Solve [12/169(13/2)^2:3/5+1]^2-11/4

$$[ \frac { 12 } { 169 } ( \frac { 13 } { 2 } ) ^ { 2 } : \frac { 3 } { 5 } + 1 ] ^ { 2 } - \frac { 11 } { 4 }$$

Evaluate

$$\frac{133}{4}=33.25$$

Solution Steps

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

$$\left(\frac{\frac{12}{169}\times \frac{169}{4}}{\frac{3}{5}}+1\right)^{2}-\frac{11}{4}$$

Multiply \frac{12}{169} and \frac{169}{4} to get 3.

$$\left(\frac{3}{\frac{3}{5}}+1\right)^{2}-\frac{11}{4}$$

Divide 3 by \frac{3}{5} by multiplying 3 by the reciprocal of \frac{3}{5}.

$$\left(3\times \frac{5}{3}+1\right)^{2}-\frac{11}{4}$$

Multiply 3 and \frac{5}{3} to get 5.

$$\left(5+1\right)^{2}-\frac{11}{4}$$

Add 5 and 1 to get 6.

$$6^{2}-\frac{11}{4}$$

Calculate 6 to the power of 2 and get 36.

$$36-\frac{11}{4}$$

Subtract \frac{11}{4} from 36 to get \frac{133}{4}.

$$\frac{133}{4}$$

Factor

$$\frac{7 \cdot 19}{2 ^ {2}} = 33\frac{1}{4} = 33.25$$