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

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

Evaluate

$$\frac{247}{240}\approx 1.029166667$$

Solution Steps

Anything divided by one gives itself.

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

Convert -2 to fraction -\frac{6}{3}.

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

Since -\frac{6}{3} and \frac{8}{3} have the same denominator, add them by adding their numerators.

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

Add -6 and 8 to get 2.

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

Multiply \frac{1}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 2}{5\times 3}.

$$\frac{2}{15}+\frac{1}{6}\left(\frac{3}{8}+\frac{5}{1}\right)$$

Anything divided by one gives itself.

$$\frac{2}{15}+\frac{1}{6}\left(\frac{3}{8}+5\right)$$

Convert 5 to fraction \frac{40}{8}.

$$\frac{2}{15}+\frac{1}{6}\left(\frac{3}{8}+\frac{40}{8}\right)$$

Since \frac{3}{8} and \frac{40}{8} have the same denominator, add them by adding their numerators.

$$\frac{2}{15}+\frac{1}{6}\times \frac{3+40}{8}$$

Add 3 and 40 to get 43.

$$\frac{2}{15}+\frac{1}{6}\times \frac{43}{8}$$

Multiply \frac{1}{6} times \frac{43}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{15}+\frac{1\times 43}{6\times 8}$$

Do the multiplications in the fraction \frac{1\times 43}{6\times 8}.

$$\frac{2}{15}+\frac{43}{48}$$

Least common multiple of 15 and 48 is 240. Convert \frac{2}{15} and \frac{43}{48} to fractions with denominator 240.

$$\frac{32}{240}+\frac{215}{240}$$

Since \frac{32}{240} and \frac{215}{240} have the same denominator, add them by adding their numerators.

$$\frac{32+215}{240}$$

Add 32 and 215 to get 247.

$$\frac{247}{240}$$

Factor

$$\frac{13 \cdot 19}{2 ^ {4} \cdot 3 \cdot 5} = 1\frac{7}{240} = 1.0291666666666666$$