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Help with this question of grade 9 chapter 1

Help with this question of grade 9 chapter 1-example-1

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0.6=(6)/(10)=(3)/(5)\\\\x=0.\overline{7}\\10x=7.\overline{7}\\10x-x=7.\overline{7}-0.\overline{7}\\9x=7\\x=(7)/(9)\\\\x=0.4\overline{7}\\10x=4.\overline{7}\\100x=47.\overline{7}\\100x-10x=47.\overline{7}-4.\overline{7}\\90x=43\\x=(43)/(90)

Therefore


0.6+0.\overline{7}+0.4\overline{7}=(3)/(5)+(7)/(9)+(43)/(90)=(54)/(90)+(70)/(90)+(43)/(90)=(167)/(90)

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