Solve 8/3+1/2:(2-(1/3+5/6))

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

Evaluate

$$\frac{49}{15}\approx 3.266666667$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

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

Since \frac{2}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

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

Add 2 and 5 to get 7.

$$\frac{8}{3}+\frac{\frac{1}{2}}{2-\frac{7}{6}}$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{8}{3}+\frac{\frac{1}{2}}{\frac{12}{6}-\frac{7}{6}}$$

Since \frac{12}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}+\frac{\frac{1}{2}}{\frac{12-7}{6}}$$

Subtract 7 from 12 to get 5.

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

Divide \frac{1}{2} by \frac{5}{6} by multiplying \frac{1}{2} by the reciprocal of \frac{5}{6}.

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

Multiply \frac{1}{2} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 6}{2\times 5}.

$$\frac{8}{3}+\frac{6}{10}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}+\frac{3}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{8}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{40}{15}+\frac{9}{15}$$

Since \frac{40}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{40+9}{15}$$

Add 40 and 9 to get 49.

$$\frac{49}{15}$$

Factor

$$\frac{7 ^ {2}}{3 \cdot 5} = 3\frac{4}{15} = 3.2666666666666666$$