Solve 1div[(3/2+3/-4)-5/7]

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

Evaluate

$$28$$

Solution Steps

Fraction \frac{3}{-4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{1}{\frac{3}{2}-\frac{3}{4}-\frac{5}{7}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{1}{\frac{6}{4}-\frac{3}{4}-\frac{5}{7}}$$

Since \frac{6}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{6-3}{4}-\frac{5}{7}}$$

Subtract 3 from 6 to get 3.

$$\frac{1}{\frac{3}{4}-\frac{5}{7}}$$

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

$$\frac{1}{\frac{21}{28}-\frac{20}{28}}$$

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

$$\frac{1}{\frac{21-20}{28}}$$

Subtract 20 from 21 to get 1.

$$\frac{1}{\frac{1}{28}}$$

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

$$1\times 28$$

Multiply 1 and 28 to get 28.

$$28$$

Factor

$$2^{2}\times 7$$