Solve 1/2frac{2{9}}-1/1{2frac{2/9}+1/2frac{1{7}}}*frac{2}{5}

$$\frac { 1 } { 2 \frac { 2 } { 9 } } - \frac { 1 } { \frac { 1 } { 2 \frac { 2 } { 9 } } + \frac { 1 } { 2 \frac { 1 } { 7 } } } \times \frac { 2 } { 5 }$$

Evaluate

$$\frac{3}{220}\approx 0.013636364$$

Solution Steps

Divide 1 by \frac{2\times 9+2}{9} by multiplying 1 by the reciprocal of \frac{2\times 9+2}{9}.

$$\frac{9}{2\times 9+2}-\frac{1}{\frac{1}{\frac{2\times 9+2}{9}}+\frac{1}{\frac{2\times 7+1}{7}}}\times \frac{2}{5}$$

Multiply 2 and 9 to get 18.

$$\frac{9}{18+2}-\frac{1}{\frac{1}{\frac{2\times 9+2}{9}}+\frac{1}{\frac{2\times 7+1}{7}}}\times \frac{2}{5}$$

Add 18 and 2 to get 20.

$$\frac{9}{20}-\frac{1}{\frac{1}{\frac{2\times 9+2}{9}}+\frac{1}{\frac{2\times 7+1}{7}}}\times \frac{2}{5}$$

Divide 1 by \frac{2\times 9+2}{9} by multiplying 1 by the reciprocal of \frac{2\times 9+2}{9}.

$$\frac{9}{20}-\frac{1}{\frac{9}{2\times 9+2}+\frac{1}{\frac{2\times 7+1}{7}}}\times \frac{2}{5}$$

Multiply 2 and 9 to get 18.

$$\frac{9}{20}-\frac{1}{\frac{9}{18+2}+\frac{1}{\frac{2\times 7+1}{7}}}\times \frac{2}{5}$$

Add 18 and 2 to get 20.

$$\frac{9}{20}-\frac{1}{\frac{9}{20}+\frac{1}{\frac{2\times 7+1}{7}}}\times \frac{2}{5}$$

Divide 1 by \frac{2\times 7+1}{7} by multiplying 1 by the reciprocal of \frac{2\times 7+1}{7}.

$$\frac{9}{20}-\frac{1}{\frac{9}{20}+\frac{7}{2\times 7+1}}\times \frac{2}{5}$$

Multiply 2 and 7 to get 14.

$$\frac{9}{20}-\frac{1}{\frac{9}{20}+\frac{7}{14+1}}\times \frac{2}{5}$$

Add 14 and 1 to get 15.

$$\frac{9}{20}-\frac{1}{\frac{9}{20}+\frac{7}{15}}\times \frac{2}{5}$$

Least common multiple of 20 and 15 is 60. Convert \frac{9}{20} and \frac{7}{15} to fractions with denominator 60.

$$\frac{9}{20}-\frac{1}{\frac{27}{60}+\frac{28}{60}}\times \frac{2}{5}$$

Since \frac{27}{60} and \frac{28}{60} have the same denominator, add them by adding their numerators.

$$\frac{9}{20}-\frac{1}{\frac{27+28}{60}}\times \frac{2}{5}$$

Add 27 and 28 to get 55.

$$\frac{9}{20}-\frac{1}{\frac{55}{60}}\times \frac{2}{5}$$

Reduce the fraction \frac{55}{60} to lowest terms by extracting and canceling out 5.

$$\frac{9}{20}-\frac{1}{\frac{11}{12}}\times \frac{2}{5}$$

Divide 1 by \frac{11}{12} by multiplying 1 by the reciprocal of \frac{11}{12}.

$$\frac{9}{20}-1\times \frac{12}{11}\times \frac{2}{5}$$

Multiply 1 and \frac{12}{11} to get \frac{12}{11}.

$$\frac{9}{20}-\frac{12}{11}\times \frac{2}{5}$$

Multiply \frac{12}{11} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{20}-\frac{12\times 2}{11\times 5}$$

Do the multiplications in the fraction \frac{12\times 2}{11\times 5}.

$$\frac{9}{20}-\frac{24}{55}$$

Least common multiple of 20 and 55 is 220. Convert \frac{9}{20} and \frac{24}{55} to fractions with denominator 220.

$$\frac{99}{220}-\frac{96}{220}$$

Since \frac{99}{220} and \frac{96}{220} have the same denominator, subtract them by subtracting their numerators.

$$\frac{99-96}{220}$$

Subtract 96 from 99 to get 3.

$$\frac{3}{220}$$

Factor

$$\frac{3}{2 ^ {2} \cdot 5 \cdot 11} = 0.013636363636363636$$