Solve -2/5-((1/3+1/-4):(1/15)+frac{1}{10})=

$$\frac { - 2 } { 5 } - ( ( \frac { 1 } { 3 } + \frac { 1 } { - 4 } ) : ( \frac { 1 } { 15 } ) + \frac { 1 } { 10 } ) =$$

Evaluate

$$-\frac{7}{4}=-1.75$$

Solution Steps

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$-\frac{2}{5}-\left(\frac{\frac{1}{3}+\frac{1}{-4}}{\frac{1}{15}}+\frac{1}{10}\right)$$

Fraction \frac{1}{-4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$-\frac{2}{5}-\left(\frac{\frac{1}{3}-\frac{1}{4}}{\frac{1}{15}}+\frac{1}{10}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{2}{5}-\left(\frac{\frac{4}{12}-\frac{3}{12}}{\frac{1}{15}}+\frac{1}{10}\right)$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{5}-\left(\frac{\frac{4-3}{12}}{\frac{1}{15}}+\frac{1}{10}\right)$$

Subtract 3 from 4 to get 1.

$$-\frac{2}{5}-\left(\frac{\frac{1}{12}}{\frac{1}{15}}+\frac{1}{10}\right)$$

Divide \frac{1}{12} by \frac{1}{15} by multiplying \frac{1}{12} by the reciprocal of \frac{1}{15}.

$$-\frac{2}{5}-\left(\frac{1}{12}\times 15+\frac{1}{10}\right)$$

Multiply \frac{1}{12} and 15 to get \frac{15}{12}.

$$-\frac{2}{5}-\left(\frac{15}{12}+\frac{1}{10}\right)$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{2}{5}-\left(\frac{5}{4}+\frac{1}{10}\right)$$

Least common multiple of 4 and 10 is 20. Convert \frac{5}{4} and \frac{1}{10} to fractions with denominator 20.

$$-\frac{2}{5}-\left(\frac{25}{20}+\frac{2}{20}\right)$$

Since \frac{25}{20} and \frac{2}{20} have the same denominator, add them by adding their numerators.

$$-\frac{2}{5}-\frac{25+2}{20}$$

Add 25 and 2 to get 27.

$$-\frac{2}{5}-\frac{27}{20}$$

Least common multiple of 5 and 20 is 20. Convert -\frac{2}{5} and \frac{27}{20} to fractions with denominator 20.

$$-\frac{8}{20}-\frac{27}{20}$$

Since -\frac{8}{20} and \frac{27}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-8-27}{20}$$

Subtract 27 from -8 to get -35.

$$\frac{-35}{20}$$

Reduce the fraction \frac{-35}{20} to lowest terms by extracting and canceling out 5.

$$-\frac{7}{4}$$

Factor

$$-\frac{7}{4} = -1\frac{3}{4} = -1.75$$