Solve [(+3/16):(-1/12)+5/2]-(9/4-frac{7}{2})

$$[ ( + \frac { 3 } { 16 } ) : ( - \frac { 1 } { 12 } ) + \frac { 5 } { 2 } ] - ( \frac { 9 } { 4 } - \frac { 7 } { 2 } )$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Divide \frac{3}{16} by -\frac{1}{12} by multiplying \frac{3}{16} by the reciprocal of -\frac{1}{12}.

$$\frac{3}{16}\left(-12\right)+\frac{5}{2}-\left(\frac{9}{4}-\frac{7}{2}\right)$$

Express \frac{3}{16}\left(-12\right) as a single fraction.

$$\frac{3\left(-12\right)}{16}+\frac{5}{2}-\left(\frac{9}{4}-\frac{7}{2}\right)$$

Multiply 3 and -12 to get -36.

$$\frac{-36}{16}+\frac{5}{2}-\left(\frac{9}{4}-\frac{7}{2}\right)$$

Reduce the fraction \frac{-36}{16} to lowest terms by extracting and canceling out 4.

$$-\frac{9}{4}+\frac{5}{2}-\left(\frac{9}{4}-\frac{7}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert -\frac{9}{4} and \frac{5}{2} to fractions with denominator 4.

$$-\frac{9}{4}+\frac{10}{4}-\left(\frac{9}{4}-\frac{7}{2}\right)$$

Since -\frac{9}{4} and \frac{10}{4} have the same denominator, add them by adding their numerators.

$$\frac{-9+10}{4}-\left(\frac{9}{4}-\frac{7}{2}\right)$$

Add -9 and 10 to get 1.

$$\frac{1}{4}-\left(\frac{9}{4}-\frac{7}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{7}{2} to fractions with denominator 4.

$$\frac{1}{4}-\left(\frac{9}{4}-\frac{14}{4}\right)$$

Since \frac{9}{4} and \frac{14}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}-\frac{9-14}{4}$$

Subtract 14 from 9 to get -5.

$$\frac{1}{4}-\left(-\frac{5}{4}\right)$$

The opposite of -\frac{5}{4} is \frac{5}{4}.

$$\frac{1}{4}+\frac{5}{4}$$

Since \frac{1}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{1+5}{4}$$

Add 1 and 5 to get 6.

$$\frac{6}{4}$$

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

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$