Solve 0.5-4/3-4/2.4frac{-4{3}+6}

$$\frac{ 0.5 \frac{ -4 }{ 3 } -4 }{ 2.4 \frac{ -4 }{ 3 } +6 }$$

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

Solution Steps

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{0.5\left(-\frac{4}{3}\right)-4}{2.4\times \frac{-4}{3}+6}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{2}\left(-\frac{4}{3}\right)-4}{2.4\times \frac{-4}{3}+6}$$

Multiply \frac{1}{2} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\left(-4\right)}{2\times 3}-4}{2.4\times \frac{-4}{3}+6}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 3}.

$$\frac{\frac{-4}{6}-4}{2.4\times \frac{-4}{3}+6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{2}{3}-4}{2.4\times \frac{-4}{3}+6}$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{-\frac{2}{3}-\frac{12}{3}}{2.4\times \frac{-4}{3}+6}$$

Since -\frac{2}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-2-12}{3}}{2.4\times \frac{-4}{3}+6}$$

Subtract 12 from -2 to get -14.

$$\frac{-\frac{14}{3}}{2.4\times \frac{-4}{3}+6}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{-\frac{14}{3}}{2.4\left(-\frac{4}{3}\right)+6}$$

Convert decimal number 2.4 to fraction \frac{24}{10}. Reduce the fraction \frac{24}{10} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{14}{3}}{\frac{12}{5}\left(-\frac{4}{3}\right)+6}$$

Multiply \frac{12}{5} times -\frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{14}{3}}{\frac{12\left(-4\right)}{5\times 3}+6}$$

Do the multiplications in the fraction \frac{12\left(-4\right)}{5\times 3}.

$$\frac{-\frac{14}{3}}{\frac{-48}{15}+6}$$

Reduce the fraction \frac{-48}{15} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{14}{3}}{-\frac{16}{5}+6}$$

Convert 6 to fraction \frac{30}{5}.

$$\frac{-\frac{14}{3}}{-\frac{16}{5}+\frac{30}{5}}$$

Since -\frac{16}{5} and \frac{30}{5} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{14}{3}}{\frac{-16+30}{5}}$$

Add -16 and 30 to get 14.

$$\frac{-\frac{14}{3}}{\frac{14}{5}}$$

Divide -\frac{14}{3} by \frac{14}{5} by multiplying -\frac{14}{3} by the reciprocal of \frac{14}{5}.

$$-\frac{14}{3}\times \frac{5}{14}$$

Multiply -\frac{14}{3} times \frac{5}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-14\times 5}{3\times 14}$$

Do the multiplications in the fraction \frac{-14\times 5}{3\times 14}.

$$\frac{-70}{42}$$

Reduce the fraction \frac{-70}{42} to lowest terms by extracting and canceling out 14.

$$-\frac{5}{3}$$

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$