Solve 100*(0.22^2div0.24+0.16^2div0.5)

$$100 \times ( { 0.22 }^{ 2 } \div 0.24+ { 0.16 }^{ 2 } \div 0.5)$$

Evaluate

$$\frac{3793}{150}\approx 25.286666667$$

Solution Steps

Calculate 0.22 to the power of 2 and get 0.0484.

$$100\left(\frac{0.0484}{0.24}+\frac{0.16^{2}}{0.5}\right)$$

Expand \frac{0.0484}{0.24} by multiplying both numerator and the denominator by 10000.

$$100\left(\frac{484}{2400}+\frac{0.16^{2}}{0.5}\right)$$

Reduce the fraction \frac{484}{2400} to lowest terms by extracting and canceling out 4.

$$100\left(\frac{121}{600}+\frac{0.16^{2}}{0.5}\right)$$

Calculate 0.16 to the power of 2 and get 0.0256.

$$100\left(\frac{121}{600}+\frac{0.0256}{0.5}\right)$$

Expand \frac{0.0256}{0.5} by multiplying both numerator and the denominator by 10000.

$$100\left(\frac{121}{600}+\frac{256}{5000}\right)$$

Reduce the fraction \frac{256}{5000} to lowest terms by extracting and canceling out 8.

$$100\left(\frac{121}{600}+\frac{32}{625}\right)$$

Least common multiple of 600 and 625 is 15000. Convert \frac{121}{600} and \frac{32}{625} to fractions with denominator 15000.

$$100\left(\frac{3025}{15000}+\frac{768}{15000}\right)$$

Since \frac{3025}{15000} and \frac{768}{15000} have the same denominator, add them by adding their numerators.

$$100\times \frac{3025+768}{15000}$$

Add 3025 and 768 to get 3793.

$$100\times \frac{3793}{15000}$$

Express 100\times \frac{3793}{15000} as a single fraction.

$$\frac{100\times 3793}{15000}$$

Multiply 100 and 3793 to get 379300.

$$\frac{379300}{15000}$$

Reduce the fraction \frac{379300}{15000} to lowest terms by extracting and canceling out 100.

$$\frac{3793}{150}$$

Factor

$$\frac{3793}{2 \cdot 3 \cdot 5 ^ {2}} = 25\frac{43}{150} = 25.286666666666665$$