Solve 8/2+3/8/frac{10{8}-5/6}-1

$$\frac { \frac { 8 } { 2 } + \frac { 3 } { 8 } } { \frac { 10 } { 8 } - \frac { 5 } { 6 } } - 1$$

Evaluate

$$\frac{19}{2}=9.5$$

Solution Steps

Divide 8 by 2 to get 4.

$$\frac{4+\frac{3}{8}}{\frac{10}{8}-\frac{5}{6}}-1$$

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

$$\frac{\frac{32}{8}+\frac{3}{8}}{\frac{10}{8}-\frac{5}{6}}-1$$

Since \frac{32}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{32+3}{8}}{\frac{10}{8}-\frac{5}{6}}-1$$

Add 32 and 3 to get 35.

$$\frac{\frac{35}{8}}{\frac{10}{8}-\frac{5}{6}}-1$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{35}{8}}{\frac{5}{4}-\frac{5}{6}}-1$$

Least common multiple of 4 and 6 is 12. Convert \frac{5}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{\frac{35}{8}}{\frac{15}{12}-\frac{10}{12}}-1$$

Since \frac{15}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35}{8}}{\frac{15-10}{12}}-1$$

Subtract 10 from 15 to get 5.

$$\frac{\frac{35}{8}}{\frac{5}{12}}-1$$

Divide \frac{35}{8} by \frac{5}{12} by multiplying \frac{35}{8} by the reciprocal of \frac{5}{12}.

$$\frac{35}{8}\times \frac{12}{5}-1$$

Multiply \frac{35}{8} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 12}{8\times 5}-1$$

Do the multiplications in the fraction \frac{35\times 12}{8\times 5}.

$$\frac{420}{40}-1$$

Reduce the fraction \frac{420}{40} to lowest terms by extracting and canceling out 20.

$$\frac{21}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{21}{2}-\frac{2}{2}$$

Since \frac{21}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21-2}{2}$$

Subtract 2 from 21 to get 19.

$$\frac{19}{2}$$

Factor

$$\frac{19}{2} = 9\frac{1}{2} = 9.5$$