Solve 1-(1/16-1/3)/(frac{1{6}+1/2)^2+frac{3}{2}}

$$\frac { 1 - ( \frac { 1 } { 16 } - \frac { 1 } { 3 } ) } { ( \frac { 1 } { 6 } + \frac { 1 } { 2 } ) ^ { 2 } + \frac { 3 } { 2 } }$$

Evaluate

$$\frac{183}{280}\approx 0.653571429$$

Solution Steps

Subtract \frac{1}{3} from \frac{1}{16} to get -\frac{13}{48}.

$$\frac{1-\left(-\frac{13}{48}\right)}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}$$

The opposite of -\frac{13}{48} is \frac{13}{48}.

$$\frac{1+\frac{13}{48}}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}$$

Add 1 and \frac{13}{48} to get \frac{61}{48}.

$$\frac{\frac{61}{48}}{\left(\frac{1}{6}+\frac{1}{2}\right)^{2}+\frac{3}{2}}$$

Add \frac{1}{6} and \frac{1}{2} to get \frac{2}{3}.

$$\frac{\frac{61}{48}}{\left(\frac{2}{3}\right)^{2}+\frac{3}{2}}$$

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

$$\frac{\frac{61}{48}}{\frac{4}{9}+\frac{3}{2}}$$

Add \frac{4}{9} and \frac{3}{2} to get \frac{35}{18}.

$$\frac{\frac{61}{48}}{\frac{35}{18}}$$

Divide \frac{61}{48} by \frac{35}{18} by multiplying \frac{61}{48} by the reciprocal of \frac{35}{18}.

$$\frac{61}{48}\times \frac{18}{35}$$

Multiply \frac{61}{48} and \frac{18}{35} to get \frac{183}{280}.

$$\frac{183}{280}$$

Factor

$$\frac{3 \cdot 61}{2 ^ {3} \cdot 5 \cdot 7} = 0.6535714285714286$$