Solve (0.5^2+0.5^2/2)19600

$$( { 0.5 }^{ 2 } + \frac{ { 0.5 }^{ 2 } }{ 2 } )19600$$

Evaluate

$$7350$$

Solution Steps

Calculate 0.5 to the power of 2 and get 0.25.

$$\left(0.25+\frac{0.5^{2}}{2}\right)\times 19600$$

Calculate 0.5 to the power of 2 and get 0.25.

$$\left(0.25+\frac{0.25}{2}\right)\times 19600$$

Expand \frac{0.25}{2} by multiplying both numerator and the denominator by 100.

$$\left(0.25+\frac{25}{200}\right)\times 19600$$

Reduce the fraction \frac{25}{200} to lowest terms by extracting and canceling out 25.

$$\left(0.25+\frac{1}{8}\right)\times 19600$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\left(\frac{1}{4}+\frac{1}{8}\right)\times 19600$$

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{1}{8} to fractions with denominator 8.

$$\left(\frac{2}{8}+\frac{1}{8}\right)\times 19600$$

Since \frac{2}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{8}\times 19600$$

Add 2 and 1 to get 3.

$$\frac{3}{8}\times 19600$$

Express \frac{3}{8}\times 19600 as a single fraction.

$$\frac{3\times 19600}{8}$$

Multiply 3 and 19600 to get 58800.

$$\frac{58800}{8}$$

Divide 58800 by 8 to get 7350.

$$7350$$

Factor

$$2\times 3\times 5^{2}\times 7^{2}$$