Solve (13/4-7/12-7/8)*(-11/7)-(-4.2)*frac{3}{7}*(-frac{5}{6})

$$( 1 \frac { 3 } { 4 } - \frac { 7 } { 12 } - \frac { 7 } { 8 } ) \times ( - 1 \frac { 1 } { 7 } ) - ( - 4.2 ) \times \frac { 3 } { 7 } \times ( - \frac { 5 } { 6 } )$$

Evaluate

$$-\frac{11}{6}\approx -1.833333333$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\left(\frac{4+3}{4}-\frac{7}{12}-\frac{7}{8}\right)\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Add 4 and 3 to get 7.

$$\left(\frac{7}{4}-\frac{7}{12}-\frac{7}{8}\right)\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Least common multiple of 4 and 12 is 12. Convert \frac{7}{4} and \frac{7}{12} to fractions with denominator 12.

$$\left(\frac{21}{12}-\frac{7}{12}-\frac{7}{8}\right)\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Since \frac{21}{12} and \frac{7}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{21-7}{12}-\frac{7}{8}\right)\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Subtract 7 from 21 to get 14.

$$\left(\frac{14}{12}-\frac{7}{8}\right)\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Reduce the fraction \frac{14}{12} to lowest terms by extracting and canceling out 2.

$$\left(\frac{7}{6}-\frac{7}{8}\right)\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Least common multiple of 6 and 8 is 24. Convert \frac{7}{6} and \frac{7}{8} to fractions with denominator 24.

$$\left(\frac{28}{24}-\frac{21}{24}\right)\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Since \frac{28}{24} and \frac{21}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-21}{24}\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Subtract 21 from 28 to get 7.

$$\frac{7}{24}\left(-\frac{1\times 7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Multiply 1 and 7 to get 7.

$$\frac{7}{24}\left(-\frac{7+1}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Add 7 and 1 to get 8.

$$\frac{7}{24}\left(-\frac{8}{7}\right)-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Multiply \frac{7}{24} times -\frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-8\right)}{24\times 7}-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Cancel out 7 in both numerator and denominator.

$$\frac{-8}{24}-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Reduce the fraction \frac{-8}{24} to lowest terms by extracting and canceling out 8.

$$-\frac{1}{3}-\left(-4.2\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

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.

$$-\frac{1}{3}-\left(-\frac{21}{5}\times \frac{3}{7}\left(-\frac{5}{6}\right)\right)$$

Multiply -\frac{21}{5} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{3}-\frac{-21\times 3}{5\times 7}\left(-\frac{5}{6}\right)$$

Do the multiplications in the fraction \frac{-21\times 3}{5\times 7}.

$$-\frac{1}{3}-\frac{-63}{35}\left(-\frac{5}{6}\right)$$

Reduce the fraction \frac{-63}{35} to lowest terms by extracting and canceling out 7.

$$-\frac{1}{3}-\left(-\frac{9}{5}\left(-\frac{5}{6}\right)\right)$$

Multiply -\frac{9}{5} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{3}-\frac{-9\left(-5\right)}{5\times 6}$$

Do the multiplications in the fraction \frac{-9\left(-5\right)}{5\times 6}.

$$-\frac{1}{3}-\frac{45}{30}$$

Reduce the fraction \frac{45}{30} to lowest terms by extracting and canceling out 15.

$$-\frac{1}{3}-\frac{3}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{1}{3} and \frac{3}{2} to fractions with denominator 6.

$$-\frac{2}{6}-\frac{9}{6}$$

Since -\frac{2}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2-9}{6}$$

Subtract 9 from -2 to get -11.

$$-\frac{11}{6}$$

Factor

$$-\frac{11}{6} = -1\frac{5}{6} = -1.8333333333333333$$