Solve 3/4*(3.14*15.92*2)*2+2*266.5=

$$\frac{ 3 }{ 4 } \times (3.14 \times 15.92 \times 2) \times 2+2 \times 266.5=$$

Evaluate

$$682.9664$$

Solution Steps

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.

$$\frac{3}{4}\times \frac{157}{50}\times 15.92\times 2\times 2+2\times 266.5$$

Multiply \frac{3}{4} times \frac{157}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 157}{4\times 50}\times 15.92\times 2\times 2+2\times 266.5$$

Do the multiplications in the fraction \frac{3\times 157}{4\times 50}.

$$\frac{471}{200}\times 15.92\times 2\times 2+2\times 266.5$$

Convert decimal number 15.92 to fraction \frac{1592}{100}. Reduce the fraction \frac{1592}{100} to lowest terms by extracting and canceling out 4.

$$\frac{471}{200}\times \frac{398}{25}\times 2\times 2+2\times 266.5$$

Multiply \frac{471}{200} times \frac{398}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{471\times 398}{200\times 25}\times 2\times 2+2\times 266.5$$

Do the multiplications in the fraction \frac{471\times 398}{200\times 25}.

$$\frac{187458}{5000}\times 2\times 2+2\times 266.5$$

Reduce the fraction \frac{187458}{5000} to lowest terms by extracting and canceling out 2.

$$\frac{93729}{2500}\times 2\times 2+2\times 266.5$$

Express \frac{93729}{2500}\times 2 as a single fraction.

$$\frac{93729\times 2}{2500}\times 2+2\times 266.5$$

Multiply 93729 and 2 to get 187458.

$$\frac{187458}{2500}\times 2+2\times 266.5$$

Reduce the fraction \frac{187458}{2500} to lowest terms by extracting and canceling out 2.

$$\frac{93729}{1250}\times 2+2\times 266.5$$

Express \frac{93729}{1250}\times 2 as a single fraction.

$$\frac{93729\times 2}{1250}+2\times 266.5$$

Multiply 93729 and 2 to get 187458.

$$\frac{187458}{1250}+2\times 266.5$$

Reduce the fraction \frac{187458}{1250} to lowest terms by extracting and canceling out 2.

$$\frac{93729}{625}+2\times 266.5$$

Multiply 2 and 266.5 to get 533.

$$\frac{93729}{625}+533$$

Convert 533 to fraction \frac{333125}{625}.

$$\frac{93729}{625}+\frac{333125}{625}$$

Since \frac{93729}{625} and \frac{333125}{625} have the same denominator, add them by adding their numerators.

$$\frac{93729+333125}{625}$$

Add 93729 and 333125 to get 426854.

$$\frac{426854}{625}$$

Factor

$$\frac{2 \cdot 19 \cdot 47 \cdot 239}{5 ^ {4}} = 682\frac{604}{625} = 682.9664$$