Solve 2/7*-3/5-1/12-3/5*frac{4}{7}

$$\frac { 2 } { 7 } \times \frac { - 3 } { 5 } - \frac { 1 } { 12 } - \frac { 3 } { 5 } \times \frac { 4 } { 7 }$$

Evaluate

$$-\frac{251}{420}\approx -0.597619048$$

Solution Steps

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$\frac{2}{7}\left(-\frac{3}{5}\right)-\frac{1}{12}-\frac{3}{5}\times \frac{4}{7}$$

Multiply \frac{2}{7} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-3\right)}{7\times 5}-\frac{1}{12}-\frac{3}{5}\times \frac{4}{7}$$

Do the multiplications in the fraction \frac{2\left(-3\right)}{7\times 5}.

$$\frac{-6}{35}-\frac{1}{12}-\frac{3}{5}\times \frac{4}{7}$$

Fraction \frac{-6}{35} can be rewritten as -\frac{6}{35} by extracting the negative sign.

$$-\frac{6}{35}-\frac{1}{12}-\frac{3}{5}\times \frac{4}{7}$$

Least common multiple of 35 and 12 is 420. Convert -\frac{6}{35} and \frac{1}{12} to fractions with denominator 420.

$$-\frac{72}{420}-\frac{35}{420}-\frac{3}{5}\times \frac{4}{7}$$

Since -\frac{72}{420} and \frac{35}{420} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-72-35}{420}-\frac{3}{5}\times \frac{4}{7}$$

Subtract 35 from -72 to get -107.

$$-\frac{107}{420}-\frac{3}{5}\times \frac{4}{7}$$

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

$$-\frac{107}{420}-\frac{3\times 4}{5\times 7}$$

Do the multiplications in the fraction \frac{3\times 4}{5\times 7}.

$$-\frac{107}{420}-\frac{12}{35}$$

Least common multiple of 420 and 35 is 420. Convert -\frac{107}{420} and \frac{12}{35} to fractions with denominator 420.

$$-\frac{107}{420}-\frac{144}{420}$$

Since -\frac{107}{420} and \frac{144}{420} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-107-144}{420}$$

Subtract 144 from -107 to get -251.

$$-\frac{251}{420}$$

Factor

$$-\frac{251}{420} = -0.5976190476190476$$