Solve 42/3-2/3div11/5+4/5*3

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

Evaluate

$$\frac{293}{45}\approx 6.511111111$$

Solution Steps

Multiply 4 and 3 to get 12.

$$\frac{12+2}{3}-\frac{\frac{2}{3}}{\frac{1\times 5+1}{5}}+\frac{4}{5}\times 3$$

Add 12 and 2 to get 14.

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

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

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

Multiply 2 and 5 to get 10.

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

Multiply 1 and 5 to get 5.

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

Add 5 and 1 to get 6.

$$\frac{14}{3}-\frac{10}{3\times 6}+\frac{4}{5}\times 3$$

Multiply 3 and 6 to get 18.

$$\frac{14}{3}-\frac{10}{18}+\frac{4}{5}\times 3$$

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

$$\frac{14}{3}-\frac{5}{9}+\frac{4}{5}\times 3$$

Least common multiple of 3 and 9 is 9. Convert \frac{14}{3} and \frac{5}{9} to fractions with denominator 9.

$$\frac{42}{9}-\frac{5}{9}+\frac{4}{5}\times 3$$

Since \frac{42}{9} and \frac{5}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{42-5}{9}+\frac{4}{5}\times 3$$

Subtract 5 from 42 to get 37.

$$\frac{37}{9}+\frac{4}{5}\times 3$$

Express \frac{4}{5}\times 3 as a single fraction.

$$\frac{37}{9}+\frac{4\times 3}{5}$$

Multiply 4 and 3 to get 12.

$$\frac{37}{9}+\frac{12}{5}$$

Least common multiple of 9 and 5 is 45. Convert \frac{37}{9} and \frac{12}{5} to fractions with denominator 45.

$$\frac{185}{45}+\frac{108}{45}$$

Since \frac{185}{45} and \frac{108}{45} have the same denominator, add them by adding their numerators.

$$\frac{185+108}{45}$$

Add 185 and 108 to get 293.

$$\frac{293}{45}$$

Factor

$$\frac{293}{3 ^ {2} \cdot 5} = 6\frac{23}{45} = 6.511111111111111$$