Solve (357)1.96^2(0.5)(0.5)/(357-1)1.96^2+1.96^2(0.5)(0.5)

$$\frac{ (357) { 1.96 }^{ 2 } (0.5)(0.5) }{ (357-1) { 1.96 }^{ 2 } + { 1.96 }^{ 2 } (0.5)(0.5) }$$

Evaluate

$$\frac{119}{475}\approx 0.250526316$$

Solution Steps

Calculate 1.96 to the power of 2 and get 3.8416.

$$\frac{357\times 3.8416\times 0.5\times 0.5}{\left(357-1\right)\times 1.96^{2}+1.96^{2}\times 0.5\times 0.5}$$

Multiply 357 and 3.8416 to get 1371.4512.

$$\frac{1371.4512\times 0.5\times 0.5}{\left(357-1\right)\times 1.96^{2}+1.96^{2}\times 0.5\times 0.5}$$

Multiply 1371.4512 and 0.5 to get 685.7256.

$$\frac{685.7256\times 0.5}{\left(357-1\right)\times 1.96^{2}+1.96^{2}\times 0.5\times 0.5}$$

Multiply 685.7256 and 0.5 to get 342.8628.

$$\frac{342.8628}{\left(357-1\right)\times 1.96^{2}+1.96^{2}\times 0.5\times 0.5}$$

Subtract 1 from 357 to get 356.

$$\frac{342.8628}{356\times 1.96^{2}+1.96^{2}\times 0.5\times 0.5}$$

Calculate 1.96 to the power of 2 and get 3.8416.

$$\frac{342.8628}{356\times 3.8416+1.96^{2}\times 0.5\times 0.5}$$

Multiply 356 and 3.8416 to get 1367.6096.

$$\frac{342.8628}{1367.6096+1.96^{2}\times 0.5\times 0.5}$$

Calculate 1.96 to the power of 2 and get 3.8416.

$$\frac{342.8628}{1367.6096+3.8416\times 0.5\times 0.5}$$

Multiply 3.8416 and 0.5 to get 1.9208.

$$\frac{342.8628}{1367.6096+1.9208\times 0.5}$$

Multiply 1.9208 and 0.5 to get 0.9604.

$$\frac{342.8628}{1367.6096+0.9604}$$

Add 1367.6096 and 0.9604 to get 1368.57.

$$\frac{342.8628}{1368.57}$$

Expand \frac{342.8628}{1368.57} by multiplying both numerator and the denominator by 10000.

$$\frac{3428628}{13685700}$$

Reduce the fraction \frac{3428628}{13685700} to lowest terms by extracting and canceling out 28812.

$$\frac{119}{475}$$

Factor

$$\frac{7 \cdot 17}{19 \cdot 5 ^ {2}} = 0.2505263157894737$$