Solve 41/12*86/7*72/3/6frac{1{4}*1frac{2}{5}*5frac{3}{4}}:frac{3frac{4}{9}*7frac{1}{5}}{5frac{1}{7}*7}

$$\frac { 4 \frac { 1 } { 12 } \cdot 8 \frac { 6 } { 7 } \cdot 7 \frac { 2 } { 3 } } { 6 \frac { 1 } { 4 } \cdot 1 \frac { 2 } { 5 } \cdot 5 \frac { 3 } { 4 } } : \frac { 3 \frac { 4 } { 9 } \cdot 7 \frac { 1 } { 5 } } { 5 \frac { 1 } { 7 } \cdot 7 }$$

Evaluate

$$8$$

Solution Steps

Divide \frac{\frac{4\times 12+1}{12}\times \frac{8\times 7+6}{7}\times \frac{7\times 3+2}{3}}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}} by \frac{\frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}{\frac{5\times 7+1}{7}\times 7} by multiplying \frac{\frac{4\times 12+1}{12}\times \frac{8\times 7+6}{7}\times \frac{7\times 3+2}{3}}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}} by the reciprocal of \frac{\frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}{\frac{5\times 7+1}{7}\times 7}.

$$\frac{\frac{4\times 12+1}{12}\times \frac{8\times 7+6}{7}\times \frac{7\times 3+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 4 and 12 to get 48.

$$\frac{\frac{48+1}{12}\times \frac{8\times 7+6}{7}\times \frac{7\times 3+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Add 48 and 1 to get 49.

$$\frac{\frac{49}{12}\times \frac{8\times 7+6}{7}\times \frac{7\times 3+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 8 and 7 to get 56.

$$\frac{\frac{49}{12}\times \frac{56+6}{7}\times \frac{7\times 3+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Add 56 and 6 to get 62.

$$\frac{\frac{49}{12}\times \frac{62}{7}\times \frac{7\times 3+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply \frac{49}{12} times \frac{62}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{49\times 62}{12\times 7}\times \frac{7\times 3+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Do the multiplications in the fraction \frac{49\times 62}{12\times 7}.

$$\frac{\frac{3038}{84}\times \frac{7\times 3+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Reduce the fraction \frac{3038}{84} to lowest terms by extracting and canceling out 14.

$$\frac{\frac{217}{6}\times \frac{7\times 3+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 7 and 3 to get 21.

$$\frac{\frac{217}{6}\times \frac{21+2}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Add 21 and 2 to get 23.

$$\frac{\frac{217}{6}\times \frac{23}{3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply \frac{217}{6} times \frac{23}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{217\times 23}{6\times 3}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Do the multiplications in the fraction \frac{217\times 23}{6\times 3}.

$$\frac{\frac{4991}{18}\times \frac{5\times 7+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 5 and 7 to get 35.

$$\frac{\frac{4991}{18}\times \frac{35+1}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Add 35 and 1 to get 36.

$$\frac{\frac{4991}{18}\times \frac{36}{7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply \frac{4991}{18} times \frac{36}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4991\times 36}{18\times 7}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Do the multiplications in the fraction \frac{4991\times 36}{18\times 7}.

$$\frac{\frac{179676}{126}\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Divide 179676 by 126 to get 1426.

$$\frac{1426\times 7}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 1426 and 7 to get 9982.

$$\frac{9982}{\frac{6\times 4+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 6 and 4 to get 24.

$$\frac{9982}{\frac{24+1}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Add 24 and 1 to get 25.

$$\frac{9982}{\frac{25}{4}\times \frac{1\times 5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 1 and 5 to get 5.

$$\frac{9982}{\frac{25}{4}\times \frac{5+2}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Add 5 and 2 to get 7.

$$\frac{9982}{\frac{25}{4}\times \frac{7}{5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply \frac{25}{4} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9982}{\frac{25\times 7}{4\times 5}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Do the multiplications in the fraction \frac{25\times 7}{4\times 5}.

$$\frac{9982}{\frac{175}{20}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Reduce the fraction \frac{175}{20} to lowest terms by extracting and canceling out 5.

$$\frac{9982}{\frac{35}{4}\times \frac{5\times 4+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 5 and 4 to get 20.

$$\frac{9982}{\frac{35}{4}\times \frac{20+3}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Add 20 and 3 to get 23.

$$\frac{9982}{\frac{35}{4}\times \frac{23}{4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply \frac{35}{4} times \frac{23}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9982}{\frac{35\times 23}{4\times 4}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Do the multiplications in the fraction \frac{35\times 23}{4\times 4}.

$$\frac{9982}{\frac{805}{16}\times \frac{3\times 9+4}{9}\times \frac{7\times 5+1}{5}}$$

Multiply 3 and 9 to get 27.

$$\frac{9982}{\frac{805}{16}\times \frac{27+4}{9}\times \frac{7\times 5+1}{5}}$$

Add 27 and 4 to get 31.

$$\frac{9982}{\frac{805}{16}\times \frac{31}{9}\times \frac{7\times 5+1}{5}}$$

Multiply \frac{805}{16} times \frac{31}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9982}{\frac{805\times 31}{16\times 9}\times \frac{7\times 5+1}{5}}$$

Do the multiplications in the fraction \frac{805\times 31}{16\times 9}.

$$\frac{9982}{\frac{24955}{144}\times \frac{7\times 5+1}{5}}$$

Multiply 7 and 5 to get 35.

$$\frac{9982}{\frac{24955}{144}\times \frac{35+1}{5}}$$

Add 35 and 1 to get 36.

$$\frac{9982}{\frac{24955}{144}\times \frac{36}{5}}$$

Multiply \frac{24955}{144} times \frac{36}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9982}{\frac{24955\times 36}{144\times 5}}$$

Do the multiplications in the fraction \frac{24955\times 36}{144\times 5}.

$$\frac{9982}{\frac{898380}{720}}$$

Reduce the fraction \frac{898380}{720} to lowest terms by extracting and canceling out 180.

$$\frac{9982}{\frac{4991}{4}}$$

Divide 9982 by \frac{4991}{4} by multiplying 9982 by the reciprocal of \frac{4991}{4}.

$$9982\times \frac{4}{4991}$$

Express 9982\times \frac{4}{4991} as a single fraction.

$$\frac{9982\times 4}{4991}$$

Multiply 9982 and 4 to get 39928.

$$\frac{39928}{4991}$$

Divide 39928 by 4991 to get 8.

$$8$$

Factor

$$2^{3}$$