Solve (2/9+4+15/6):(22/3-1/6)+frac{2}{3}*1frac{1}{5}

$$( \frac { 2 } { 9 } + 4 + 1 \frac { 5 } { 6 } ) : ( 2 \frac { 2 } { 3 } - \frac { 1 } { 6 } ) + \frac { 2 } { 3 } \cdot 1 \frac { 1 } { 5 }$$

Evaluate

$$\frac{29}{9}\approx 3.222222222$$

Solution Steps

Convert 4 to fraction \frac{36}{9}.

$$\frac{\frac{2}{9}+\frac{36}{9}+\frac{1\times 6+5}{6}}{\frac{2\times 3+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Since \frac{2}{9} and \frac{36}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+36}{9}+\frac{1\times 6+5}{6}}{\frac{2\times 3+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Add 2 and 36 to get 38.

$$\frac{\frac{38}{9}+\frac{1\times 6+5}{6}}{\frac{2\times 3+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Multiply 1 and 6 to get 6.

$$\frac{\frac{38}{9}+\frac{6+5}{6}}{\frac{2\times 3+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Add 6 and 5 to get 11.

$$\frac{\frac{38}{9}+\frac{11}{6}}{\frac{2\times 3+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Least common multiple of 9 and 6 is 18. Convert \frac{38}{9} and \frac{11}{6} to fractions with denominator 18.

$$\frac{\frac{76}{18}+\frac{33}{18}}{\frac{2\times 3+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Since \frac{76}{18} and \frac{33}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{76+33}{18}}{\frac{2\times 3+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Add 76 and 33 to get 109.

$$\frac{\frac{109}{18}}{\frac{2\times 3+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{109}{18}}{\frac{6+2}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Add 6 and 2 to get 8.

$$\frac{\frac{109}{18}}{\frac{8}{3}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Least common multiple of 3 and 6 is 6. Convert \frac{8}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{\frac{109}{18}}{\frac{16}{6}-\frac{1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Since \frac{16}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{109}{18}}{\frac{16-1}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Subtract 1 from 16 to get 15.

$$\frac{\frac{109}{18}}{\frac{15}{6}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{109}{18}}{\frac{5}{2}}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Divide \frac{109}{18} by \frac{5}{2} by multiplying \frac{109}{18} by the reciprocal of \frac{5}{2}.

$$\frac{109}{18}\times \frac{2}{5}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Multiply \frac{109}{18} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{109\times 2}{18\times 5}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Do the multiplications in the fraction \frac{109\times 2}{18\times 5}.

$$\frac{218}{90}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Reduce the fraction \frac{218}{90} to lowest terms by extracting and canceling out 2.

$$\frac{109}{45}+\frac{2}{3}\times \frac{1\times 5+1}{5}$$

Multiply 1 and 5 to get 5.

$$\frac{109}{45}+\frac{2}{3}\times \frac{5+1}{5}$$

Add 5 and 1 to get 6.

$$\frac{109}{45}+\frac{2}{3}\times \frac{6}{5}$$

Multiply \frac{2}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{109}{45}+\frac{2\times 6}{3\times 5}$$

Do the multiplications in the fraction \frac{2\times 6}{3\times 5}.

$$\frac{109}{45}+\frac{12}{15}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{109}{45}+\frac{4}{5}$$

Least common multiple of 45 and 5 is 45. Convert \frac{109}{45} and \frac{4}{5} to fractions with denominator 45.

$$\frac{109}{45}+\frac{36}{45}$$

Since \frac{109}{45} and \frac{36}{45} have the same denominator, add them by adding their numerators.

$$\frac{109+36}{45}$$

Add 109 and 36 to get 145.

$$\frac{145}{45}$$

Reduce the fraction \frac{145}{45} to lowest terms by extracting and canceling out 5.

$$\frac{29}{9}$$

Factor

$$\frac{29}{3 ^ {2}} = 3\frac{2}{9} = 3.2222222222222223$$