Solve {[21/2-11/4][-2+3-2/1+3-1]}

$$\{ [ 2 \frac { 1 } { 2 } - 1 \frac { 1 } { 4 } ] [ \frac { - 2 + 3 - 2 } { 1 + 3 - 1 } ] \}$$

Evaluate

$$-\frac{5}{12}\approx -0.416666667$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Multiply 1 and 4 to get 4.

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

Add 4 and 1 to get 5.

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

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

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

Since \frac{10}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-5}{4}\times \frac{-2+3-2}{1+3-1}$$

Subtract 5 from 10 to get 5.

$$\frac{5}{4}\times \frac{-2+3-2}{1+3-1}$$

Add -2 and 3 to get 1.

$$\frac{5}{4}\times \frac{1-2}{1+3-1}$$

Subtract 2 from 1 to get -1.

$$\frac{5}{4}\times \frac{-1}{1+3-1}$$

Add 1 and 3 to get 4.

$$\frac{5}{4}\times \frac{-1}{4-1}$$

Subtract 1 from 4 to get 3.

$$\frac{5}{4}\times \frac{-1}{3}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

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

Multiply \frac{5}{4} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-1\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{5\left(-1\right)}{4\times 3}.

$$\frac{-5}{12}$$

Fraction \frac{-5}{12} can be rewritten as -\frac{5}{12} by extracting the negative sign.

$$-\frac{5}{12}$$

Factor

$$-\frac{5}{12} = -0.4166666666666667$$