Solve (1/4-1/6)0F(2/3-5/12)*(frac{5}{8}-frac{7}{12})

$$( \frac { 1 } { 4 } - \frac { 1 } { 6 } ) 0 F ( \frac { 2 } { 3 } - \frac { 5 } { 12 } ) \times ( \frac { 5 } { 8 } - \frac { 7 } { 12 } )$$

Evaluate

$$0$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{1}{4} and \frac{1}{6} to fractions with denominator 12.

$$\left(\frac{3}{12}-\frac{2}{12}\right)\times 0F\left(\frac{2}{3}-\frac{5}{12}\right)\left(\frac{5}{8}-\frac{7}{12}\right)$$

Since \frac{3}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{12}\times 0F\left(\frac{2}{3}-\frac{5}{12}\right)\left(\frac{5}{8}-\frac{7}{12}\right)$$

Subtract 2 from 3 to get 1.

$$\frac{1}{12}\times 0F\left(\frac{2}{3}-\frac{5}{12}\right)\left(\frac{5}{8}-\frac{7}{12}\right)$$

Multiply \frac{1}{12} and 0 to get 0.

$$0F\left(\frac{2}{3}-\frac{5}{12}\right)\left(\frac{5}{8}-\frac{7}{12}\right)$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{5}{12} to fractions with denominator 12.

$$0F\left(\frac{8}{12}-\frac{5}{12}\right)\left(\frac{5}{8}-\frac{7}{12}\right)$$

Since \frac{8}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$0F\times \frac{8-5}{12}\left(\frac{5}{8}-\frac{7}{12}\right)$$

Subtract 5 from 8 to get 3.

$$0F\times \frac{3}{12}\left(\frac{5}{8}-\frac{7}{12}\right)$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$0F\times \frac{1}{4}\left(\frac{5}{8}-\frac{7}{12}\right)$$

Multiply 0 and \frac{1}{4} to get 0.

$$0F\left(\frac{5}{8}-\frac{7}{12}\right)$$

Least common multiple of 8 and 12 is 24. Convert \frac{5}{8} and \frac{7}{12} to fractions with denominator 24.

$$0F\left(\frac{15}{24}-\frac{14}{24}\right)$$

Since \frac{15}{24} and \frac{14}{24} have the same denominator, subtract them by subtracting their numerators.

$$0F\times \frac{15-14}{24}$$

Subtract 14 from 15 to get 1.

$$0F\times \frac{1}{24}$$

Multiply 0 and \frac{1}{24} to get 0.

$$0F$$

Anything times zero gives zero.

$$0$$

Factor

$$0$$