Question Number 167241 by mathlove last updated on 10/Mar/22
$$\frac{{b}}{\mathrm{11}}\:\:{is}\:{General}\:{fraction}\:\:{and}\:\mathrm{0}.\overline {\mathrm{3}{a}} \\ $$$${faind}\:\:\left({a}−\mathrm{9}{b}\right)=? \\ $$
Answered by mr W last updated on 10/Mar/22
$$\frac{{b}}{\mathrm{11}}=\mathrm{0}.\overline {\mathrm{3}{a}} \\ $$$$\mathrm{100}×\frac{{b}}{\mathrm{11}}=\mathrm{30}+{a}+\frac{{b}}{\mathrm{11}} \\ $$$$\mathrm{9}{b}=\mathrm{30}+{a} \\ $$$$\Rightarrow\mathrm{9}{b}−{a}=\mathrm{30} \\ $$
Answered by HeferH last updated on 10/Mar/22
$$\:\frac{\overline {\mathrm{3}{a}}}{\mathrm{99}}\:=\:\frac{{b}}{\mathrm{11}}\: \\ $$$$\:``\mathrm{3}{a}''\:{needs}\:{to}\:{be}\:{a}\:{multiple}\:{of}\:\mathrm{9}\:{in}\:{order}\:{to} \\ $$$$\:{simplify}. \\ $$$$\:\frac{\mathrm{36}}{\mathrm{99}}\:=\:\frac{\mathrm{4}}{\mathrm{11}} \\ $$$$\:{a}\:=\:\mathrm{6} \\ $$$$\:{b}\:=\:\mathrm{4} \\ $$$$\:\left(\mathrm{6}\:−\:\mathrm{9}\centerdot\mathrm{4}\right)\:=\:\left(\mathrm{6}\:−\:\mathrm{36}\right)\:=\:−\mathrm{30} \\ $$$$\: \\ $$$$\:\left({Sorry}\:{if}\:{I}'{m}\:{wrong},\:{I}'{m}\:{new}\:{doing}\:{this}\right) \\ $$