Solve 15/6-1/4:(3/2-1+3/8)-frac{3}{14}]-(frac{9}{7}-frac{5}{3}+2)*frac{3}{2}}*(-frac{7}{9})

$$\frac { 15 } { 6 } - \frac { 1 } { 4 } : ( \frac { 3 } { 2 } - 1 + \frac { 3 } { 8 } ) - \frac { 3 } { 14 } ] - ( \frac { 9 } { 7 } - \frac { 5 } { 3 } + 2 ) \cdot \frac { 3 } { 2 } \} \cdot ( - \frac { 7 } { 9 } )$$

Evaluate

$$2$$

Solution Steps

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{2}-\frac{\frac{1}{4}}{\frac{3}{2}-1+\frac{3}{8}}-\frac{3}{14}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{5}{2}-\frac{\frac{1}{4}}{\frac{3}{2}-\frac{2}{2}+\frac{3}{8}}-\frac{3}{14}$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}-\frac{\frac{1}{4}}{\frac{3-2}{2}+\frac{3}{8}}-\frac{3}{14}$$

Subtract 2 from 3 to get 1.

$$\frac{5}{2}-\frac{\frac{1}{4}}{\frac{1}{2}+\frac{3}{8}}-\frac{3}{14}$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

$$\frac{5}{2}-\frac{\frac{1}{4}}{\frac{4}{8}+\frac{3}{8}}-\frac{3}{14}$$

Since \frac{4}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{5}{2}-\frac{\frac{1}{4}}{\frac{4+3}{8}}-\frac{3}{14}$$

Add 4 and 3 to get 7.

$$\frac{5}{2}-\frac{\frac{1}{4}}{\frac{7}{8}}-\frac{3}{14}$$

Divide \frac{1}{4} by \frac{7}{8} by multiplying \frac{1}{4} by the reciprocal of \frac{7}{8}.

$$\frac{5}{2}-\frac{1}{4}\times \frac{8}{7}-\frac{3}{14}$$

Multiply \frac{1}{4} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{2}-\frac{1\times 8}{4\times 7}-\frac{3}{14}$$

Do the multiplications in the fraction \frac{1\times 8}{4\times 7}.

$$\frac{5}{2}-\frac{8}{28}-\frac{3}{14}$$

Reduce the fraction \frac{8}{28} to lowest terms by extracting and canceling out 4.

$$\frac{5}{2}-\frac{2}{7}-\frac{3}{14}$$

Least common multiple of 2 and 7 is 14. Convert \frac{5}{2} and \frac{2}{7} to fractions with denominator 14.

$$\frac{35}{14}-\frac{4}{14}-\frac{3}{14}$$

Since \frac{35}{14} and \frac{4}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-4}{14}-\frac{3}{14}$$

Subtract 4 from 35 to get 31.

$$\frac{31}{14}-\frac{3}{14}$$

Since \frac{31}{14} and \frac{3}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31-3}{14}$$

Subtract 3 from 31 to get 28.

$$\frac{28}{14}$$

Divide 28 by 14 to get 2.

$$2$$

Factor

$$2$$