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

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

Evaluate

$$-56$$

Solution Steps

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

$$\frac{2}{\frac{21}{28}-\frac{20}{28}+\frac{-3}{14}+\frac{1}{7}}$$

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

$$\frac{2}{\frac{21-20}{28}+\frac{-3}{14}+\frac{1}{7}}$$

Subtract 20 from 21 to get 1.

$$\frac{2}{\frac{1}{28}+\frac{-3}{14}+\frac{1}{7}}$$

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

$$\frac{2}{\frac{1}{28}-\frac{3}{14}+\frac{1}{7}}$$

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

$$\frac{2}{\frac{1}{28}-\frac{6}{28}+\frac{1}{7}}$$

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

$$\frac{2}{\frac{1-6}{28}+\frac{1}{7}}$$

Subtract 6 from 1 to get -5.

$$\frac{2}{-\frac{5}{28}+\frac{1}{7}}$$

Least common multiple of 28 and 7 is 28. Convert -\frac{5}{28} and \frac{1}{7} to fractions with denominator 28.

$$\frac{2}{-\frac{5}{28}+\frac{4}{28}}$$

Since -\frac{5}{28} and \frac{4}{28} have the same denominator, add them by adding their numerators.

$$\frac{2}{\frac{-5+4}{28}}$$

Add -5 and 4 to get -1.

$$\frac{2}{-\frac{1}{28}}$$

Divide 2 by -\frac{1}{28} by multiplying 2 by the reciprocal of -\frac{1}{28}.

$$2\left(-28\right)$$

Multiply 2 and -28 to get -56.

$$-56$$

Factor

$$-56$$