Solve 3/5div(3/10+11/2)+5/18*3frac{1}{5}

$$\frac { 3 } { 5 } \div ( \frac { 3 } { 10 } + 1 \frac { 1 } { 2 } ) + \frac { 5 } { 18 } \times 3 \frac { 1 } { 5 }$$

Evaluate

$$\frac{11}{9}\approx 1.222222222$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{\frac{3}{5}}{\frac{3}{10}+\frac{2+1}{2}}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Add 2 and 1 to get 3.

$$\frac{\frac{3}{5}}{\frac{3}{10}+\frac{3}{2}}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Least common multiple of 10 and 2 is 10. Convert \frac{3}{10} and \frac{3}{2} to fractions with denominator 10.

$$\frac{\frac{3}{5}}{\frac{3}{10}+\frac{15}{10}}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Since \frac{3}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{5}}{\frac{3+15}{10}}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Add 3 and 15 to get 18.

$$\frac{\frac{3}{5}}{\frac{18}{10}}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{5}}{\frac{9}{5}}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Divide \frac{3}{5} by \frac{9}{5} by multiplying \frac{3}{5} by the reciprocal of \frac{9}{5}.

$$\frac{3}{5}\times \frac{5}{9}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Multiply \frac{3}{5} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 5}{5\times 9}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3}{9}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

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

$$\frac{1}{3}+\frac{5}{18}\times \frac{3\times 5+1}{5}$$

Multiply 3 and 5 to get 15.

$$\frac{1}{3}+\frac{5}{18}\times \frac{15+1}{5}$$

Add 15 and 1 to get 16.

$$\frac{1}{3}+\frac{5}{18}\times \frac{16}{5}$$

Multiply \frac{5}{18} times \frac{16}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{5\times 16}{18\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{1}{3}+\frac{16}{18}$$

Reduce the fraction \frac{16}{18} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}+\frac{8}{9}$$

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{8}{9} to fractions with denominator 9.

$$\frac{3}{9}+\frac{8}{9}$$

Since \frac{3}{9} and \frac{8}{9} have the same denominator, add them by adding their numerators.

$$\frac{3+8}{9}$$

Add 3 and 8 to get 11.

$$\frac{11}{9}$$

Factor

$$\frac{11}{3 ^ {2}} = 1\frac{2}{9} = 1.2222222222222223$$