Solve 0,625*(12/3+31/6)+1/6div13/5-frac{5}{8}

$$0,625 \times ( 1 \frac { 2 } { 3 } + 3 \frac { 1 } { 6 } ) + \frac { 1 } { 6 } \div 1 \frac { 3 } { 5 } - \frac { 5 } { 8 }$$

Evaluate

$$2,5$$

Solution Steps

Multiply 1 and 3 to get 3.

$$0,625\left(\frac{3+2}{3}+\frac{3\times 6+1}{6}\right)+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Add 3 and 2 to get 5.

$$0,625\left(\frac{5}{3}+\frac{3\times 6+1}{6}\right)+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Multiply 3 and 6 to get 18.

$$0,625\left(\frac{5}{3}+\frac{18+1}{6}\right)+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Add 18 and 1 to get 19.

$$0,625\left(\frac{5}{3}+\frac{19}{6}\right)+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Least common multiple of 3 and 6 is 6. Convert \frac{5}{3} and \frac{19}{6} to fractions with denominator 6.

$$0,625\left(\frac{10}{6}+\frac{19}{6}\right)+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Since \frac{10}{6} and \frac{19}{6} have the same denominator, add them by adding their numerators.

$$0,625\times \frac{10+19}{6}+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Add 10 and 19 to get 29.

$$0,625\times \frac{29}{6}+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Convert decimal number 0,625 to fraction \frac{625}{1000}. Reduce the fraction \frac{625}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{5}{8}\times \frac{29}{6}+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Multiply \frac{5}{8} times \frac{29}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 29}{8\times 6}+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Do the multiplications in the fraction \frac{5\times 29}{8\times 6}.

$$\frac{145}{48}+\frac{\frac{1}{6}}{\frac{1\times 5+3}{5}}-\frac{5}{8}$$

Divide \frac{1}{6} by \frac{1\times 5+3}{5} by multiplying \frac{1}{6} by the reciprocal of \frac{1\times 5+3}{5}.

$$\frac{145}{48}+\frac{5}{6\left(1\times 5+3\right)}-\frac{5}{8}$$

Multiply 1 and 5 to get 5.

$$\frac{145}{48}+\frac{5}{6\left(5+3\right)}-\frac{5}{8}$$

Add 5 and 3 to get 8.

$$\frac{145}{48}+\frac{5}{6\times 8}-\frac{5}{8}$$

Multiply 6 and 8 to get 48.

$$\frac{145}{48}+\frac{5}{48}-\frac{5}{8}$$

Since \frac{145}{48} and \frac{5}{48} have the same denominator, add them by adding their numerators.

$$\frac{145+5}{48}-\frac{5}{8}$$

Add 145 and 5 to get 150.

$$\frac{150}{48}-\frac{5}{8}$$

Reduce the fraction \frac{150}{48} to lowest terms by extracting and canceling out 6.

$$\frac{25}{8}-\frac{5}{8}$$

Since \frac{25}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-5}{8}$$

Subtract 5 from 25 to get 20.

$$\frac{20}{8}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$