Solve left(5/8-0.2right)left(1/3+1/2right)

$$\left( \frac{ 5 }{ 8 } -0.2 \right) \left( \frac{ 1 }{ 3 } + \frac{ 1 }{ 2 } \right)$$

Evaluate

$$\frac{17}{48}\approx 0.354166667$$

Solution Steps

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 8 and 5 is 40. Convert \frac{5}{8} and \frac{1}{5} to fractions with denominator 40.

$$\left(\frac{25}{40}-\frac{8}{40}\right)\left(\frac{1}{3}+\frac{1}{2}\right)$$

Since \frac{25}{40} and \frac{8}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-8}{40}\left(\frac{1}{3}+\frac{1}{2}\right)$$

Subtract 8 from 25 to get 17.

$$\frac{17}{40}\left(\frac{1}{3}+\frac{1}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{17}{40}\left(\frac{2}{6}+\frac{3}{6}\right)$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{17}{40}\times \frac{2+3}{6}$$

Add 2 and 3 to get 5.

$$\frac{17}{40}\times \frac{5}{6}$$

Multiply \frac{17}{40} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 5}{40\times 6}$$

Do the multiplications in the fraction \frac{17\times 5}{40\times 6}.

$$\frac{85}{240}$$

Reduce the fraction \frac{85}{240} to lowest terms by extracting and canceling out 5.

$$\frac{17}{48}$$

Factor

$$\frac{17}{3 \cdot 2 ^ {4}} = 0.3541666666666667$$