Solve (5/4-11/6)*20/7+7/6

$$( \frac { 5 } { 4 } - \frac { 11 } { 6 } ) \cdot \frac { 20 } { 7 } + \frac { 7 } { 6 }$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{5}{4} and \frac{11}{6} to fractions with denominator 12.

$$\left(\frac{15}{12}-\frac{22}{12}\right)\times \frac{20}{7}+\frac{7}{6}$$

Since \frac{15}{12} and \frac{22}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-22}{12}\times \frac{20}{7}+\frac{7}{6}$$

Subtract 22 from 15 to get -7.

$$-\frac{7}{12}\times \frac{20}{7}+\frac{7}{6}$$

Multiply -\frac{7}{12} times \frac{20}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-7\times 20}{12\times 7}+\frac{7}{6}$$

Do the multiplications in the fraction \frac{-7\times 20}{12\times 7}.

$$\frac{-140}{84}+\frac{7}{6}$$

Reduce the fraction \frac{-140}{84} to lowest terms by extracting and canceling out 28.

$$-\frac{5}{3}+\frac{7}{6}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{5}{3} and \frac{7}{6} to fractions with denominator 6.

$$-\frac{10}{6}+\frac{7}{6}$$

Since -\frac{10}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{-10+7}{6}$$

Add -10 and 7 to get -3.

$$\frac{-3}{6}$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$