$$\:\:\:\:\:\:\:\:\:=\mathrm{6}\left({m}+{n}\right)+\mathrm{6}+\mathrm{3}= \\ $$$$\:\:\:\:\:\:\:\:\:=\mathrm{6}\left({m}+{n}+\mathrm{1}\right)+\mathrm{3}= \\ $$$$\:\:\:\:\:\:\:\:\:=\mathrm{6}{k}+\mathrm{3} \\ $$
Commented by mathlove last updated on 09/Oct/23
$${thanks} \\ $$