Solve 532.094*(1/0.06+0.33*0.06-1)

$$532.094 \times ( \frac{ 1 }{ 0.06 } +0.33 \times 0.06-1)$$

Evaluate

$$\frac{62600060959}{7500000}\approx 8346.674794533$$

Solution Steps

Expand \frac{1}{0.06} by multiplying both numerator and the denominator by 100.

$$532.094\left(\frac{100}{6}+0.33\times 0.06-1\right)$$

Reduce the fraction \frac{100}{6} to lowest terms by extracting and canceling out 2.

$$532.094\left(\frac{50}{3}+0.33\times 0.06-1\right)$$

Multiply 0.33 and 0.06 to get 0.0198.

$$532.094\left(\frac{50}{3}+0.0198-1\right)$$

Convert decimal number 0.0198 to fraction \frac{198}{10000}. Reduce the fraction \frac{198}{10000} to lowest terms by extracting and canceling out 2.

$$532.094\left(\frac{50}{3}+\frac{99}{5000}-1\right)$$

Least common multiple of 3 and 5000 is 15000. Convert \frac{50}{3} and \frac{99}{5000} to fractions with denominator 15000.

$$532.094\left(\frac{250000}{15000}+\frac{297}{15000}-1\right)$$

Since \frac{250000}{15000} and \frac{297}{15000} have the same denominator, add them by adding their numerators.

$$532.094\left(\frac{250000+297}{15000}-1\right)$$

Add 250000 and 297 to get 250297.

$$532.094\left(\frac{250297}{15000}-1\right)$$

Convert 1 to fraction \frac{15000}{15000}.

$$532.094\left(\frac{250297}{15000}-\frac{15000}{15000}\right)$$

Since \frac{250297}{15000} and \frac{15000}{15000} have the same denominator, subtract them by subtracting their numerators.

$$532.094\times \frac{250297-15000}{15000}$$

Subtract 15000 from 250297 to get 235297.

$$532.094\times \frac{235297}{15000}$$

Convert decimal number 532.094 to fraction \frac{532094}{1000}. Reduce the fraction \frac{532094}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{266047}{500}\times \frac{235297}{15000}$$

Multiply \frac{266047}{500} times \frac{235297}{15000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{266047\times 235297}{500\times 15000}$$

Do the multiplications in the fraction \frac{266047\times 235297}{500\times 15000}.

$$\frac{62600060959}{7500000}$$

Factor

$$\frac{17 \cdot 13841 \cdot 266047}{3 \cdot 2 ^ {5} \cdot 5 ^ {7}} = 8346\frac{5060959}{7500000} = 8346.674794533334$$