Question

Represent the following mixed infinite decimal periodic fractions as common fractions:
Find $x$ if $\frac{0.1\left(6\right)+0.\left(3\right)}{0.\left(3\right)+1.1\left(6\right)}x=10$

Calculate (5 31)

Answer 1

Change the mixed infinite decimal into a common fraction first

$0.1\left(6\right)$ in common fraction is $\frac{15}{90}$

$0.\left(3\right)$ in common fraction is $\frac{1}{3}$

$1.1\left(6\right)$ in common fraction is $\frac{105}{90}$

Now put the value in the given expression, we have

$\frac{\frac{15}{90}+\frac{1}{3}}{\frac{1}{3}+\frac{105}{90}}x$

After solving the expression, we get $0.3333333x$

This can also be written as $\frac{1}{3}x$

which is equal to $10$

$\therefore \frac{1}{3}x=10$

$\Rightarrow x=30$