Solve (21/2)^3-(31/4)^2/frac{162{16}}

$$\frac { ( 2 \frac { 1 } { 2 } ) ^ { 3 } - ( 3 \frac { 1 } { 4 } ) ^ { 2 } } { \frac { 162 } { 16 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{\left(\frac{4+1}{2}\right)^{3}-\left(\frac{3\times 4+1}{4}\right)^{2}}{\frac{162}{16}}$$

Add 4 and 1 to get 5.

$$\frac{\left(\frac{5}{2}\right)^{3}-\left(\frac{3\times 4+1}{4}\right)^{2}}{\frac{162}{16}}$$

Calculate \frac{5}{2} to the power of 3 and get \frac{125}{8}.

$$\frac{\frac{125}{8}-\left(\frac{3\times 4+1}{4}\right)^{2}}{\frac{162}{16}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{125}{8}-\left(\frac{12+1}{4}\right)^{2}}{\frac{162}{16}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{125}{8}-\left(\frac{13}{4}\right)^{2}}{\frac{162}{16}}$$

Calculate \frac{13}{4} to the power of 2 and get \frac{169}{16}.

$$\frac{\frac{125}{8}-\frac{169}{16}}{\frac{162}{16}}$$

Subtract \frac{169}{16} from \frac{125}{8} to get \frac{81}{16}.

$$\frac{\frac{81}{16}}{\frac{162}{16}}$$

Reduce the fraction \frac{162}{16} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{81}{16}}{\frac{81}{8}}$$

Divide \frac{81}{16} by \frac{81}{8} by multiplying \frac{81}{16} by the reciprocal of \frac{81}{8}.

$$\frac{81}{16}\times \frac{8}{81}$$

Multiply \frac{81}{16} and \frac{8}{81} to get \frac{1}{2}.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$