Solve -11/2/(frac{3{4}-5/7+-3/14)divfrac{1}{7}}

$$\frac { - \frac { 11 } { 2 } } { ( \frac { 3 } { 4 } - \frac { 5 } { 7 } + \frac { - 3 } { 14 } ) \div \frac { 1 } { 7 } }$$

Evaluate

$$\frac{22}{5}=4.4$$

Solution Steps

Divide -\frac{11}{2} by \frac{\frac{3}{4}-\frac{5}{7}+\frac{-3}{14}}{\frac{1}{7}} by multiplying -\frac{11}{2} by the reciprocal of \frac{\frac{3}{4}-\frac{5}{7}+\frac{-3}{14}}{\frac{1}{7}}.

$$\frac{-11\times \frac{1}{7}}{2\left(\frac{3}{4}-\frac{5}{7}+\frac{-3}{14}\right)}$$

Multiply -11 and \frac{1}{7} to get \frac{-11}{7}.

$$\frac{\frac{-11}{7}}{2\left(\frac{3}{4}-\frac{5}{7}+\frac{-3}{14}\right)}$$

Fraction \frac{-11}{7} can be rewritten as -\frac{11}{7} by extracting the negative sign.

$$\frac{-\frac{11}{7}}{2\left(\frac{3}{4}-\frac{5}{7}+\frac{-3}{14}\right)}$$

Least common multiple of 4 and 7 is 28. Convert \frac{3}{4} and \frac{5}{7} to fractions with denominator 28.

$$\frac{-\frac{11}{7}}{2\left(\frac{21}{28}-\frac{20}{28}+\frac{-3}{14}\right)}$$

Since \frac{21}{28} and \frac{20}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{11}{7}}{2\left(\frac{21-20}{28}+\frac{-3}{14}\right)}$$

Subtract 20 from 21 to get 1.

$$\frac{-\frac{11}{7}}{2\left(\frac{1}{28}+\frac{-3}{14}\right)}$$

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$\frac{-\frac{11}{7}}{2\left(\frac{1}{28}-\frac{3}{14}\right)}$$

Least common multiple of 28 and 14 is 28. Convert \frac{1}{28} and \frac{3}{14} to fractions with denominator 28.

$$\frac{-\frac{11}{7}}{2\left(\frac{1}{28}-\frac{6}{28}\right)}$$

Since \frac{1}{28} and \frac{6}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{11}{7}}{2\times \frac{1-6}{28}}$$

Subtract 6 from 1 to get -5.

$$\frac{-\frac{11}{7}}{2\left(-\frac{5}{28}\right)}$$

Express 2\left(-\frac{5}{28}\right) as a single fraction.

$$\frac{-\frac{11}{7}}{\frac{2\left(-5\right)}{28}}$$

Multiply 2 and -5 to get -10.

$$\frac{-\frac{11}{7}}{\frac{-10}{28}}$$

Reduce the fraction \frac{-10}{28} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{11}{7}}{-\frac{5}{14}}$$

Divide -\frac{11}{7} by -\frac{5}{14} by multiplying -\frac{11}{7} by the reciprocal of -\frac{5}{14}.

$$-\frac{11}{7}\left(-\frac{14}{5}\right)$$

Multiply -\frac{11}{7} times -\frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\left(-14\right)}{7\times 5}$$

Do the multiplications in the fraction \frac{-11\left(-14\right)}{7\times 5}.

$$\frac{154}{35}$$

Reduce the fraction \frac{154}{35} to lowest terms by extracting and canceling out 7.

$$\frac{22}{5}$$

Factor

$$\frac{2 \cdot 11}{5} = 4\frac{2}{5} = 4.4$$