Solve {l}{2/5*3/7-1/14-9/7*frac{5}{5}}{-3quad1quad3quad3quad2}

$$\left. \begin{array} { l } { \frac { 2 } { 5 } \times \frac { 3 } { 7 } - \frac { 1 } { 14 } - \frac { 9 } { 7 } \times \frac { 5 } { 5 } } \\ { - 3 \quad 1 \quad 3 \quad 3 \quad 2 } \end{array} \right.$$

Evaluate

$$-\frac{3863}{70}\approx -55.185714286$$

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{2}{5}\times \frac{3}{7}-\frac{1}{14}-\frac{9}{7}\times 1-3\times 1\times 3\times 3\times 2$$

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

$$\frac{2\times 3}{5\times 7}-\frac{1}{14}-\frac{9}{7}\times 1-3\times 1\times 3\times 3\times 2$$

Do the multiplications in the fraction \frac{2\times 3}{5\times 7}.

$$\frac{6}{35}-\frac{1}{14}-\frac{9}{7}\times 1-3\times 1\times 3\times 3\times 2$$

Least common multiple of 35 and 14 is 70. Convert \frac{6}{35} and \frac{1}{14} to fractions with denominator 70.

$$\frac{12}{70}-\frac{5}{70}-\frac{9}{7}\times 1-3\times 1\times 3\times 3\times 2$$

Since \frac{12}{70} and \frac{5}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-5}{70}-\frac{9}{7}\times 1-3\times 1\times 3\times 3\times 2$$

Subtract 5 from 12 to get 7.

$$\frac{7}{70}-\frac{9}{7}\times 1-3\times 1\times 3\times 3\times 2$$

Reduce the fraction \frac{7}{70} to lowest terms by extracting and canceling out 7.

$$\frac{1}{10}-\frac{9}{7}\times 1-3\times 1\times 3\times 3\times 2$$

Multiply \frac{9}{7} and 1 to get \frac{9}{7}.

$$\frac{1}{10}-\frac{9}{7}-3\times 1\times 3\times 3\times 2$$

Least common multiple of 10 and 7 is 70. Convert \frac{1}{10} and \frac{9}{7} to fractions with denominator 70.

$$\frac{7}{70}-\frac{90}{70}-3\times 1\times 3\times 3\times 2$$

Since \frac{7}{70} and \frac{90}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-90}{70}-3\times 1\times 3\times 3\times 2$$

Subtract 90 from 7 to get -83.

$$-\frac{83}{70}-3\times 1\times 3\times 3\times 2$$

Multiply 3 and 1 to get 3.

$$-\frac{83}{70}-3\times 3\times 3\times 2$$

Multiply 3 and 3 to get 9.

$$-\frac{83}{70}-9\times 3\times 2$$

Multiply 9 and 3 to get 27.

$$-\frac{83}{70}-27\times 2$$

Multiply 27 and 2 to get 54.

$$-\frac{83}{70}-54$$

Convert 54 to fraction \frac{3780}{70}.

$$-\frac{83}{70}-\frac{3780}{70}$$

Since -\frac{83}{70} and \frac{3780}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-83-3780}{70}$$

Subtract 3780 from -83 to get -3863.

$$-\frac{3863}{70}$$

Factor

$$-\frac{3863}{70} = -55\frac{13}{70} = -55.18571428571428$$