Solve -4+3/4-1/2*5+5/8(-2/15)-frac{3}{2}(-frac{1}{2}+frac{1}{2}(-4)

$$- 4 + \frac { 3 } { 4 } - \frac { 1 } { 2 } \times 5 + \frac { 5 } { 8 } ( - \frac { 2 } { 15 } ) - \frac { 3 } { 2 } ( - \frac { 1 } { 2 } + \frac { 1 } { 2 } ( - 4 )$$

Evaluate

$$-\frac{25}{12}\approx -2.083333333$$

Solution Steps

Convert -4 to fraction -\frac{16}{4}.

$$-\frac{16}{4}+\frac{3}{4}-\frac{1}{2}\times 5+\frac{5}{8}\left(-\frac{2}{15}\right)-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Since -\frac{16}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{-16+3}{4}-\frac{1}{2}\times 5+\frac{5}{8}\left(-\frac{2}{15}\right)-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Add -16 and 3 to get -13.

$$-\frac{13}{4}-\frac{1}{2}\times 5+\frac{5}{8}\left(-\frac{2}{15}\right)-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

$$-\frac{13}{4}-\frac{5}{2}+\frac{5}{8}\left(-\frac{2}{15}\right)-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Least common multiple of 4 and 2 is 4. Convert -\frac{13}{4} and \frac{5}{2} to fractions with denominator 4.

$$-\frac{13}{4}-\frac{10}{4}+\frac{5}{8}\left(-\frac{2}{15}\right)-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Since -\frac{13}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-13-10}{4}+\frac{5}{8}\left(-\frac{2}{15}\right)-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Subtract 10 from -13 to get -23.

$$-\frac{23}{4}+\frac{5}{8}\left(-\frac{2}{15}\right)-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Multiply \frac{5}{8} times -\frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{23}{4}+\frac{5\left(-2\right)}{8\times 15}-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Do the multiplications in the fraction \frac{5\left(-2\right)}{8\times 15}.

$$-\frac{23}{4}+\frac{-10}{120}-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Reduce the fraction \frac{-10}{120} to lowest terms by extracting and canceling out 10.

$$-\frac{23}{4}-\frac{1}{12}-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Least common multiple of 4 and 12 is 12. Convert -\frac{23}{4} and \frac{1}{12} to fractions with denominator 12.

$$-\frac{69}{12}-\frac{1}{12}-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Since -\frac{69}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-69-1}{12}-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Subtract 1 from -69 to get -70.

$$\frac{-70}{12}-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Reduce the fraction \frac{-70}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{35}{6}-\frac{3}{2}\left(-\frac{1}{2}+\frac{1}{2}\left(-4\right)\right)$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$-\frac{35}{6}-\frac{3}{2}\left(-\frac{1}{2}+\frac{-4}{2}\right)$$

Divide -4 by 2 to get -2.

$$-\frac{35}{6}-\frac{3}{2}\left(-\frac{1}{2}-2\right)$$

Convert 2 to fraction \frac{4}{2}.

$$-\frac{35}{6}-\frac{3}{2}\left(-\frac{1}{2}-\frac{4}{2}\right)$$

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{35}{6}-\frac{3}{2}\times \frac{-1-4}{2}$$

Subtract 4 from -1 to get -5.

$$-\frac{35}{6}-\frac{3}{2}\left(-\frac{5}{2}\right)$$

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

$$-\frac{35}{6}-\frac{3\left(-5\right)}{2\times 2}$$

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

$$-\frac{35}{6}-\frac{-15}{4}$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$-\frac{35}{6}-\left(-\frac{15}{4}\right)$$

The opposite of -\frac{15}{4} is \frac{15}{4}.

$$-\frac{35}{6}+\frac{15}{4}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{35}{6} and \frac{15}{4} to fractions with denominator 12.

$$-\frac{70}{12}+\frac{45}{12}$$

Since -\frac{70}{12} and \frac{45}{12} have the same denominator, add them by adding their numerators.

$$\frac{-70+45}{12}$$

Add -70 and 45 to get -25.

$$-\frac{25}{12}$$

Factor

$$-\frac{25}{12} = -2\frac{1}{12} = -2.0833333333333335$$