Solve 52/3-31/3div22/3*4/5+2frac{1}{5}div2frac{3}{4}

$$5 \frac { 2 } { 3 } - 3 \frac { 1 } { 3 } \div 2 \frac { 2 } { 3 } \times \frac { 4 } { 5 } + 2 \frac { 1 } { 5 } \div 2 \frac { 3 } { 4 }$$

Evaluate

$$\frac{82}{15}\approx 5.466666667$$

Solution Steps

Multiply 5 and 3 to get 15.

$$\frac{15+2}{3}-\frac{\frac{3\times 3+1}{3}}{\frac{2\times 3+2}{3}}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Add 15 and 2 to get 17.

$$\frac{17}{3}-\frac{\frac{3\times 3+1}{3}}{\frac{2\times 3+2}{3}}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Divide \frac{3\times 3+1}{3} by \frac{2\times 3+2}{3} by multiplying \frac{3\times 3+1}{3} by the reciprocal of \frac{2\times 3+2}{3}.

$$\frac{17}{3}-\frac{\left(3\times 3+1\right)\times 3}{3\left(2\times 3+2\right)}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{17}{3}-\frac{1+3\times 3}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Multiply 3 and 3 to get 9.

$$\frac{17}{3}-\frac{1+9}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Add 1 and 9 to get 10.

$$\frac{17}{3}-\frac{10}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Multiply 2 and 3 to get 6.

$$\frac{17}{3}-\frac{10}{2+6}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Add 2 and 6 to get 8.

$$\frac{17}{3}-\frac{10}{8}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{17}{3}-\frac{5}{4}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Cancel out \frac{5}{4} and its reciprocal \frac{4}{5}.

$$\frac{17}{3}-1+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{17}{3}-\frac{3}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Since \frac{17}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-3}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Subtract 3 from 17 to get 14.

$$\frac{14}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Divide \frac{2\times 5+1}{5} by \frac{2\times 4+3}{4} by multiplying \frac{2\times 5+1}{5} by the reciprocal of \frac{2\times 4+3}{4}.

$$\frac{14}{3}+\frac{\left(2\times 5+1\right)\times 4}{5\left(2\times 4+3\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{14}{3}+\frac{\left(10+1\right)\times 4}{5\left(2\times 4+3\right)}$$

Add 10 and 1 to get 11.

$$\frac{14}{3}+\frac{11\times 4}{5\left(2\times 4+3\right)}$$

Multiply 11 and 4 to get 44.

$$\frac{14}{3}+\frac{44}{5\left(2\times 4+3\right)}$$

Multiply 2 and 4 to get 8.

$$\frac{14}{3}+\frac{44}{5\left(8+3\right)}$$

Add 8 and 3 to get 11.

$$\frac{14}{3}+\frac{44}{5\times 11}$$

Multiply 5 and 11 to get 55.

$$\frac{14}{3}+\frac{44}{55}$$

Reduce the fraction \frac{44}{55} to lowest terms by extracting and canceling out 11.

$$\frac{14}{3}+\frac{4}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{14}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{70}{15}+\frac{12}{15}$$

Since \frac{70}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{70+12}{15}$$

Add 70 and 12 to get 82.

$$\frac{82}{15}$$

Factor

$$\frac{2 \cdot 41}{3 \cdot 5} = 5\frac{7}{15} = 5.466666666666667$$