Solve 68/3:{[(1+1/3-2/5)*15/8]:(frac{13}{7}-frac{3}{4}-frac{5}{14})-frac{10}{3}*frac{1}{2}}

$$\frac { 68 } { 3 } : \{ [ ( 1 + \frac { 1 } { 3 } - \frac { 2 } { 5 } ) \cdot \frac { 15 } { 8 } ] : ( \frac { 13 } { 7 } - \frac { 3 } { 4 } - \frac { 5 } { 14 } ) - \frac { 10 } { 3 } \cdot \frac { 1 } { 2 } \}$$

Evaluate

$$34$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{68}{3}}{\frac{\left(\frac{3}{3}+\frac{1}{3}-\frac{2}{5}\right)\times \frac{15}{8}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{68}{3}}{\frac{\left(\frac{3+1}{3}-\frac{2}{5}\right)\times \frac{15}{8}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{68}{3}}{\frac{\left(\frac{4}{3}-\frac{2}{5}\right)\times \frac{15}{8}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{\frac{68}{3}}{\frac{\left(\frac{20}{15}-\frac{6}{15}\right)\times \frac{15}{8}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Since \frac{20}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{68}{3}}{\frac{\frac{20-6}{15}\times \frac{15}{8}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Subtract 6 from 20 to get 14.

$$\frac{\frac{68}{3}}{\frac{\frac{14}{15}\times \frac{15}{8}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Multiply \frac{14}{15} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{68}{3}}{\frac{\frac{14\times 15}{15\times 8}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Cancel out 15 in both numerator and denominator.

$$\frac{\frac{68}{3}}{\frac{\frac{14}{8}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Reduce the fraction \frac{14}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{68}{3}}{\frac{\frac{7}{4}}{\frac{13}{7}-\frac{3}{4}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Least common multiple of 7 and 4 is 28. Convert \frac{13}{7} and \frac{3}{4} to fractions with denominator 28.

$$\frac{\frac{68}{3}}{\frac{\frac{7}{4}}{\frac{52}{28}-\frac{21}{28}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Since \frac{52}{28} and \frac{21}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{68}{3}}{\frac{\frac{7}{4}}{\frac{52-21}{28}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Subtract 21 from 52 to get 31.

$$\frac{\frac{68}{3}}{\frac{\frac{7}{4}}{\frac{31}{28}-\frac{5}{14}}-\frac{10}{3}\times \frac{1}{2}}$$

Least common multiple of 28 and 14 is 28. Convert \frac{31}{28} and \frac{5}{14} to fractions with denominator 28.

$$\frac{\frac{68}{3}}{\frac{\frac{7}{4}}{\frac{31}{28}-\frac{10}{28}}-\frac{10}{3}\times \frac{1}{2}}$$

Since \frac{31}{28} and \frac{10}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{68}{3}}{\frac{\frac{7}{4}}{\frac{31-10}{28}}-\frac{10}{3}\times \frac{1}{2}}$$

Subtract 10 from 31 to get 21.

$$\frac{\frac{68}{3}}{\frac{\frac{7}{4}}{\frac{21}{28}}-\frac{10}{3}\times \frac{1}{2}}$$

Reduce the fraction \frac{21}{28} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{68}{3}}{\frac{\frac{7}{4}}{\frac{3}{4}}-\frac{10}{3}\times \frac{1}{2}}$$

Divide \frac{7}{4} by \frac{3}{4} by multiplying \frac{7}{4} by the reciprocal of \frac{3}{4}.

$$\frac{\frac{68}{3}}{\frac{7}{4}\times \frac{4}{3}-\frac{10}{3}\times \frac{1}{2}}$$

Multiply \frac{7}{4} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{68}{3}}{\frac{7\times 4}{4\times 3}-\frac{10}{3}\times \frac{1}{2}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{68}{3}}{\frac{7}{3}-\frac{10}{3}\times \frac{1}{2}}$$

Multiply \frac{10}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{68}{3}}{\frac{7}{3}-\frac{10\times 1}{3\times 2}}$$

Do the multiplications in the fraction \frac{10\times 1}{3\times 2}.

$$\frac{\frac{68}{3}}{\frac{7}{3}-\frac{10}{6}}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{68}{3}}{\frac{7}{3}-\frac{5}{3}}$$

Since \frac{7}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{68}{3}}{\frac{7-5}{3}}$$

Subtract 5 from 7 to get 2.

$$\frac{\frac{68}{3}}{\frac{2}{3}}$$

Divide \frac{68}{3} by \frac{2}{3} by multiplying \frac{68}{3} by the reciprocal of \frac{2}{3}.

$$\frac{68}{3}\times \frac{3}{2}$$

Multiply \frac{68}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{68\times 3}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{68}{2}$$

Divide 68 by 2 to get 34.

$$34$$

Factor

$$2\times 17$$