Solve [(45/7+111/14)*22/3+(32/9-1frac{5}{6})div1frac{7}{13}]div2frac{3}{4}

$$[ ( 4 \frac { 5 } { 7 } + 1 \frac { 11 } { 14 } ) \times 2 \frac { 2 } { 3 } + ( 3 \frac { 2 } { 9 } - 1 \frac { 5 } { 6 } ) \div 1 \frac { 7 } { 13 } ] \div 2 \frac { 3 } { 4 }$$

Evaluate

$$\frac{1313}{198}\approx 6.631313131$$

Solution Steps

Multiply 4 and 7 to get 28.

$$\frac{\left(\frac{28+5}{7}+\frac{1\times 14+11}{14}\right)\times \frac{2\times 3+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Add 28 and 5 to get 33.

$$\frac{\left(\frac{33}{7}+\frac{1\times 14+11}{14}\right)\times \frac{2\times 3+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Multiply 1 and 14 to get 14.

$$\frac{\left(\frac{33}{7}+\frac{14+11}{14}\right)\times \frac{2\times 3+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Add 14 and 11 to get 25.

$$\frac{\left(\frac{33}{7}+\frac{25}{14}\right)\times \frac{2\times 3+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Least common multiple of 7 and 14 is 14. Convert \frac{33}{7} and \frac{25}{14} to fractions with denominator 14.

$$\frac{\left(\frac{66}{14}+\frac{25}{14}\right)\times \frac{2\times 3+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Since \frac{66}{14} and \frac{25}{14} have the same denominator, add them by adding their numerators.

$$\frac{\frac{66+25}{14}\times \frac{2\times 3+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Add 66 and 25 to get 91.

$$\frac{\frac{91}{14}\times \frac{2\times 3+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Reduce the fraction \frac{91}{14} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{13}{2}\times \frac{2\times 3+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{13}{2}\times \frac{6+2}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Add 6 and 2 to get 8.

$$\frac{\frac{13}{2}\times \frac{8}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Multiply \frac{13}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 8}{2\times 3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Do the multiplications in the fraction \frac{13\times 8}{2\times 3}.

$$\frac{\frac{104}{6}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Reduce the fraction \frac{104}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{52}{3}+\frac{\frac{3\times 9+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Multiply 3 and 9 to get 27.

$$\frac{\frac{52}{3}+\frac{\frac{27+2}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Add 27 and 2 to get 29.

$$\frac{\frac{52}{3}+\frac{\frac{29}{9}-\frac{1\times 6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Multiply 1 and 6 to get 6.

$$\frac{\frac{52}{3}+\frac{\frac{29}{9}-\frac{6+5}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Add 6 and 5 to get 11.

$$\frac{\frac{52}{3}+\frac{\frac{29}{9}-\frac{11}{6}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Least common multiple of 9 and 6 is 18. Convert \frac{29}{9} and \frac{11}{6} to fractions with denominator 18.

$$\frac{\frac{52}{3}+\frac{\frac{58}{18}-\frac{33}{18}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Since \frac{58}{18} and \frac{33}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{52}{3}+\frac{\frac{58-33}{18}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Subtract 33 from 58 to get 25.

$$\frac{\frac{52}{3}+\frac{\frac{25}{18}}{\frac{1\times 13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Multiply 1 and 13 to get 13.

$$\frac{\frac{52}{3}+\frac{\frac{25}{18}}{\frac{13+7}{13}}}{\frac{2\times 4+3}{4}}$$

Add 13 and 7 to get 20.

$$\frac{\frac{52}{3}+\frac{\frac{25}{18}}{\frac{20}{13}}}{\frac{2\times 4+3}{4}}$$

Divide \frac{25}{18} by \frac{20}{13} by multiplying \frac{25}{18} by the reciprocal of \frac{20}{13}.

$$\frac{\frac{52}{3}+\frac{25}{18}\times \frac{13}{20}}{\frac{2\times 4+3}{4}}$$

Multiply \frac{25}{18} times \frac{13}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{52}{3}+\frac{25\times 13}{18\times 20}}{\frac{2\times 4+3}{4}}$$

Do the multiplications in the fraction \frac{25\times 13}{18\times 20}.

$$\frac{\frac{52}{3}+\frac{325}{360}}{\frac{2\times 4+3}{4}}$$

Reduce the fraction \frac{325}{360} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{52}{3}+\frac{65}{72}}{\frac{2\times 4+3}{4}}$$

Least common multiple of 3 and 72 is 72. Convert \frac{52}{3} and \frac{65}{72} to fractions with denominator 72.

$$\frac{\frac{1248}{72}+\frac{65}{72}}{\frac{2\times 4+3}{4}}$$

Since \frac{1248}{72} and \frac{65}{72} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1248+65}{72}}{\frac{2\times 4+3}{4}}$$

Add 1248 and 65 to get 1313.

$$\frac{\frac{1313}{72}}{\frac{2\times 4+3}{4}}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{1313}{72}}{\frac{8+3}{4}}$$

Add 8 and 3 to get 11.

$$\frac{\frac{1313}{72}}{\frac{11}{4}}$$

Divide \frac{1313}{72} by \frac{11}{4} by multiplying \frac{1313}{72} by the reciprocal of \frac{11}{4}.

$$\frac{1313}{72}\times \frac{4}{11}$$

Multiply \frac{1313}{72} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1313\times 4}{72\times 11}$$

Do the multiplications in the fraction \frac{1313\times 4}{72\times 11}.

$$\frac{5252}{792}$$

Reduce the fraction \frac{5252}{792} to lowest terms by extracting and canceling out 4.

$$\frac{1313}{198}$$

Factor

$$\frac{13 \cdot 101}{2 \cdot 3 ^ {2} \cdot 11} = 6\frac{125}{198} = 6.6313131313131315$$