Solve [(5/4+9/10-5/3):58/45]^2:(-frac{3}{4})^2+frac{1}{2}-2

$$[ ( \frac { 5 } { 4 } + \frac { 9 } { 10 } - \frac { 5 } { 3 } ) : \frac { 58 } { 45 } ] ^ { 2 } : ( - \frac { 3 } { 4 } ) ^ { 2 } + \frac { 1 } { 2 } - 2$$

Evaluate

$$-\frac{5}{4}=-1.25$$

Solution Steps

Add \frac{5}{4} and \frac{9}{10} to get \frac{43}{20}.

$$\frac{\left(\frac{\frac{43}{20}-\frac{5}{3}}{\frac{58}{45}}\right)^{2}}{\left(-\frac{3}{4}\right)^{2}}+\frac{1}{2}-2$$

Subtract \frac{5}{3} from \frac{43}{20} to get \frac{29}{60}.

$$\frac{\left(\frac{\frac{29}{60}}{\frac{58}{45}}\right)^{2}}{\left(-\frac{3}{4}\right)^{2}}+\frac{1}{2}-2$$

Divide \frac{29}{60} by \frac{58}{45} by multiplying \frac{29}{60} by the reciprocal of \frac{58}{45}.

$$\frac{\left(\frac{29}{60}\times \frac{45}{58}\right)^{2}}{\left(-\frac{3}{4}\right)^{2}}+\frac{1}{2}-2$$

Multiply \frac{29}{60} and \frac{45}{58} to get \frac{3}{8}.

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

Calculate \frac{3}{8} to the power of 2 and get \frac{9}{64}.

$$\frac{\frac{9}{64}}{\left(-\frac{3}{4}\right)^{2}}+\frac{1}{2}-2$$

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{\frac{9}{64}}{\frac{9}{16}}+\frac{1}{2}-2$$

Divide \frac{9}{64} by \frac{9}{16} by multiplying \frac{9}{64} by the reciprocal of \frac{9}{16}.

$$\frac{9}{64}\times \frac{16}{9}+\frac{1}{2}-2$$

Multiply \frac{9}{64} and \frac{16}{9} to get \frac{1}{4}.

$$\frac{1}{4}+\frac{1}{2}-2$$

Add \frac{1}{4} and \frac{1}{2} to get \frac{3}{4}.

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

Subtract 2 from \frac{3}{4} to get -\frac{5}{4}.

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

Factor

$$-\frac{5}{4} = -1\frac{1}{4} = -1.25$$