Solve 0.4+1+0.18+0.24+0.20/1^2+2^2+3^2+4^2+{5^2-5*{3}^2}

$$\frac{ 0.4+1+0.18+0.24+0.20 }{ { 1 }^{ 2 } + { 2 }^{ 2 } + { 3 }^{ 2 } + { 4 }^{ 2 } + { 5 }^{ 2 } -5 \times { 3 }^{ 2 } }$$

Evaluate

$$0.202$$

Solution Steps

Add 0.4 and 1 to get 1.4.

$$\frac{1.4+0.18+0.24+0.2}{1^{2}+2^{2}+3^{2}+4^{2}+5^{2}-5\times 3^{2}}$$

Add 1.4 and 0.18 to get 1.58.

$$\frac{1.58+0.24+0.2}{1^{2}+2^{2}+3^{2}+4^{2}+5^{2}-5\times 3^{2}}$$

Add 1.58 and 0.24 to get 1.82.

$$\frac{1.82+0.2}{1^{2}+2^{2}+3^{2}+4^{2}+5^{2}-5\times 3^{2}}$$

Add 1.82 and 0.2 to get 2.02.

$$\frac{2.02}{1^{2}+2^{2}+3^{2}+4^{2}+5^{2}-5\times 3^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{2.02}{1+2^{2}+3^{2}+4^{2}+5^{2}-5\times 3^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2.02}{1+4+3^{2}+4^{2}+5^{2}-5\times 3^{2}}$$

Add 1 and 4 to get 5.

$$\frac{2.02}{5+3^{2}+4^{2}+5^{2}-5\times 3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2.02}{5+9+4^{2}+5^{2}-5\times 3^{2}}$$

Add 5 and 9 to get 14.

$$\frac{2.02}{14+4^{2}+5^{2}-5\times 3^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{2.02}{14+16+5^{2}-5\times 3^{2}}$$

Add 14 and 16 to get 30.

$$\frac{2.02}{30+5^{2}-5\times 3^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{2.02}{30+25-5\times 3^{2}}$$

Add 30 and 25 to get 55.

$$\frac{2.02}{55-5\times 3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2.02}{55-5\times 9}$$

Multiply 5 and 9 to get 45.

$$\frac{2.02}{55-45}$$

Subtract 45 from 55 to get 10.

$$\frac{2.02}{10}$$

Expand \frac{2.02}{10} by multiplying both numerator and the denominator by 100.

$$\frac{202}{1000}$$

Reduce the fraction \frac{202}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{101}{500}$$

Factor

$$\frac{101}{2 ^ {2} \cdot 5 ^ {3}} = 0.202$$