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Question Number 128126 by Agnibhoo last updated on 04/Jan/21

(4/(99)) + (7/(999)) + ((11)/(999999)) = ?

$$\:\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{999}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:? \\ $$

Answered by Geovanek last updated on 04/Jan/21

(4/(99)) + (7/(99)) + ((11)/(999999)) = X We can see that ((999999)/(99)) = 10101 AND ((999999)/(999)) = 1001 So, we have (4/(99)) = (4/(99)) ∙ 1 = (4/(99)) ∙ ((10101)/(10101)) = ((40404)/(999999)) AND (7/(999)) = (7/(999)) ∙ 1 = (7/(999)) ∙ ((1001)/(1001)) = ((7007)/(999999)) So, X = ((40404)/(999999)) + ((7007)/(999999)) + ((11)/(999999)) X = ((40404 + 7007 + 11)/(999999)) X = ((47422)/(999999)) You can to use a calculator for this division.

$$\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{99}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:{X} \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{see}\:\mathrm{that} \\ $$$$\frac{\mathrm{999999}}{\mathrm{99}}\:=\:\mathrm{10101}\:\:\:\boldsymbol{\mathrm{AND}} \\ $$$$\frac{\mathrm{999999}}{\mathrm{999}}\:=\:\mathrm{1001} \\ $$$$\mathrm{So},\:\mathrm{we}\:\mathrm{have} \\ $$$$\frac{\mathrm{4}}{\mathrm{99}}\:=\:\frac{\mathrm{4}}{\mathrm{99}}\:\centerdot\:\mathrm{1}\:=\:\frac{\mathrm{4}}{\mathrm{99}}\:\centerdot\:\frac{\mathrm{10101}}{\mathrm{10101}}\:=\:\frac{\mathrm{40404}}{\mathrm{999999}}\:\:\boldsymbol{\mathrm{AND}} \\ $$$$\frac{\mathrm{7}}{\mathrm{999}}\:=\:\frac{\mathrm{7}}{\mathrm{999}}\:\centerdot\:\mathrm{1}\:=\:\frac{\mathrm{7}}{\mathrm{999}}\:\centerdot\:\frac{\mathrm{1001}}{\mathrm{1001}}\:=\:\frac{\mathrm{7007}}{\mathrm{999999}} \\ $$$$\mathrm{So}, \\ $$$${X}\:=\:\frac{\mathrm{40404}}{\mathrm{999999}}\:+\:\frac{\mathrm{7007}}{\mathrm{999999}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}} \\ $$$${X}\:=\:\frac{\mathrm{40404}\:+\:\mathrm{7007}\:+\:\mathrm{11}}{\mathrm{999999}} \\ $$$${X}\:=\:\frac{\mathrm{47422}}{\mathrm{999999}} \\ $$$$\mathrm{You}\:\mathrm{can}\:\mathrm{to}\:\mathrm{use}\:\mathrm{a}\:\mathrm{calculator}\:\mathrm{for}\:\mathrm{this}\:\mathrm{division}. \\ $$

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