Solve (-1/2-0.8+3/5)*(3+5/8+5

$$(- \frac{ 1 }{ 2 } -0.8+ \frac{ 3 }{ 5 } ) \times (3+ \frac{ 5 }{ 8+5 }$$

Evaluate

$$-\frac{154}{65}\approx -2.369230769$$

Solution Steps

Convert decimal number 0.8 to fraction \frac{8}{10}. Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\left(-\frac{1}{2}-\frac{4}{5}+\frac{3}{5}\right)\left(3+\frac{5}{8+5}\right)$$

Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{4}{5} to fractions with denominator 10.

$$\left(-\frac{5}{10}-\frac{8}{10}+\frac{3}{5}\right)\left(3+\frac{5}{8+5}\right)$$

Since -\frac{5}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-5-8}{10}+\frac{3}{5}\right)\left(3+\frac{5}{8+5}\right)$$

Subtract 8 from -5 to get -13.

$$\left(-\frac{13}{10}+\frac{3}{5}\right)\left(3+\frac{5}{8+5}\right)$$

Least common multiple of 10 and 5 is 10. Convert -\frac{13}{10} and \frac{3}{5} to fractions with denominator 10.

$$\left(-\frac{13}{10}+\frac{6}{10}\right)\left(3+\frac{5}{8+5}\right)$$

Since -\frac{13}{10} and \frac{6}{10} have the same denominator, add them by adding their numerators.

$$\frac{-13+6}{10}\left(3+\frac{5}{8+5}\right)$$

Add -13 and 6 to get -7.

$$-\frac{7}{10}\left(3+\frac{5}{8+5}\right)$$

Add 8 and 5 to get 13.

$$-\frac{7}{10}\left(3+\frac{5}{13}\right)$$

Convert 3 to fraction \frac{39}{13}.

$$-\frac{7}{10}\left(\frac{39}{13}+\frac{5}{13}\right)$$

Since \frac{39}{13} and \frac{5}{13} have the same denominator, add them by adding their numerators.

$$-\frac{7}{10}\times \frac{39+5}{13}$$

Add 39 and 5 to get 44.

$$-\frac{7}{10}\times \frac{44}{13}$$

Multiply -\frac{7}{10} times \frac{44}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-7\times 44}{10\times 13}$$

Do the multiplications in the fraction \frac{-7\times 44}{10\times 13}.

$$\frac{-308}{130}$$

Reduce the fraction \frac{-308}{130} to lowest terms by extracting and canceling out 2.

$$-\frac{154}{65}$$

Factor

$$-\frac{154}{65} = -2\frac{24}{65} = -2.3692307692307693$$