Question Number 104450 by Anindita last updated on 21/Jul/20
$$\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{999}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:? \\ $$$$\boldsymbol{\mathrm{Can}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}? \\ $$
Answered by OlafThorendsen last updated on 21/Jul/20
$$\mathrm{999999}\:=\:\mathrm{999000}+\mathrm{999}\:=\:\mathrm{999}×\mathrm{1001} \\ $$$$\mathrm{999999}\:=\:\mathrm{990000}+\mathrm{9900}+\mathrm{99}\:=\:\mathrm{99}×\mathrm{10101} \\ $$$$\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{999}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:= \\ $$$$\frac{\mathrm{4}×\mathrm{10101}+\mathrm{7}×\mathrm{1001}+\mathrm{11}}{\mathrm{999999}}\:= \\ $$$$\frac{\mathrm{40404}+\mathrm{7007}+\mathrm{11}}{\mathrm{999999}}\:= \\ $$$$\frac{\mathrm{47422}}{\mathrm{999999}} \\ $$