Solve 400(3.14-3.14/2+1/2)

$$400 ( 3.14 - \frac { 3.14 } { 2 } + \frac { 1 } { 2 } )$$

Evaluate

$$828$$

Solution Steps

Expand \frac{3.14}{2} by multiplying both numerator and the denominator by 100.

$$400\left(3.14-\frac{314}{200}+\frac{1}{2}\right)$$

Reduce the fraction \frac{314}{200} to lowest terms by extracting and canceling out 2.

$$400\left(3.14-\frac{157}{100}+\frac{1}{2}\right)$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$400\left(\frac{157}{50}-\frac{157}{100}+\frac{1}{2}\right)$$

Least common multiple of 50 and 100 is 100. Convert \frac{157}{50} and \frac{157}{100} to fractions with denominator 100.

$$400\left(\frac{314}{100}-\frac{157}{100}+\frac{1}{2}\right)$$

Since \frac{314}{100} and \frac{157}{100} have the same denominator, subtract them by subtracting their numerators.

$$400\left(\frac{314-157}{100}+\frac{1}{2}\right)$$

Subtract 157 from 314 to get 157.

$$400\left(\frac{157}{100}+\frac{1}{2}\right)$$

Least common multiple of 100 and 2 is 100. Convert \frac{157}{100} and \frac{1}{2} to fractions with denominator 100.

$$400\left(\frac{157}{100}+\frac{50}{100}\right)$$

Since \frac{157}{100} and \frac{50}{100} have the same denominator, add them by adding their numerators.

$$400\times \frac{157+50}{100}$$

Add 157 and 50 to get 207.

$$400\times \frac{207}{100}$$

Express 400\times \frac{207}{100} as a single fraction.

$$\frac{400\times 207}{100}$$

Multiply 400 and 207 to get 82800.

$$\frac{82800}{100}$$

Divide 82800 by 100 to get 828.

$$828$$

Factor

$$23\times 2^{2}\times 3^{2}$$