Solve 2/3/-4-1/4-0.4/frac{1{3}}--2

$$\frac{ \frac{ \frac{ 2 }{ 3 } }{ -4 } - \frac{ 1 }{ 4 } -0.4 }{ \frac{ 1 }{ 3 } } --2$$

Evaluate

$$-0.45$$

Solution Steps

Express \frac{\frac{2}{3}}{-4} as a single fraction.

$$\frac{\frac{2}{3\left(-4\right)}-\frac{1}{4}-0.4}{\frac{1}{3}}-\left(-2\right)$$

Multiply 3 and -4 to get -12.

$$\frac{\frac{2}{-12}-\frac{1}{4}-0.4}{\frac{1}{3}}-\left(-2\right)$$

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

$$\frac{-\frac{1}{6}-\frac{1}{4}-0.4}{\frac{1}{3}}-\left(-2\right)$$

Least common multiple of 6 and 4 is 12. Convert -\frac{1}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{-\frac{2}{12}-\frac{3}{12}-0.4}{\frac{1}{3}}-\left(-2\right)$$

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

$$\frac{\frac{-2-3}{12}-0.4}{\frac{1}{3}}-\left(-2\right)$$

Subtract 3 from -2 to get -5.

$$\frac{-\frac{5}{12}-0.4}{\frac{1}{3}}-\left(-2\right)$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{5}{12}-\frac{2}{5}}{\frac{1}{3}}-\left(-2\right)$$

Least common multiple of 12 and 5 is 60. Convert -\frac{5}{12} and \frac{2}{5} to fractions with denominator 60.

$$\frac{-\frac{25}{60}-\frac{24}{60}}{\frac{1}{3}}-\left(-2\right)$$

Since -\frac{25}{60} and \frac{24}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-25-24}{60}}{\frac{1}{3}}-\left(-2\right)$$

Subtract 24 from -25 to get -49.

$$\frac{-\frac{49}{60}}{\frac{1}{3}}-\left(-2\right)$$

Divide -\frac{49}{60} by \frac{1}{3} by multiplying -\frac{49}{60} by the reciprocal of \frac{1}{3}.

$$-\frac{49}{60}\times 3-\left(-2\right)$$

Express -\frac{49}{60}\times 3 as a single fraction.

$$\frac{-49\times 3}{60}-\left(-2\right)$$

Multiply -49 and 3 to get -147.

$$\frac{-147}{60}-\left(-2\right)$$

Reduce the fraction \frac{-147}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{49}{20}-\left(-2\right)$$

The opposite of -2 is 2.

$$-\frac{49}{20}+2$$

Convert 2 to fraction \frac{40}{20}.

$$-\frac{49}{20}+\frac{40}{20}$$

Since -\frac{49}{20} and \frac{40}{20} have the same denominator, add them by adding their numerators.

$$\frac{-49+40}{20}$$

Add -49 and 40 to get -9.

$$-\frac{9}{20}$$

Factor

$$-0.45$$