Solve 31/6*(31/7-71/3)*6/19div1frac{1}{21}

$$3 \frac { 1 } { 6 } \times ( 3 \frac { 1 } { 7 } - 7 \frac { 1 } { 3 } ) \times \frac { 6 } { 19 } \div 1 \frac { 1 } { 21 }$$

Evaluate

$$-4$$

Solution Steps

Multiply 3 and 6 to get 18.

$$\frac{\frac{18+1}{6}\left(\frac{3\times 7+1}{7}-\frac{7\times 3+1}{3}\right)\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Add 18 and 1 to get 19.

$$\frac{\frac{19}{6}\left(\frac{3\times 7+1}{7}-\frac{7\times 3+1}{3}\right)\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Multiply 3 and 7 to get 21.

$$\frac{\frac{19}{6}\left(\frac{21+1}{7}-\frac{7\times 3+1}{3}\right)\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Add 21 and 1 to get 22.

$$\frac{\frac{19}{6}\left(\frac{22}{7}-\frac{7\times 3+1}{3}\right)\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Multiply 7 and 3 to get 21.

$$\frac{\frac{19}{6}\left(\frac{22}{7}-\frac{21+1}{3}\right)\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Add 21 and 1 to get 22.

$$\frac{\frac{19}{6}\left(\frac{22}{7}-\frac{22}{3}\right)\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Least common multiple of 7 and 3 is 21. Convert \frac{22}{7} and \frac{22}{3} to fractions with denominator 21.

$$\frac{\frac{19}{6}\left(\frac{66}{21}-\frac{154}{21}\right)\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Since \frac{66}{21} and \frac{154}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{6}\times \frac{66-154}{21}\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Subtract 154 from 66 to get -88.

$$\frac{\frac{19}{6}\left(-\frac{88}{21}\right)\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Multiply \frac{19}{6} times -\frac{88}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{19\left(-88\right)}{6\times 21}\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Do the multiplications in the fraction \frac{19\left(-88\right)}{6\times 21}.

$$\frac{\frac{-1672}{126}\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Reduce the fraction \frac{-1672}{126} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{836}{63}\times \frac{6}{19}}{\frac{1\times 21+1}{21}}$$

Multiply -\frac{836}{63} times \frac{6}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-836\times 6}{63\times 19}}{\frac{1\times 21+1}{21}}$$

Do the multiplications in the fraction \frac{-836\times 6}{63\times 19}.

$$\frac{\frac{-5016}{1197}}{\frac{1\times 21+1}{21}}$$

Reduce the fraction \frac{-5016}{1197} to lowest terms by extracting and canceling out 57.

$$\frac{-\frac{88}{21}}{\frac{1\times 21+1}{21}}$$

Multiply 1 and 21 to get 21.

$$\frac{-\frac{88}{21}}{\frac{21+1}{21}}$$

Add 21 and 1 to get 22.

$$\frac{-\frac{88}{21}}{\frac{22}{21}}$$

Divide -\frac{88}{21} by \frac{22}{21} by multiplying -\frac{88}{21} by the reciprocal of \frac{22}{21}.

$$-\frac{88}{21}\times \frac{21}{22}$$

Multiply -\frac{88}{21} times \frac{21}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-88\times 21}{21\times 22}$$

Cancel out 21 in both numerator and denominator.

$$\frac{-88}{22}$$

Divide -88 by 22 to get -4.

$$-4$$

Factor

$$-4$$