Solve 14/5:21/4:13/8:31/2:2frac{1}{6}:4frac{3}{10}:2frac{3}{5}:4frac{5}{6}=

$$1 \frac { 4 } { 5 } : 2 \frac { 1 } { 4 } : 1 \frac { 3 } { 8 } : 3 \frac { 1 } { 2 } : 2 \frac { 1 } { 6 } : 4 \frac { 3 } { 10 } : 2 \frac { 3 } { 5 } : 4 \frac { 5 } { 6 } =$$

Evaluate

$$\frac{23040}{16227211}\approx 0.001419837$$

Solution Steps

Divide \frac{\frac{\frac{\frac{\frac{\frac{\frac{1\times 5+4}{5}}{\frac{2\times 4+1}{4}}}{\frac{1\times 8+3}{8}}}{\frac{3\times 2+1}{2}}}{\frac{2\times 6+1}{6}}}{\frac{4\times 10+3}{10}}}{\frac{2\times 5+3}{5}} by \frac{4\times 6+5}{6} by multiplying \frac{\frac{\frac{\frac{\frac{\frac{\frac{1\times 5+4}{5}}{\frac{2\times 4+1}{4}}}{\frac{1\times 8+3}{8}}}{\frac{3\times 2+1}{2}}}{\frac{2\times 6+1}{6}}}{\frac{4\times 10+3}{10}}}{\frac{2\times 5+3}{5}} by the reciprocal of \frac{4\times 6+5}{6}.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{1\times 5+4}{5}}{\frac{2\times 4+1}{4}}}{\frac{1\times 8+3}{8}}}{\frac{3\times 2+1}{2}}}{\frac{2\times 6+1}{6}}}{\frac{4\times 10+3}{10}}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Divide \frac{\frac{\frac{\frac{\frac{1\times 5+4}{5}}{\frac{2\times 4+1}{4}}}{\frac{1\times 8+3}{8}}}{\frac{3\times 2+1}{2}}}{\frac{2\times 6+1}{6}} by \frac{4\times 10+3}{10} by multiplying \frac{\frac{\frac{\frac{\frac{1\times 5+4}{5}}{\frac{2\times 4+1}{4}}}{\frac{1\times 8+3}{8}}}{\frac{3\times 2+1}{2}}}{\frac{2\times 6+1}{6}} by the reciprocal of \frac{4\times 10+3}{10}.

$$\frac{\frac{\frac{\frac{\frac{\frac{1\times 5+4}{5}}{\frac{2\times 4+1}{4}}}{\frac{1\times 8+3}{8}}}{\frac{3\times 2+1}{2}}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

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

$$\frac{\frac{\frac{\frac{\frac{1\times 5+4}{5}}{\frac{2\times 4+1}{4}}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Divide \frac{1\times 5+4}{5} by \frac{2\times 4+1}{4} by multiplying \frac{1\times 5+4}{5} by the reciprocal of \frac{2\times 4+1}{4}.

$$\frac{\frac{\frac{\frac{\left(1\times 5+4\right)\times 4}{5\left(2\times 4+1\right)}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{\frac{\frac{\left(5+4\right)\times 4}{5\left(2\times 4+1\right)}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Add 5 and 4 to get 9.

$$\frac{\frac{\frac{\frac{9\times 4}{5\left(2\times 4+1\right)}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 9 and 4 to get 36.

$$\frac{\frac{\frac{\frac{36}{5\left(2\times 4+1\right)}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{\frac{\frac{36}{5\left(8+1\right)}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Add 8 and 1 to get 9.

$$\frac{\frac{\frac{\frac{36}{5\times 9}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 5 and 9 to get 45.

$$\frac{\frac{\frac{\frac{36}{45}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Reduce the fraction \frac{36}{45} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{\frac{\frac{4}{5}\times 2}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Express \frac{4}{5}\times 2 as a single fraction.

$$\frac{\frac{\frac{\frac{4\times 2}{5}}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{\frac{\frac{8}{5}}{\frac{1\times 8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 1 and 8 to get 8.

$$\frac{\frac{\frac{\frac{8}{5}}{\frac{8+3}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Add 8 and 3 to get 11.

$$\frac{\frac{\frac{\frac{8}{5}}{\frac{11}{8}\left(3\times 2+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{\frac{\frac{8}{5}}{\frac{11}{8}\left(6+1\right)}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Add 6 and 1 to get 7.

$$\frac{\frac{\frac{\frac{8}{5}}{\frac{11}{8}\times 7}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Express \frac{11}{8}\times 7 as a single fraction.

$$\frac{\frac{\frac{\frac{8}{5}}{\frac{11\times 7}{8}}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 11 and 7 to get 77.

$$\frac{\frac{\frac{\frac{8}{5}}{\frac{77}{8}}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Divide \frac{8}{5} by \frac{77}{8} by multiplying \frac{8}{5} by the reciprocal of \frac{77}{8}.

$$\frac{\frac{\frac{8}{5}\times \frac{8}{77}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply \frac{8}{5} times \frac{8}{77} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{8\times 8}{5\times 77}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Do the multiplications in the fraction \frac{8\times 8}{5\times 77}.

$$\frac{\frac{\frac{64}{385}\times 10}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Express \frac{64}{385}\times 10 as a single fraction.

$$\frac{\frac{\frac{64\times 10}{385}}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 64 and 10 to get 640.

$$\frac{\frac{\frac{640}{385}}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Reduce the fraction \frac{640}{385} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{\frac{128}{77}}{\frac{2\times 6+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 2 and 6 to get 12.

$$\frac{\frac{\frac{128}{77}}{\frac{12+1}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Add 12 and 1 to get 13.

$$\frac{\frac{\frac{128}{77}}{\frac{13}{6}\left(4\times 10+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 4 and 10 to get 40.

$$\frac{\frac{\frac{128}{77}}{\frac{13}{6}\left(40+3\right)}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Add 40 and 3 to get 43.

$$\frac{\frac{\frac{128}{77}}{\frac{13}{6}\times 43}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Express \frac{13}{6}\times 43 as a single fraction.

$$\frac{\frac{\frac{128}{77}}{\frac{13\times 43}{6}}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 13 and 43 to get 559.

$$\frac{\frac{\frac{128}{77}}{\frac{559}{6}}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Divide \frac{128}{77} by \frac{559}{6} by multiplying \frac{128}{77} by the reciprocal of \frac{559}{6}.

$$\frac{\frac{128}{77}\times \frac{6}{559}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply \frac{128}{77} times \frac{6}{559} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{128\times 6}{77\times 559}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Do the multiplications in the fraction \frac{128\times 6}{77\times 559}.

$$\frac{\frac{768}{43043}\times 6}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Express \frac{768}{43043}\times 6 as a single fraction.

$$\frac{\frac{768\times 6}{43043}}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 768 and 6 to get 4608.

$$\frac{\frac{4608}{43043}}{\frac{2\times 5+3}{5}\left(4\times 6+5\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{4608}{43043}}{\frac{10+3}{5}\left(4\times 6+5\right)}$$

Add 10 and 3 to get 13.

$$\frac{\frac{4608}{43043}}{\frac{13}{5}\left(4\times 6+5\right)}$$

Multiply 4 and 6 to get 24.

$$\frac{\frac{4608}{43043}}{\frac{13}{5}\left(24+5\right)}$$

Add 24 and 5 to get 29.

$$\frac{\frac{4608}{43043}}{\frac{13}{5}\times 29}$$

Express \frac{13}{5}\times 29 as a single fraction.

$$\frac{\frac{4608}{43043}}{\frac{13\times 29}{5}}$$

Multiply 13 and 29 to get 377.

$$\frac{\frac{4608}{43043}}{\frac{377}{5}}$$

Divide \frac{4608}{43043} by \frac{377}{5} by multiplying \frac{4608}{43043} by the reciprocal of \frac{377}{5}.

$$\frac{4608}{43043}\times \frac{5}{377}$$

Multiply \frac{4608}{43043} times \frac{5}{377} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4608\times 5}{43043\times 377}$$

Do the multiplications in the fraction \frac{4608\times 5}{43043\times 377}.

$$\frac{23040}{16227211}$$

Factor

$$\frac{2 ^ {9} \cdot 3 ^ {2} \cdot 5}{7 \cdot 11 \cdot 13 ^ {2} \cdot 29 \cdot 43} = 0.001419837333722967$$