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

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

Evaluate

$$0$$

Solution Steps

Multiply \frac{2}{7} times -\frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\left(-5\right)}{7\times 12}.

$$\frac{-10}{84}-\frac{5}{7}\times \frac{5}{12}-\frac{5}{3}\left(-\frac{1}{4}\right)$$

Reduce the fraction \frac{-10}{84} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{42}-\frac{5}{7}\times \frac{5}{12}-\frac{5}{3}\left(-\frac{1}{4}\right)$$

Multiply \frac{5}{7} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{42}-\frac{5\times 5}{7\times 12}-\frac{5}{3}\left(-\frac{1}{4}\right)$$

Do the multiplications in the fraction \frac{5\times 5}{7\times 12}.

$$-\frac{5}{42}-\frac{25}{84}-\frac{5}{3}\left(-\frac{1}{4}\right)$$

Least common multiple of 42 and 84 is 84. Convert -\frac{5}{42} and \frac{25}{84} to fractions with denominator 84.

$$-\frac{10}{84}-\frac{25}{84}-\frac{5}{3}\left(-\frac{1}{4}\right)$$

Since -\frac{10}{84} and \frac{25}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-10-25}{84}-\frac{5}{3}\left(-\frac{1}{4}\right)$$

Subtract 25 from -10 to get -35.

$$\frac{-35}{84}-\frac{5}{3}\left(-\frac{1}{4}\right)$$

Reduce the fraction \frac{-35}{84} to lowest terms by extracting and canceling out 7.

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

Multiply -\frac{5}{3} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-5\left(-1\right)}{3\times 4}.

$$-\frac{5}{12}+\frac{5}{12}$$

Add -\frac{5}{12} and \frac{5}{12} to get 0.

$$0$$

Factor

$$0$$