Solve 11/12-5/8/frac{1{6}-3/4}*(frac{3}{2}-frac{1}{4})

$$\frac{ \frac{ 11 }{ 12 } - \frac{ 5 }{ 8 } }{ \frac{ 1 }{ 6 } - \frac{ 3 }{ 4 } } \times ( \frac{ 3 }{ 2 } - \frac{ 1 }{ 4 } )$$

Evaluate

$$-\frac{5}{8}=-0.625$$

Solution Steps

Least common multiple of 12 and 8 is 24. Convert \frac{11}{12} and \frac{5}{8} to fractions with denominator 24.

$$\frac{\frac{22}{24}-\frac{15}{24}}{\frac{1}{6}-\frac{3}{4}}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Since \frac{22}{24} and \frac{15}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{22-15}{24}}{\frac{1}{6}-\frac{3}{4}}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Subtract 15 from 22 to get 7.

$$\frac{\frac{7}{24}}{\frac{1}{6}-\frac{3}{4}}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{7}{24}}{\frac{2}{12}-\frac{9}{12}}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Since \frac{2}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{24}}{\frac{2-9}{12}}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Subtract 9 from 2 to get -7.

$$\frac{\frac{7}{24}}{-\frac{7}{12}}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Divide \frac{7}{24} by -\frac{7}{12} by multiplying \frac{7}{24} by the reciprocal of -\frac{7}{12}.

$$\frac{7}{24}\left(-\frac{12}{7}\right)\left(\frac{3}{2}-\frac{1}{4}\right)$$

Multiply \frac{7}{24} times -\frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-12\right)}{24\times 7}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Cancel out 7 in both numerator and denominator.

$$\frac{-12}{24}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Reduce the fraction \frac{-12}{24} to lowest terms by extracting and canceling out 12.

$$-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$-\frac{1}{2}\left(\frac{6}{4}-\frac{1}{4}\right)$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}\times \frac{6-1}{4}$$

Subtract 1 from 6 to get 5.

$$-\frac{1}{2}\times \frac{5}{4}$$

Multiply -\frac{1}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5}{2\times 4}$$

Do the multiplications in the fraction \frac{-5}{2\times 4}.

$$\frac{-5}{8}$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$-\frac{5}{8}$$

Factor

$$-\frac{5}{8} = -0.625$$