Solve 51/6-21/32+7/64-1/18

$$5 \frac { 1 } { 6 } - 2 \frac { 1 } { 32 } + \frac { 7 } { 64 } - \frac { 1 } { 18 }$$

Evaluate

$$\frac{1837}{576}\approx 3.189236111$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\frac{30+1}{6}-\frac{2\times 32+1}{32}+\frac{7}{64}-\frac{1}{18}$$

Add 30 and 1 to get 31.

$$\frac{31}{6}-\frac{2\times 32+1}{32}+\frac{7}{64}-\frac{1}{18}$$

Multiply 2 and 32 to get 64.

$$\frac{31}{6}-\frac{64+1}{32}+\frac{7}{64}-\frac{1}{18}$$

Add 64 and 1 to get 65.

$$\frac{31}{6}-\frac{65}{32}+\frac{7}{64}-\frac{1}{18}$$

Least common multiple of 6 and 32 is 96. Convert \frac{31}{6} and \frac{65}{32} to fractions with denominator 96.

$$\frac{496}{96}-\frac{195}{96}+\frac{7}{64}-\frac{1}{18}$$

Since \frac{496}{96} and \frac{195}{96} have the same denominator, subtract them by subtracting their numerators.

$$\frac{496-195}{96}+\frac{7}{64}-\frac{1}{18}$$

Subtract 195 from 496 to get 301.

$$\frac{301}{96}+\frac{7}{64}-\frac{1}{18}$$

Least common multiple of 96 and 64 is 192. Convert \frac{301}{96} and \frac{7}{64} to fractions with denominator 192.

$$\frac{602}{192}+\frac{21}{192}-\frac{1}{18}$$

Since \frac{602}{192} and \frac{21}{192} have the same denominator, add them by adding their numerators.

$$\frac{602+21}{192}-\frac{1}{18}$$

Add 602 and 21 to get 623.

$$\frac{623}{192}-\frac{1}{18}$$

Least common multiple of 192 and 18 is 576. Convert \frac{623}{192} and \frac{1}{18} to fractions with denominator 576.

$$\frac{1869}{576}-\frac{32}{576}$$

Since \frac{1869}{576} and \frac{32}{576} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1869-32}{576}$$

Subtract 32 from 1869 to get 1837.

$$\frac{1837}{576}$$

Factor

$$\frac{11 \cdot 167}{2 ^ {6} \cdot 3 ^ {2}} = 3\frac{109}{576} = 3.189236111111111$$