Solve 6/7*2/3div9/14/1frac{1{3}*(4frac{1}{2}-1frac{3}{4})}

$$\frac { \frac { 6 } { 7 } \times \frac { 2 } { 3 } \div \frac { 9 } { 14 } } { 1 \frac { 1 } { 3 } \times ( 4 \frac { 1 } { 2 } - 1 \frac { 3 } { 4 } ) }$$

Evaluate

$$\frac{8}{33}\approx 0.242424242$$

Solution Steps

Multiply \frac{6}{7} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{6\times 2}{7\times 3}}{\frac{9}{14}}}{\frac{1\times 3+1}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Do the multiplications in the fraction \frac{6\times 2}{7\times 3}.

$$\frac{\frac{\frac{12}{21}}{\frac{9}{14}}}{\frac{1\times 3+1}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Reduce the fraction \frac{12}{21} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{\frac{4}{7}}{\frac{9}{14}}}{\frac{1\times 3+1}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Divide \frac{4}{7} by \frac{9}{14} by multiplying \frac{4}{7} by the reciprocal of \frac{9}{14}.

$$\frac{\frac{4}{7}\times \frac{14}{9}}{\frac{1\times 3+1}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Multiply \frac{4}{7} times \frac{14}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 14}{7\times 9}}{\frac{1\times 3+1}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Do the multiplications in the fraction \frac{4\times 14}{7\times 9}.

$$\frac{\frac{56}{63}}{\frac{1\times 3+1}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Reduce the fraction \frac{56}{63} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{8}{9}}{\frac{1\times 3+1}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{8}{9}}{\frac{3+1}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Add 3 and 1 to get 4.

$$\frac{\frac{8}{9}}{\frac{4}{3}\left(\frac{4\times 2+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{8}{9}}{\frac{4}{3}\left(\frac{8+1}{2}-\frac{1\times 4+3}{4}\right)}$$

Add 8 and 1 to get 9.

$$\frac{\frac{8}{9}}{\frac{4}{3}\left(\frac{9}{2}-\frac{1\times 4+3}{4}\right)}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{8}{9}}{\frac{4}{3}\left(\frac{9}{2}-\frac{4+3}{4}\right)}$$

Add 4 and 3 to get 7.

$$\frac{\frac{8}{9}}{\frac{4}{3}\left(\frac{9}{2}-\frac{7}{4}\right)}$$

Least common multiple of 2 and 4 is 4. Convert \frac{9}{2} and \frac{7}{4} to fractions with denominator 4.

$$\frac{\frac{8}{9}}{\frac{4}{3}\left(\frac{18}{4}-\frac{7}{4}\right)}$$

Since \frac{18}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8}{9}}{\frac{4}{3}\times \frac{18-7}{4}}$$

Subtract 7 from 18 to get 11.

$$\frac{\frac{8}{9}}{\frac{4}{3}\times \frac{11}{4}}$$

Multiply \frac{4}{3} times \frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8}{9}}{\frac{4\times 11}{3\times 4}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{8}{9}}{\frac{11}{3}}$$

Divide \frac{8}{9} by \frac{11}{3} by multiplying \frac{8}{9} by the reciprocal of \frac{11}{3}.

$$\frac{8}{9}\times \frac{3}{11}$$

Multiply \frac{8}{9} times \frac{3}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 3}{9\times 11}$$

Do the multiplications in the fraction \frac{8\times 3}{9\times 11}.

$$\frac{24}{99}$$

Reduce the fraction \frac{24}{99} to lowest terms by extracting and canceling out 3.

$$\frac{8}{33}$$

Factor

$$\frac{2 ^ {3}}{3 \cdot 11} = 0.24242424242424243$$