Solve 1/3-(0.875*2/13+1div6.5div8)*16/7

$$\frac { 1 } { 3 } - ( 0.875 \times \frac { 2 } { 13 } + 1 \div 6.5 \div 8 ) \times 1 \frac { 6 } { 7 }$$

Evaluate

$$\frac{1}{21}\approx 0.047619048$$

Solution Steps

Convert decimal number 0.875 to fraction \frac{875}{1000}. Reduce the fraction \frac{875}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{1}{3}-\left(\frac{7}{8}\times \frac{2}{13}+\frac{\frac{1}{6.5}}{8}\right)\times \frac{1\times 7+6}{7}$$

Multiply \frac{7}{8} times \frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}-\left(\frac{7\times 2}{8\times 13}+\frac{\frac{1}{6.5}}{8}\right)\times \frac{1\times 7+6}{7}$$

Do the multiplications in the fraction \frac{7\times 2}{8\times 13}.

$$\frac{1}{3}-\left(\frac{14}{104}+\frac{\frac{1}{6.5}}{8}\right)\times \frac{1\times 7+6}{7}$$

Reduce the fraction \frac{14}{104} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}-\left(\frac{7}{52}+\frac{\frac{1}{6.5}}{8}\right)\times \frac{1\times 7+6}{7}$$

Express \frac{\frac{1}{6.5}}{8} as a single fraction.

$$\frac{1}{3}-\left(\frac{7}{52}+\frac{1}{6.5\times 8}\right)\times \frac{1\times 7+6}{7}$$

Multiply 6.5 and 8 to get 52.

$$\frac{1}{3}-\left(\frac{7}{52}+\frac{1}{52}\right)\times \frac{1\times 7+6}{7}$$

Since \frac{7}{52} and \frac{1}{52} have the same denominator, add them by adding their numerators.

$$\frac{1}{3}-\frac{7+1}{52}\times \frac{1\times 7+6}{7}$$

Add 7 and 1 to get 8.

$$\frac{1}{3}-\frac{8}{52}\times \frac{1\times 7+6}{7}$$

Reduce the fraction \frac{8}{52} to lowest terms by extracting and canceling out 4.

$$\frac{1}{3}-\frac{2}{13}\times \frac{1\times 7+6}{7}$$

Multiply 1 and 7 to get 7.

$$\frac{1}{3}-\frac{2}{13}\times \frac{7+6}{7}$$

Add 7 and 6 to get 13.

$$\frac{1}{3}-\frac{2}{13}\times \frac{13}{7}$$

Multiply \frac{2}{13} times \frac{13}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}-\frac{2\times 13}{13\times 7}$$

Cancel out 13 in both numerator and denominator.

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

Least common multiple of 3 and 7 is 21. Convert \frac{1}{3} and \frac{2}{7} to fractions with denominator 21.

$$\frac{7}{21}-\frac{6}{21}$$

Since \frac{7}{21} and \frac{6}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-6}{21}$$

Subtract 6 from 7 to get 1.

$$\frac{1}{21}$$

Factor

$$\frac{1}{3 \cdot 7} = 0.047619047619047616$$