Solve (7)-14/21div(-11/14)*1/2+(-1/3)

$$( 7 ) - 1 \frac { 4 } { 21 } \div ( - 1 \frac { 1 } { 14 } ) \times \frac { 1 } { 2 } + ( - \frac { 1 } { 3 } )$$

Evaluate

$$\frac{65}{9}\approx 7.222222222$$

Solution Steps

Multiply 1 and 21 to get 21.

$$7-\frac{\frac{21+4}{21}}{-\frac{1\times 14+1}{14}}\times \frac{1}{2}-\frac{1}{3}$$

Add 21 and 4 to get 25.

$$7-\frac{\frac{25}{21}}{-\frac{1\times 14+1}{14}}\times \frac{1}{2}-\frac{1}{3}$$

Multiply 1 and 14 to get 14.

$$7-\frac{\frac{25}{21}}{-\frac{14+1}{14}}\times \frac{1}{2}-\frac{1}{3}$$

Add 14 and 1 to get 15.

$$7-\frac{\frac{25}{21}}{-\frac{15}{14}}\times \frac{1}{2}-\frac{1}{3}$$

Divide \frac{25}{21} by -\frac{15}{14} by multiplying \frac{25}{21} by the reciprocal of -\frac{15}{14}.

$$7-\frac{25}{21}\left(-\frac{14}{15}\right)\times \frac{1}{2}-\frac{1}{3}$$

Multiply \frac{25}{21} times -\frac{14}{15} by multiplying numerator times numerator and denominator times denominator.

$$7-\frac{25\left(-14\right)}{21\times 15}\times \frac{1}{2}-\frac{1}{3}$$

Do the multiplications in the fraction \frac{25\left(-14\right)}{21\times 15}.

$$7-\frac{-350}{315}\times \frac{1}{2}-\frac{1}{3}$$

Reduce the fraction \frac{-350}{315} to lowest terms by extracting and canceling out 35.

$$7-\left(-\frac{10}{9}\times \frac{1}{2}\right)-\frac{1}{3}$$

Multiply -\frac{10}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-10}{9\times 2}.

$$7-\frac{-10}{18}-\frac{1}{3}$$

Reduce the fraction \frac{-10}{18} to lowest terms by extracting and canceling out 2.

$$7-\left(-\frac{5}{9}\right)-\frac{1}{3}$$

The opposite of -\frac{5}{9} is \frac{5}{9}.

$$7+\frac{5}{9}-\frac{1}{3}$$

Convert 7 to fraction \frac{63}{9}.

$$\frac{63}{9}+\frac{5}{9}-\frac{1}{3}$$

Since \frac{63}{9} and \frac{5}{9} have the same denominator, add them by adding their numerators.

$$\frac{63+5}{9}-\frac{1}{3}$$

Add 63 and 5 to get 68.

$$\frac{68}{9}-\frac{1}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{68}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{68}{9}-\frac{3}{9}$$

Since \frac{68}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{68-3}{9}$$

Subtract 3 from 68 to get 65.

$$\frac{65}{9}$$

Factor

$$\frac{5 \cdot 13}{3 ^ {2}} = 7\frac{2}{9} = 7.222222222222222$$