Solve {-[(5/4)+(-2)]+(2/3)+(-1)^3+2*(4-3)}

$$\{ - [ ( \frac { 5 } { 4 } ) + ( - 2 ) ] + ( \frac { 2 } { 3 } ) + ( - 1 ) ^ { 3 } + 2 \cdot ( 4 - 3 ) \}$$

Evaluate

$$\frac{29}{12}\approx 2.416666667$$

Solution Steps

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

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

Since \frac{5}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 8 from 5 to get -3.

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

The opposite of -\frac{3}{4} is \frac{3}{4}.

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

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{9}{12}+\frac{8}{12}+\left(-1\right)^{3}+2\left(4-3\right)$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{9+8}{12}+\left(-1\right)^{3}+2\left(4-3\right)$$

Add 9 and 8 to get 17.

$$\frac{17}{12}+\left(-1\right)^{3}+2\left(4-3\right)$$

Calculate -1 to the power of 3 and get -1.

$$\frac{17}{12}-1+2\left(4-3\right)$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{17}{12}-\frac{12}{12}+2\left(4-3\right)$$

Since \frac{17}{12} and \frac{12}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-12}{12}+2\left(4-3\right)$$

Subtract 12 from 17 to get 5.

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

Subtract 3 from 4 to get 1.

$$\frac{5}{12}+2\times 1$$

Multiply 2 and 1 to get 2.

$$\frac{5}{12}+2$$

Convert 2 to fraction \frac{24}{12}.

$$\frac{5}{12}+\frac{24}{12}$$

Since \frac{5}{12} and \frac{24}{12} have the same denominator, add them by adding their numerators.

$$\frac{5+24}{12}$$

Add 5 and 24 to get 29.

$$\frac{29}{12}$$

Factor

$$\frac{29}{2 ^ {2} \cdot 3} = 2\frac{5}{12} = 2.4166666666666665$$