Solve -330*6.74/102-6.74+15/frac{-330left(100+100right){100}+100-(100+100)}

$$\frac{ \frac{ -330 \cdot 6.74 }{ 102 } -6.74+15 }{ \frac{ -330 \left( 100+100 \right) }{ 100 } +100-(100+100) }$$

Evaluate

$$\frac{303}{17000}\approx 0.017823529$$

Solution Steps

Multiply -330 and 6.74 to get -2224.2.

$$\frac{\frac{-2224.2}{102}-6.74+15}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Expand \frac{-2224.2}{102} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{-22242}{1020}-6.74+15}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Reduce the fraction \frac{-22242}{1020} to lowest terms by extracting and canceling out 6.

$$\frac{-\frac{3707}{170}-6.74+15}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Convert decimal number 6.74 to fraction \frac{674}{100}. Reduce the fraction \frac{674}{100} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{3707}{170}-\frac{337}{50}+15}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Least common multiple of 170 and 50 is 850. Convert -\frac{3707}{170} and \frac{337}{50} to fractions with denominator 850.

$$\frac{-\frac{18535}{850}-\frac{5729}{850}+15}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Since -\frac{18535}{850} and \frac{5729}{850} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-18535-5729}{850}+15}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Subtract 5729 from -18535 to get -24264.

$$\frac{\frac{-24264}{850}+15}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Reduce the fraction \frac{-24264}{850} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{12132}{425}+15}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Convert 15 to fraction \frac{6375}{425}.

$$\frac{-\frac{12132}{425}+\frac{6375}{425}}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Since -\frac{12132}{425} and \frac{6375}{425} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-12132+6375}{425}}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Add -12132 and 6375 to get -5757.

$$\frac{-\frac{5757}{425}}{\frac{-330\left(100+100\right)}{100}+100-\left(100+100\right)}$$

Add 100 and 100 to get 200.

$$\frac{-\frac{5757}{425}}{\frac{-330\times 200}{100}+100-\left(100+100\right)}$$

Multiply -330 and 200 to get -66000.

$$\frac{-\frac{5757}{425}}{\frac{-66000}{100}+100-\left(100+100\right)}$$

Divide -66000 by 100 to get -660.

$$\frac{-\frac{5757}{425}}{-660+100-\left(100+100\right)}$$

Add -660 and 100 to get -560.

$$\frac{-\frac{5757}{425}}{-560-\left(100+100\right)}$$

Add 100 and 100 to get 200.

$$\frac{-\frac{5757}{425}}{-560-200}$$

Subtract 200 from -560 to get -760.

$$\frac{-\frac{5757}{425}}{-760}$$

Express \frac{-\frac{5757}{425}}{-760} as a single fraction.

$$\frac{-5757}{425\left(-760\right)}$$

Multiply 425 and -760 to get -323000.

$$\frac{-5757}{-323000}$$

Reduce the fraction \frac{-5757}{-323000} to lowest terms by extracting and canceling out -19.

$$\frac{303}{17000}$$

Factor

$$\frac{3 \cdot 101}{17 \cdot 2 ^ {3} \cdot 5 ^ {3}} = 0.017823529411764707$$