Solve 1/4-3/2/frac{5{6}+1/3}

$$\frac { \frac { 1 } { 4 } - \frac { 3 } { 2 } } { \frac { 5 } { 6 } + \frac { 1 } { 3 } }$$

Evaluate

$$-\frac{15}{14}\approx -1.071428571$$

Solution Steps

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

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

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

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

Subtract 6 from 1 to get -5.

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

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{-\frac{5}{4}}{\frac{5}{6}+\frac{2}{6}}$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{5}{4}}{\frac{5+2}{6}}$$

Add 5 and 2 to get 7.

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

Divide -\frac{5}{4} by \frac{7}{6} by multiplying -\frac{5}{4} by the reciprocal of \frac{7}{6}.

$$-\frac{5}{4}\times \frac{6}{7}$$

Multiply -\frac{5}{4} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 6}{4\times 7}$$

Do the multiplications in the fraction \frac{-5\times 6}{4\times 7}.

$$\frac{-30}{28}$$

Reduce the fraction \frac{-30}{28} to lowest terms by extracting and canceling out 2.

$$-\frac{15}{14}$$

Factor

$$-\frac{15}{14} = -1\frac{1}{14} = -1.0714285714285714$$