Solve (10/7*5-(1/2+3/14):1/5]:(2+1/2)-2/3-1/7

$$( 10 / 7 \cdot 5 - ( 1 / 2 + 3 / 14 ) : 1 / 5 ] : ( 2 + 1 / 2 ) - 2 / 3 - 1 / 7$$

Evaluate

$$\frac{13}{21}\approx 0.619047619$$

Solution Steps

Express \frac{10}{7}\times 5 as a single fraction.

$$\frac{\frac{10\times 5}{7}-\frac{\frac{1}{2}+\frac{3}{14}}{\frac{1}{5}}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Multiply 10 and 5 to get 50.

$$\frac{\frac{50}{7}-\frac{\frac{1}{2}+\frac{3}{14}}{\frac{1}{5}}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Least common multiple of 2 and 14 is 14. Convert \frac{1}{2} and \frac{3}{14} to fractions with denominator 14.

$$\frac{\frac{50}{7}-\frac{\frac{7}{14}+\frac{3}{14}}{\frac{1}{5}}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Since \frac{7}{14} and \frac{3}{14} have the same denominator, add them by adding their numerators.

$$\frac{\frac{50}{7}-\frac{\frac{7+3}{14}}{\frac{1}{5}}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Add 7 and 3 to get 10.

$$\frac{\frac{50}{7}-\frac{\frac{10}{14}}{\frac{1}{5}}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{50}{7}-\frac{\frac{5}{7}}{\frac{1}{5}}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Divide \frac{5}{7} by \frac{1}{5} by multiplying \frac{5}{7} by the reciprocal of \frac{1}{5}.

$$\frac{\frac{50}{7}-\frac{5}{7}\times 5}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Express \frac{5}{7}\times 5 as a single fraction.

$$\frac{\frac{50}{7}-\frac{5\times 5}{7}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Multiply 5 and 5 to get 25.

$$\frac{\frac{50}{7}-\frac{25}{7}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Since \frac{50}{7} and \frac{25}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{50-25}{7}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Subtract 25 from 50 to get 25.

$$\frac{\frac{25}{7}}{2+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{\frac{25}{7}}{\frac{4}{2}+\frac{1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25}{7}}{\frac{4+1}{2}}-\frac{2}{3}-\frac{1}{7}$$

Add 4 and 1 to get 5.

$$\frac{\frac{25}{7}}{\frac{5}{2}}-\frac{2}{3}-\frac{1}{7}$$

Divide \frac{25}{7} by \frac{5}{2} by multiplying \frac{25}{7} by the reciprocal of \frac{5}{2}.

$$\frac{25}{7}\times \frac{2}{5}-\frac{2}{3}-\frac{1}{7}$$

Multiply \frac{25}{7} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 2}{7\times 5}-\frac{2}{3}-\frac{1}{7}$$

Do the multiplications in the fraction \frac{25\times 2}{7\times 5}.

$$\frac{50}{35}-\frac{2}{3}-\frac{1}{7}$$

Reduce the fraction \frac{50}{35} to lowest terms by extracting and canceling out 5.

$$\frac{10}{7}-\frac{2}{3}-\frac{1}{7}$$

Least common multiple of 7 and 3 is 21. Convert \frac{10}{7} and \frac{2}{3} to fractions with denominator 21.

$$\frac{30}{21}-\frac{14}{21}-\frac{1}{7}$$

Since \frac{30}{21} and \frac{14}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-14}{21}-\frac{1}{7}$$

Subtract 14 from 30 to get 16.

$$\frac{16}{21}-\frac{1}{7}$$

Least common multiple of 21 and 7 is 21. Convert \frac{16}{21} and \frac{1}{7} to fractions with denominator 21.

$$\frac{16}{21}-\frac{3}{21}$$

Since \frac{16}{21} and \frac{3}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-3}{21}$$

Subtract 3 from 16 to get 13.

$$\frac{13}{21}$$

Factor

$$\frac{13}{3 \cdot 7} = 0.6190476190476191$$