Solve 31/36*1/9+31/36*8/9*frac{31}{36}*frac{1}{9}+frac{31}{36}*frac{8}{9}*frac{31}{36}*frac{8}{9}*frac{31}{36}*frac{1}{9}

$$\frac { 31 } { 36 } \times \frac { 1 } { 9 } + \frac { 31 } { 36 } \times \frac { 8 } { 9 } \times \frac { 31 } { 36 } \times \frac { 1 } { 9 } + \frac { 31 } { 36 } \times \frac { 8 } { 9 } \times \frac { 31 } { 36 } \times \frac { 8 } { 9 } \times \frac { 31 } { 36 } \times \frac { 1 } { 9 }$$

Evaluate

$$\frac{478237}{2125764}\approx 0.224971822$$

Solution Steps

Multiply \frac{31}{36} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31\times 1}{36\times 9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{31\times 1}{36\times 9}.

$$\frac{31}{324}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Multiply \frac{31}{36} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31}{324}+\frac{31\times 8}{36\times 9}\times \frac{31}{36}\times \frac{1}{9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{31\times 8}{36\times 9}.

$$\frac{31}{324}+\frac{248}{324}\times \frac{31}{36}\times \frac{1}{9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Reduce the fraction \frac{248}{324} to lowest terms by extracting and canceling out 4.

$$\frac{31}{324}+\frac{62}{81}\times \frac{31}{36}\times \frac{1}{9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Multiply \frac{62}{81} times \frac{31}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31}{324}+\frac{62\times 31}{81\times 36}\times \frac{1}{9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{62\times 31}{81\times 36}.

$$\frac{31}{324}+\frac{1922}{2916}\times \frac{1}{9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Reduce the fraction \frac{1922}{2916} to lowest terms by extracting and canceling out 2.

$$\frac{31}{324}+\frac{961}{1458}\times \frac{1}{9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Multiply \frac{961}{1458} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{31}{324}+\frac{961\times 1}{1458\times 9}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{961\times 1}{1458\times 9}.

$$\frac{31}{324}+\frac{961}{13122}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Least common multiple of 324 and 13122 is 26244. Convert \frac{31}{324} and \frac{961}{13122} to fractions with denominator 26244.

$$\frac{2511}{26244}+\frac{1922}{26244}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Since \frac{2511}{26244} and \frac{1922}{26244} have the same denominator, add them by adding their numerators.

$$\frac{2511+1922}{26244}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Add 2511 and 1922 to get 4433.

$$\frac{4433}{26244}+\frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Multiply \frac{31}{36} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4433}{26244}+\frac{31\times 8}{36\times 9}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{31\times 8}{36\times 9}.

$$\frac{4433}{26244}+\frac{248}{324}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Reduce the fraction \frac{248}{324} to lowest terms by extracting and canceling out 4.

$$\frac{4433}{26244}+\frac{62}{81}\times \frac{31}{36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Multiply \frac{62}{81} times \frac{31}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4433}{26244}+\frac{62\times 31}{81\times 36}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{62\times 31}{81\times 36}.

$$\frac{4433}{26244}+\frac{1922}{2916}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Reduce the fraction \frac{1922}{2916} to lowest terms by extracting and canceling out 2.

$$\frac{4433}{26244}+\frac{961}{1458}\times \frac{8}{9}\times \frac{31}{36}\times \frac{1}{9}$$

Multiply \frac{961}{1458} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4433}{26244}+\frac{961\times 8}{1458\times 9}\times \frac{31}{36}\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{961\times 8}{1458\times 9}.

$$\frac{4433}{26244}+\frac{7688}{13122}\times \frac{31}{36}\times \frac{1}{9}$$

Reduce the fraction \frac{7688}{13122} to lowest terms by extracting and canceling out 2.

$$\frac{4433}{26244}+\frac{3844}{6561}\times \frac{31}{36}\times \frac{1}{9}$$

Multiply \frac{3844}{6561} times \frac{31}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4433}{26244}+\frac{3844\times 31}{6561\times 36}\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{3844\times 31}{6561\times 36}.

$$\frac{4433}{26244}+\frac{119164}{236196}\times \frac{1}{9}$$

Reduce the fraction \frac{119164}{236196} to lowest terms by extracting and canceling out 4.

$$\frac{4433}{26244}+\frac{29791}{59049}\times \frac{1}{9}$$

Multiply \frac{29791}{59049} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4433}{26244}+\frac{29791\times 1}{59049\times 9}$$

Do the multiplications in the fraction \frac{29791\times 1}{59049\times 9}.

$$\frac{4433}{26244}+\frac{29791}{531441}$$

Least common multiple of 26244 and 531441 is 2125764. Convert \frac{4433}{26244} and \frac{29791}{531441} to fractions with denominator 2125764.

$$\frac{359073}{2125764}+\frac{119164}{2125764}$$

Since \frac{359073}{2125764} and \frac{119164}{2125764} have the same denominator, add them by adding their numerators.

$$\frac{359073+119164}{2125764}$$

Add 359073 and 119164 to get 478237.

$$\frac{478237}{2125764}$$

Factor

$$\frac{31 \cdot 15427}{2 ^ {2} \cdot 3 ^ {12}} = 0.2249718218955632$$