Solve |-1-3/2|+36*(1/3-1/2)-3div(-3/4)

$$| - 1 - \frac { 3 } { 2 } | + 36 \times ( \frac { 1 } { 3 } - \frac { 1 } { 2 } ) - 3 \div ( - \frac { 3 } { 4 } )$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Convert -1 to fraction -\frac{2}{2}.

$$|-\frac{2}{2}-\frac{3}{2}|+36\left(\frac{1}{3}-\frac{1}{2}\right)-\frac{3}{-\frac{3}{4}}$$

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

$$|\frac{-2-3}{2}|+36\left(\frac{1}{3}-\frac{1}{2}\right)-\frac{3}{-\frac{3}{4}}$$

Subtract 3 from -2 to get -5.

$$|-\frac{5}{2}|+36\left(\frac{1}{3}-\frac{1}{2}\right)-\frac{3}{-\frac{3}{4}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{5}{2} is \frac{5}{2}.

$$\frac{5}{2}+36\left(\frac{1}{3}-\frac{1}{2}\right)-\frac{3}{-\frac{3}{4}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{5}{2}+36\left(\frac{2}{6}-\frac{3}{6}\right)-\frac{3}{-\frac{3}{4}}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}+36\times \frac{2-3}{6}-\frac{3}{-\frac{3}{4}}$$

Subtract 3 from 2 to get -1.

$$\frac{5}{2}+36\left(-\frac{1}{6}\right)-\frac{3}{-\frac{3}{4}}$$

Express 36\left(-\frac{1}{6}\right) as a single fraction.

$$\frac{5}{2}+\frac{36\left(-1\right)}{6}-\frac{3}{-\frac{3}{4}}$$

Multiply 36 and -1 to get -36.

$$\frac{5}{2}+\frac{-36}{6}-\frac{3}{-\frac{3}{4}}$$

Divide -36 by 6 to get -6.

$$\frac{5}{2}-6-\frac{3}{-\frac{3}{4}}$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{5}{2}-\frac{12}{2}-\frac{3}{-\frac{3}{4}}$$

Since \frac{5}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-12}{2}-\frac{3}{-\frac{3}{4}}$$

Subtract 12 from 5 to get -7.

$$-\frac{7}{2}-\frac{3}{-\frac{3}{4}}$$

Divide 3 by -\frac{3}{4} by multiplying 3 by the reciprocal of -\frac{3}{4}.

$$-\frac{7}{2}-3\left(-\frac{4}{3}\right)$$

Cancel out 3 and 3.

$$-\frac{7}{2}-\left(-4\right)$$

The opposite of -4 is 4.

$$-\frac{7}{2}+4$$

Convert 4 to fraction \frac{8}{2}.

$$-\frac{7}{2}+\frac{8}{2}$$

Since -\frac{7}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{-7+8}{2}$$

Add -7 and 8 to get 1.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$