Solve 3/5*(-1/2)-5/6+3/7div(-frac{5}{4})

$$\frac { 3 } { 5 } \cdot ( - \frac { 1 } { 2 } ) - \frac { 5 } { 6 } + \frac { 3 } { 7 } \div ( - \frac { 5 } { 4 } )$$

Evaluate

$$-\frac{31}{21}\approx -1.476190476$$

Solution Steps

Multiply \frac{3}{5} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-1\right)}{5\times 2}-\frac{5}{6}+\frac{\frac{3}{7}}{-\frac{5}{4}}$$

Do the multiplications in the fraction \frac{3\left(-1\right)}{5\times 2}.

$$\frac{-3}{10}-\frac{5}{6}+\frac{\frac{3}{7}}{-\frac{5}{4}}$$

Fraction \frac{-3}{10} can be rewritten as -\frac{3}{10} by extracting the negative sign.

$$-\frac{3}{10}-\frac{5}{6}+\frac{\frac{3}{7}}{-\frac{5}{4}}$$

Least common multiple of 10 and 6 is 30. Convert -\frac{3}{10} and \frac{5}{6} to fractions with denominator 30.

$$-\frac{9}{30}-\frac{25}{30}+\frac{\frac{3}{7}}{-\frac{5}{4}}$$

Since -\frac{9}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-25}{30}+\frac{\frac{3}{7}}{-\frac{5}{4}}$$

Subtract 25 from -9 to get -34.

$$\frac{-34}{30}+\frac{\frac{3}{7}}{-\frac{5}{4}}$$

Reduce the fraction \frac{-34}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{17}{15}+\frac{\frac{3}{7}}{-\frac{5}{4}}$$

Divide \frac{3}{7} by -\frac{5}{4} by multiplying \frac{3}{7} by the reciprocal of -\frac{5}{4}.

$$-\frac{17}{15}+\frac{3}{7}\left(-\frac{4}{5}\right)$$

Multiply \frac{3}{7} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{17}{15}+\frac{3\left(-4\right)}{7\times 5}$$

Do the multiplications in the fraction \frac{3\left(-4\right)}{7\times 5}.

$$-\frac{17}{15}+\frac{-12}{35}$$

Fraction \frac{-12}{35} can be rewritten as -\frac{12}{35} by extracting the negative sign.

$$-\frac{17}{15}-\frac{12}{35}$$

Least common multiple of 15 and 35 is 105. Convert -\frac{17}{15} and \frac{12}{35} to fractions with denominator 105.

$$-\frac{119}{105}-\frac{36}{105}$$

Since -\frac{119}{105} and \frac{36}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-119-36}{105}$$

Subtract 36 from -119 to get -155.

$$\frac{-155}{105}$$

Reduce the fraction \frac{-155}{105} to lowest terms by extracting and canceling out 5.

$$-\frac{31}{21}$$

Factor

$$-\frac{31}{21} = -1\frac{10}{21} = -1.4761904761904763$$