Solve 1/64+1/72+1/81+9/512=

$$\frac{ 1 }{ 64 } + \frac{ 1 }{ 72 } + \frac{ 1 }{ 81 } + \frac{ 9 }{ 512 } =$$

Evaluate

$$\frac{2465}{41472}\approx 0.059437693$$

Solution Steps

Least common multiple of 64 and 72 is 576. Convert \frac{1}{64} and \frac{1}{72} to fractions with denominator 576.

$$\frac{9}{576}+\frac{8}{576}+\frac{1}{81}+\frac{9}{512}$$

Since \frac{9}{576} and \frac{8}{576} have the same denominator, add them by adding their numerators.

$$\frac{9+8}{576}+\frac{1}{81}+\frac{9}{512}$$

Add 9 and 8 to get 17.

$$\frac{17}{576}+\frac{1}{81}+\frac{9}{512}$$

Least common multiple of 576 and 81 is 5184. Convert \frac{17}{576} and \frac{1}{81} to fractions with denominator 5184.

$$\frac{153}{5184}+\frac{64}{5184}+\frac{9}{512}$$

Since \frac{153}{5184} and \frac{64}{5184} have the same denominator, add them by adding their numerators.

$$\frac{153+64}{5184}+\frac{9}{512}$$

Add 153 and 64 to get 217.

$$\frac{217}{5184}+\frac{9}{512}$$

Least common multiple of 5184 and 512 is 41472. Convert \frac{217}{5184} and \frac{9}{512} to fractions with denominator 41472.

$$\frac{1736}{41472}+\frac{729}{41472}$$

Since \frac{1736}{41472} and \frac{729}{41472} have the same denominator, add them by adding their numerators.

$$\frac{1736+729}{41472}$$

Add 1736 and 729 to get 2465.

$$\frac{2465}{41472}$$

Factor

$$\frac{5 \cdot 17 \cdot 29}{2 ^ {9} \cdot 3 ^ {4}} = 0.059437692901234566$$