Solve (1/7-1)*(1/3-3/2)

$$( \frac { 1 } { 7 } - 1 ) \cdot ( \frac { 1 } { 3 } - \frac { 3 } { 2 } )$$

Evaluate

$$1$$

Solution Steps

Convert 1 to fraction \frac{7}{7}.

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

Since \frac{1}{7} and \frac{7}{7} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 7 from 1 to get -6.

$$-\frac{6}{7}\left(\frac{1}{3}-\frac{3}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{3}{2} to fractions with denominator 6.

$$-\frac{6}{7}\left(\frac{2}{6}-\frac{9}{6}\right)$$

Since \frac{2}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{6}{7}\times \frac{2-9}{6}$$

Subtract 9 from 2 to get -7.

$$-\frac{6}{7}\left(-\frac{7}{6}\right)$$

Multiply -\frac{6}{7} times -\frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-6\left(-7\right)}{7\times 6}$$

Do the multiplications in the fraction \frac{-6\left(-7\right)}{7\times 6}.

$$\frac{42}{42}$$

Divide 42 by 42 to get 1.

$$1$$

Factor

$$1$$