Solve -0.8+4.2*(0.002div0.004-4.1)=

$$-0.8+4.2 \times (0.002 \div 0.004-4.1)=$$

Evaluate

$$-15.92$$

Solution Steps

Expand \frac{0.002}{0.004} by multiplying both numerator and the denominator by 1000.

$$-0.8+4.2\left(\frac{2}{4}-4.1\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$-0.8+4.2\left(\frac{1}{2}-4.1\right)$$

Convert decimal number 4.1 to fraction \frac{41}{10}.

$$-0.8+4.2\left(\frac{1}{2}-\frac{41}{10}\right)$$

Least common multiple of 2 and 10 is 10. Convert \frac{1}{2} and \frac{41}{10} to fractions with denominator 10.

$$-0.8+4.2\left(\frac{5}{10}-\frac{41}{10}\right)$$

Since \frac{5}{10} and \frac{41}{10} have the same denominator, subtract them by subtracting their numerators.

$$-0.8+4.2\times \frac{5-41}{10}$$

Subtract 41 from 5 to get -36.

$$-0.8+4.2\times \frac{-36}{10}$$

Reduce the fraction \frac{-36}{10} to lowest terms by extracting and canceling out 2.

$$-0.8+4.2\left(-\frac{18}{5}\right)$$

Convert decimal number 4.2 to fraction \frac{42}{10}. Reduce the fraction \frac{42}{10} to lowest terms by extracting and canceling out 2.

$$-0.8+\frac{21}{5}\left(-\frac{18}{5}\right)$$

Multiply \frac{21}{5} times -\frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$-0.8+\frac{21\left(-18\right)}{5\times 5}$$

Do the multiplications in the fraction \frac{21\left(-18\right)}{5\times 5}.

$$-0.8+\frac{-378}{25}$$

Fraction \frac{-378}{25} can be rewritten as -\frac{378}{25} by extracting the negative sign.

$$-0.8-\frac{378}{25}$$

Convert decimal number -0.8 to fraction -\frac{8}{10}. Reduce the fraction -\frac{8}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{4}{5}-\frac{378}{25}$$

Least common multiple of 5 and 25 is 25. Convert -\frac{4}{5} and \frac{378}{25} to fractions with denominator 25.

$$-\frac{20}{25}-\frac{378}{25}$$

Since -\frac{20}{25} and \frac{378}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20-378}{25}$$

Subtract 378 from -20 to get -398.

$$-\frac{398}{25}$$

Factor

$$-15.92$$