Express 0.6 + 0.overline{7} + 0.4overline{7} | vedclass

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Question

(C) First, convert each term into a fraction:$0.6 = \frac{6}{10} = \frac{3}{5}$For $x = 0.\overline{7} = 0.777\ldots$$10x = 7.777\ldots$Subtracting $x

Vedclass · Accepted Answer

$\frac{167}{90}$

Vedclass · Answer

(C) First, convert each term into a fraction:$0.6 = \frac{6}{10} = \frac{3}{5}$For $x = 0.\overline{7} = 0.777\ldots$$10x = 7.777\ldots$Subtracting $x$ from $10x$ gives $9x = 7$, so $x = \frac{7}{9}$.For $y = 0.4\overline{7} = 0.4777\ldots$$10y = 4.777\ldots$$100y = 47.777\ldots$Subtracting $10y$ from $100y$ gives $90y = 43$, so $y = \frac{43}{90}$.Now, add the fractions:$\frac{6}{10} + \frac{7}{9} + \frac{43}{90} = \frac{54}{90} + \frac{70}{90} + \frac{43}{90} = \frac{54 + 70 + 43}{90} = \frac{167}{90}$.Thus, the expression is $\frac{167}{90}$.

Express $0.6 + 0.\overline{7} + 0.4\overline{7}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

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