Solve 2/3-5/4+-10/35/2-frac{-16}{3}frac{-55}{32}

$$\frac{ 2 }{ 3 } \frac{ -5 }{ 4 } + \frac{ -10 }{ 3 } \frac{ 5 }{ 2 } - \frac{ -16 }{ 3 } \frac{ -55 }{ 32 }$$

Evaluate

$$-\frac{55}{3}\approx -18.333333333$$

Solution Steps

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$\frac{2}{3}\left(-\frac{5}{4}\right)+\frac{-10}{3}\times \frac{5}{2}-\frac{-16}{3}\times \frac{-55}{32}$$

Multiply \frac{2}{3} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-5\right)}{3\times 4}+\frac{-10}{3}\times \frac{5}{2}-\frac{-16}{3}\times \frac{-55}{32}$$

Do the multiplications in the fraction \frac{2\left(-5\right)}{3\times 4}.

$$\frac{-10}{12}+\frac{-10}{3}\times \frac{5}{2}-\frac{-16}{3}\times \frac{-55}{32}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{6}+\frac{-10}{3}\times \frac{5}{2}-\frac{-16}{3}\times \frac{-55}{32}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$-\frac{5}{6}-\frac{10}{3}\times \frac{5}{2}-\frac{-16}{3}\times \frac{-55}{32}$$

Multiply -\frac{10}{3} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{6}+\frac{-10\times 5}{3\times 2}-\frac{-16}{3}\times \frac{-55}{32}$$

Do the multiplications in the fraction \frac{-10\times 5}{3\times 2}.

$$-\frac{5}{6}+\frac{-50}{6}-\frac{-16}{3}\times \frac{-55}{32}$$

Reduce the fraction \frac{-50}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{6}-\frac{25}{3}-\frac{-16}{3}\times \frac{-55}{32}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{5}{6} and \frac{25}{3} to fractions with denominator 6.

$$-\frac{5}{6}-\frac{50}{6}-\frac{-16}{3}\times \frac{-55}{32}$$

Since -\frac{5}{6} and \frac{50}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-50}{6}-\frac{-16}{3}\times \frac{-55}{32}$$

Subtract 50 from -5 to get -55.

$$-\frac{55}{6}-\frac{-16}{3}\times \frac{-55}{32}$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$-\frac{55}{6}-\left(-\frac{16}{3}\times \frac{-55}{32}\right)$$

Fraction \frac{-55}{32} can be rewritten as -\frac{55}{32} by extracting the negative sign.

$$-\frac{55}{6}-\left(-\frac{16}{3}\left(-\frac{55}{32}\right)\right)$$

Multiply -\frac{16}{3} times -\frac{55}{32} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{55}{6}-\frac{-16\left(-55\right)}{3\times 32}$$

Do the multiplications in the fraction \frac{-16\left(-55\right)}{3\times 32}.

$$-\frac{55}{6}-\frac{880}{96}$$

Reduce the fraction \frac{880}{96} to lowest terms by extracting and canceling out 16.

$$-\frac{55}{6}-\frac{55}{6}$$

Since -\frac{55}{6} and \frac{55}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-55-55}{6}$$

Subtract 55 from -55 to get -110.

$$\frac{-110}{6}$$

Reduce the fraction \frac{-110}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{55}{3}$$

Factor

$$-\frac{55}{3} = -18\frac{1}{3} = -18.333333333333332$$