Solve 1/6div[9/17*(3/4+2/3)]

$$\frac { 1 } { 6 } \div [ \frac { 9 } { 17 } \times ( \frac { 3 } { 4 } + \frac { 2 } { 3 } ) ]$$

Evaluate

$$\frac{2}{9}\approx 0.222222222$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{\frac{1}{6}}{\frac{9}{17}\left(\frac{9}{12}+\frac{8}{12}\right)}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{6}}{\frac{9}{17}\times \frac{9+8}{12}}$$

Add 9 and 8 to get 17.

$$\frac{\frac{1}{6}}{\frac{9}{17}\times \frac{17}{12}}$$

Multiply \frac{9}{17} times \frac{17}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{6}}{\frac{9\times 17}{17\times 12}}$$

Cancel out 17 in both numerator and denominator.

$$\frac{\frac{1}{6}}{\frac{9}{12}}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{6}}{\frac{3}{4}}$$

Divide \frac{1}{6} by \frac{3}{4} by multiplying \frac{1}{6} by the reciprocal of \frac{3}{4}.

$$\frac{1}{6}\times \frac{4}{3}$$

Multiply \frac{1}{6} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{6\times 3}$$

Do the multiplications in the fraction \frac{1\times 4}{6\times 3}.

$$\frac{4}{18}$$

Reduce the fraction \frac{4}{18} to lowest terms by extracting and canceling out 2.

$$\frac{2}{9}$$

Factor

$$\frac{2}{3 ^ {2}} = 0.2222222222222222$$