Solve 1/8+4-(4/3*2/6-1/4)+frac{8}{5}:frac{1}{2}

$$\frac { 1 } { 8 } + 4 - ( \frac { 4 } { 3 } \cdot \frac { 2 } { 6 } - \frac { 1 } { 4 } ) + \frac { 8 } { 5 } : \frac { 1 } { 2 }$$

Evaluate

$$\frac{2567}{360}\approx 7.130555556$$

Solution Steps

Convert 4 to fraction \frac{32}{8}.

$$\frac{1}{8}+\frac{32}{8}-\left(\frac{4}{3}\times \frac{2}{6}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Since \frac{1}{8} and \frac{32}{8} have the same denominator, add them by adding their numerators.

$$\frac{1+32}{8}-\left(\frac{4}{3}\times \frac{2}{6}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Add 1 and 32 to get 33.

$$\frac{33}{8}-\left(\frac{4}{3}\times \frac{2}{6}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{33}{8}-\left(\frac{4}{3}\times \frac{1}{3}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Multiply \frac{4}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33}{8}-\left(\frac{4\times 1}{3\times 3}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Do the multiplications in the fraction \frac{4\times 1}{3\times 3}.

$$\frac{33}{8}-\left(\frac{4}{9}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Least common multiple of 9 and 4 is 36. Convert \frac{4}{9} and \frac{1}{4} to fractions with denominator 36.

$$\frac{33}{8}-\left(\frac{16}{36}-\frac{9}{36}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Since \frac{16}{36} and \frac{9}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33}{8}-\frac{16-9}{36}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Subtract 9 from 16 to get 7.

$$\frac{33}{8}-\frac{7}{36}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Least common multiple of 8 and 36 is 72. Convert \frac{33}{8} and \frac{7}{36} to fractions with denominator 72.

$$\frac{297}{72}-\frac{14}{72}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Since \frac{297}{72} and \frac{14}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{297-14}{72}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Subtract 14 from 297 to get 283.

$$\frac{283}{72}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Divide \frac{8}{5} by \frac{1}{2} by multiplying \frac{8}{5} by the reciprocal of \frac{1}{2}.

$$\frac{283}{72}+\frac{8}{5}\times 2$$

Express \frac{8}{5}\times 2 as a single fraction.

$$\frac{283}{72}+\frac{8\times 2}{5}$$

Multiply 8 and 2 to get 16.

$$\frac{283}{72}+\frac{16}{5}$$

Least common multiple of 72 and 5 is 360. Convert \frac{283}{72} and \frac{16}{5} to fractions with denominator 360.

$$\frac{1415}{360}+\frac{1152}{360}$$

Since \frac{1415}{360} and \frac{1152}{360} have the same denominator, add them by adding their numerators.

$$\frac{1415+1152}{360}$$

Add 1415 and 1152 to get 2567.

$$\frac{2567}{360}$$

Factor

$$\frac{17 \cdot 151}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 7\frac{47}{360} = 7.1305555555555555$$