Solve (0.13^2/0.13+0.31+0.26^2/0.26+0.18)*30^2/4

$$( \frac { 0.13 ^ { 2 } } { 0.13 + 0.31 } + \frac { 0.26 ^ { 2 } } { 0.26 + 0.18 } ) * \frac { 30 ^ { 2 } } { 4 }$$

Evaluate

$$\frac{7605}{176}\approx 43.210227273$$

Solution Steps

Calculate 0.13 to the power of 2 and get 0.0169.

$$\left(\frac{0.0169}{0.13+0.31}+\frac{0.26^{2}}{0.26+0.18}\right)\times \frac{30^{2}}{4}$$

Add 0.13 and 0.31 to get 0.44.

$$\left(\frac{0.0169}{0.44}+\frac{0.26^{2}}{0.26+0.18}\right)\times \frac{30^{2}}{4}$$

Expand \frac{0.0169}{0.44} by multiplying both numerator and the denominator by 10000.

$$\left(\frac{169}{4400}+\frac{0.26^{2}}{0.26+0.18}\right)\times \frac{30^{2}}{4}$$

Calculate 0.26 to the power of 2 and get 0.0676.

$$\left(\frac{169}{4400}+\frac{0.0676}{0.26+0.18}\right)\times \frac{30^{2}}{4}$$

Add 0.26 and 0.18 to get 0.44.

$$\left(\frac{169}{4400}+\frac{0.0676}{0.44}\right)\times \frac{30^{2}}{4}$$

Expand \frac{0.0676}{0.44} by multiplying both numerator and the denominator by 10000.

$$\left(\frac{169}{4400}+\frac{676}{4400}\right)\times \frac{30^{2}}{4}$$

Since \frac{169}{4400} and \frac{676}{4400} have the same denominator, add them by adding their numerators.

$$\frac{169+676}{4400}\times \frac{30^{2}}{4}$$

Add 169 and 676 to get 845.

$$\frac{845}{4400}\times \frac{30^{2}}{4}$$

Reduce the fraction \frac{845}{4400} to lowest terms by extracting and canceling out 5.

$$\frac{169}{880}\times \frac{30^{2}}{4}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{169}{880}\times \frac{900}{4}$$

Divide 900 by 4 to get 225.

$$\frac{169}{880}\times 225$$

Express \frac{169}{880}\times 225 as a single fraction.

$$\frac{169\times 225}{880}$$

Multiply 169 and 225 to get 38025.

$$\frac{38025}{880}$$

Reduce the fraction \frac{38025}{880} to lowest terms by extracting and canceling out 5.

$$\frac{7605}{176}$$

Factor

$$\frac{5 \cdot 3 ^ {2} \cdot 13 ^ {2}}{11 \cdot 2 ^ {4}} = 43\frac{37}{176} = 43.21022727272727$$