Solve 500*6.6/3*10.56*(2.5div0.93-1)+0.1*10.56*10.56

$$500 \times \frac{ 6.6 }{ 3 \times 10.56 } \times (2.5 \div 0.93-1)+0.1 \times 10.56 \times 10.56$$

Evaluate

$$\frac{326085809}{1743750}\approx 187.00261448$$

Solution Steps

Multiply 3 and 10.56 to get 31.68.

$$500\times \frac{6.6}{31.68}\left(\frac{2.5}{0.93}-1\right)+0.1\times 10.56\times 10.56$$

Expand \frac{6.6}{31.68} by multiplying both numerator and the denominator by 100.

$$500\times \frac{660}{3168}\left(\frac{2.5}{0.93}-1\right)+0.1\times 10.56\times 10.56$$

Reduce the fraction \frac{660}{3168} to lowest terms by extracting and canceling out 132.

$$500\times \frac{5}{24}\left(\frac{2.5}{0.93}-1\right)+0.1\times 10.56\times 10.56$$

Express 500\times \frac{5}{24} as a single fraction.

$$\frac{500\times 5}{24}\left(\frac{2.5}{0.93}-1\right)+0.1\times 10.56\times 10.56$$

Multiply 500 and 5 to get 2500.

$$\frac{2500}{24}\left(\frac{2.5}{0.93}-1\right)+0.1\times 10.56\times 10.56$$

Reduce the fraction \frac{2500}{24} to lowest terms by extracting and canceling out 4.

$$\frac{625}{6}\left(\frac{2.5}{0.93}-1\right)+0.1\times 10.56\times 10.56$$

Expand \frac{2.5}{0.93} by multiplying both numerator and the denominator by 100.

$$\frac{625}{6}\left(\frac{250}{93}-1\right)+0.1\times 10.56\times 10.56$$

Convert 1 to fraction \frac{93}{93}.

$$\frac{625}{6}\left(\frac{250}{93}-\frac{93}{93}\right)+0.1\times 10.56\times 10.56$$

Since \frac{250}{93} and \frac{93}{93} have the same denominator, subtract them by subtracting their numerators.

$$\frac{625}{6}\times \frac{250-93}{93}+0.1\times 10.56\times 10.56$$

Subtract 93 from 250 to get 157.

$$\frac{625}{6}\times \frac{157}{93}+0.1\times 10.56\times 10.56$$

Multiply \frac{625}{6} times \frac{157}{93} by multiplying numerator times numerator and denominator times denominator.

$$\frac{625\times 157}{6\times 93}+0.1\times 10.56\times 10.56$$

Do the multiplications in the fraction \frac{625\times 157}{6\times 93}.

$$\frac{98125}{558}+0.1\times 10.56\times 10.56$$

Multiply 0.1 and 10.56 to get 1.056.

$$\frac{98125}{558}+1.056\times 10.56$$

Multiply 1.056 and 10.56 to get 11.15136.

$$\frac{98125}{558}+11.15136$$

Convert decimal number 11.15136 to fraction \frac{1115136}{100000}. Reduce the fraction \frac{1115136}{100000} to lowest terms by extracting and canceling out 32.

$$\frac{98125}{558}+\frac{34848}{3125}$$

Least common multiple of 558 and 3125 is 1743750. Convert \frac{98125}{558} and \frac{34848}{3125} to fractions with denominator 1743750.

$$\frac{306640625}{1743750}+\frac{19445184}{1743750}$$

Since \frac{306640625}{1743750} and \frac{19445184}{1743750} have the same denominator, add them by adding their numerators.

$$\frac{306640625+19445184}{1743750}$$

Add 306640625 and 19445184 to get 326085809.

$$\frac{326085809}{1743750}$$

Factor

$$\frac{7 \cdot 19 \cdot 61 \cdot 40193}{2 \cdot 31 \cdot 3 ^ {2} \cdot 5 ^ {5}} = 187\frac{4559}{1743750} = 187.00261448028675$$