Solve (2)(7/3)-(5/3)+1/frac{1{2}+2/3}

$$\frac { ( 2 ) ( \frac { 7 } { 3 } ) - ( \frac { 5 } { 3 } ) + 1 } { \frac { 1 } { 2 } + \frac { 2 } { 3 } }$$

Evaluate

$$\frac{24}{7}\approx 3.428571429$$

Solution Steps

Express 2\times \frac{7}{3} as a single fraction.

$$\frac{\frac{2\times 7}{3}-\frac{5}{3}+1}{\frac{1}{2}+\frac{2}{3}}$$

Multiply 2 and 7 to get 14.

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

Since \frac{14}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 14 to get 9.

$$\frac{\frac{9}{3}+1}{\frac{1}{2}+\frac{2}{3}}$$

Divide 9 by 3 to get 3.

$$\frac{3+1}{\frac{1}{2}+\frac{2}{3}}$$

Add 3 and 1 to get 4.

$$\frac{4}{\frac{1}{2}+\frac{2}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{4}{\frac{3}{6}+\frac{4}{6}}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{4}{\frac{3+4}{6}}$$

Add 3 and 4 to get 7.

$$\frac{4}{\frac{7}{6}}$$

Divide 4 by \frac{7}{6} by multiplying 4 by the reciprocal of \frac{7}{6}.

$$4\times \frac{6}{7}$$

Express 4\times \frac{6}{7} as a single fraction.

$$\frac{4\times 6}{7}$$

Multiply 4 and 6 to get 24.

$$\frac{24}{7}$$

Factor

$$\frac{2 ^ {3} \cdot 3}{7} = 3\frac{3}{7} = 3.4285714285714284$$