Solve 1div(2/3+4/21+8/15*7+16/31*15+frac{32}{63*31})*frac{4}{21}

$$1 \div ( \frac{ 2 }{ 3 } + \frac{ 4 }{ 21 } + \frac{ 8 }{ 15 \times 7 } + \frac{ 16 }{ 31 \times 15 } + \frac{ 32 }{ 63 \times 31 } ) \times \frac{ 4 }{ 21 }$$

Evaluate

$$\frac{6}{31}\approx 0.193548387$$

Solution Steps

Least common multiple of 3 and 21 is 21. Convert \frac{2}{3} and \frac{4}{21} to fractions with denominator 21.

$$\frac{1}{\frac{14}{21}+\frac{4}{21}+\frac{8}{15\times 7}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Since \frac{14}{21} and \frac{4}{21} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{14+4}{21}+\frac{8}{15\times 7}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Add 14 and 4 to get 18.

$$\frac{1}{\frac{18}{21}+\frac{8}{15\times 7}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Reduce the fraction \frac{18}{21} to lowest terms by extracting and canceling out 3.

$$\frac{1}{\frac{6}{7}+\frac{8}{15\times 7}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Multiply 15 and 7 to get 105.

$$\frac{1}{\frac{6}{7}+\frac{8}{105}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Least common multiple of 7 and 105 is 105. Convert \frac{6}{7} and \frac{8}{105} to fractions with denominator 105.

$$\frac{1}{\frac{90}{105}+\frac{8}{105}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Since \frac{90}{105} and \frac{8}{105} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{90+8}{105}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Add 90 and 8 to get 98.

$$\frac{1}{\frac{98}{105}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Reduce the fraction \frac{98}{105} to lowest terms by extracting and canceling out 7.

$$\frac{1}{\frac{14}{15}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Multiply 31 and 15 to get 465.

$$\frac{1}{\frac{14}{15}+\frac{16}{465}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Least common multiple of 15 and 465 is 465. Convert \frac{14}{15} and \frac{16}{465} to fractions with denominator 465.

$$\frac{1}{\frac{434}{465}+\frac{16}{465}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Since \frac{434}{465} and \frac{16}{465} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{434+16}{465}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Add 434 and 16 to get 450.

$$\frac{1}{\frac{450}{465}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Reduce the fraction \frac{450}{465} to lowest terms by extracting and canceling out 15.

$$\frac{1}{\frac{30}{31}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Multiply 63 and 31 to get 1953.

$$\frac{1}{\frac{30}{31}+\frac{32}{1953}}\times \frac{4}{21}$$

Least common multiple of 31 and 1953 is 1953. Convert \frac{30}{31} and \frac{32}{1953} to fractions with denominator 1953.

$$\frac{1}{\frac{1890}{1953}+\frac{32}{1953}}\times \frac{4}{21}$$

Since \frac{1890}{1953} and \frac{32}{1953} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{1890+32}{1953}}\times \frac{4}{21}$$

Add 1890 and 32 to get 1922.

$$\frac{1}{\frac{1922}{1953}}\times \frac{4}{21}$$

Reduce the fraction \frac{1922}{1953} to lowest terms by extracting and canceling out 31.

$$\frac{1}{\frac{62}{63}}\times \frac{4}{21}$$

Divide 1 by \frac{62}{63} by multiplying 1 by the reciprocal of \frac{62}{63}.

$$1\times \frac{63}{62}\times \frac{4}{21}$$

Multiply 1 and \frac{63}{62} to get \frac{63}{62}.

$$\frac{63}{62}\times \frac{4}{21}$$

Multiply \frac{63}{62} times \frac{4}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{63\times 4}{62\times 21}$$

Do the multiplications in the fraction \frac{63\times 4}{62\times 21}.

$$\frac{252}{1302}$$

Reduce the fraction \frac{252}{1302} to lowest terms by extracting and canceling out 42.

$$\frac{6}{31}$$

Factor

$$\frac{2 \cdot 3}{31} = 0.1935483870967742$$