Solve (7/3+1/9+3+1/3):(1/18+1)

$$( \frac { 7 } { 3 } + \frac { 1 } { 9 } + 3 + \frac { 1 } { 3 } ) : ( \frac { 1 } { 18 } + 1 )$$

Evaluate

$$\frac{104}{19}\approx 5.473684211$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{7}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{\frac{21}{9}+\frac{1}{9}+3+\frac{1}{3}}{\frac{1}{18}+1}$$

Since \frac{21}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21+1}{9}+3+\frac{1}{3}}{\frac{1}{18}+1}$$

Add 21 and 1 to get 22.

$$\frac{\frac{22}{9}+3+\frac{1}{3}}{\frac{1}{18}+1}$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{\frac{22}{9}+\frac{27}{9}+\frac{1}{3}}{\frac{1}{18}+1}$$

Since \frac{22}{9} and \frac{27}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{22+27}{9}+\frac{1}{3}}{\frac{1}{18}+1}$$

Add 22 and 27 to get 49.

$$\frac{\frac{49}{9}+\frac{1}{3}}{\frac{1}{18}+1}$$

Least common multiple of 9 and 3 is 9. Convert \frac{49}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{\frac{49}{9}+\frac{3}{9}}{\frac{1}{18}+1}$$

Since \frac{49}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{49+3}{9}}{\frac{1}{18}+1}$$

Add 49 and 3 to get 52.

$$\frac{\frac{52}{9}}{\frac{1}{18}+1}$$

Convert 1 to fraction \frac{18}{18}.

$$\frac{\frac{52}{9}}{\frac{1}{18}+\frac{18}{18}}$$

Since \frac{1}{18} and \frac{18}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{52}{9}}{\frac{1+18}{18}}$$

Add 1 and 18 to get 19.

$$\frac{\frac{52}{9}}{\frac{19}{18}}$$

Divide \frac{52}{9} by \frac{19}{18} by multiplying \frac{52}{9} by the reciprocal of \frac{19}{18}.

$$\frac{52}{9}\times \frac{18}{19}$$

Multiply \frac{52}{9} times \frac{18}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{52\times 18}{9\times 19}$$

Do the multiplications in the fraction \frac{52\times 18}{9\times 19}.

$$\frac{936}{171}$$

Reduce the fraction \frac{936}{171} to lowest terms by extracting and canceling out 9.

$$\frac{104}{19}$$

Factor

$$\frac{2 ^ {3} \cdot 13}{19} = 5\frac{9}{19} = 5.473684210526316$$