Solve 5/6*(1+1/3+1/12+1/54+frac{5}{216})

$$\frac { 5 } { 6 } \times ( 1 + \frac { 1 } { 3 } + \frac { 1 } { 12 } + \frac { 1 } { 54 } + \frac { 5 } { 216 } )$$

Evaluate

$$\frac{175}{144}\approx 1.215277778$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{5}{6}\left(\frac{3}{3}+\frac{1}{3}+\frac{1}{12}+\frac{1}{54}+\frac{5}{216}\right)$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}\left(\frac{3+1}{3}+\frac{1}{12}+\frac{1}{54}+\frac{5}{216}\right)$$

Add 3 and 1 to get 4.

$$\frac{5}{6}\left(\frac{4}{3}+\frac{1}{12}+\frac{1}{54}+\frac{5}{216}\right)$$

Least common multiple of 3 and 12 is 12. Convert \frac{4}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{5}{6}\left(\frac{16}{12}+\frac{1}{12}+\frac{1}{54}+\frac{5}{216}\right)$$

Since \frac{16}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}\left(\frac{16+1}{12}+\frac{1}{54}+\frac{5}{216}\right)$$

Add 16 and 1 to get 17.

$$\frac{5}{6}\left(\frac{17}{12}+\frac{1}{54}+\frac{5}{216}\right)$$

Least common multiple of 12 and 54 is 108. Convert \frac{17}{12} and \frac{1}{54} to fractions with denominator 108.

$$\frac{5}{6}\left(\frac{153}{108}+\frac{2}{108}+\frac{5}{216}\right)$$

Since \frac{153}{108} and \frac{2}{108} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}\left(\frac{153+2}{108}+\frac{5}{216}\right)$$

Add 153 and 2 to get 155.

$$\frac{5}{6}\left(\frac{155}{108}+\frac{5}{216}\right)$$

Least common multiple of 108 and 216 is 216. Convert \frac{155}{108} and \frac{5}{216} to fractions with denominator 216.

$$\frac{5}{6}\left(\frac{310}{216}+\frac{5}{216}\right)$$

Since \frac{310}{216} and \frac{5}{216} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}\times \frac{310+5}{216}$$

Add 310 and 5 to get 315.

$$\frac{5}{6}\times \frac{315}{216}$$

Reduce the fraction \frac{315}{216} to lowest terms by extracting and canceling out 9.

$$\frac{5}{6}\times \frac{35}{24}$$

Multiply \frac{5}{6} times \frac{35}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 35}{6\times 24}$$

Do the multiplications in the fraction \frac{5\times 35}{6\times 24}.

$$\frac{175}{144}$$

Factor

$$\frac{5 ^ {2} \cdot 7}{2 ^ {4} \cdot 3 ^ {2}} = 1\frac{31}{144} = 1.2152777777777777$$