Solve (-11/6-7/8)div7/12+31/3

$$( - 1 \frac { 1 } { 6 } - \frac { 7 } { 8 } ) \div \frac { 7 } { 12 } + 3 \frac { 1 } { 3 }$$

Evaluate

$$-\frac{1}{6}\approx -0.166666667$$

Solution Steps

Multiply 1 and 6 to get 6.

$$\frac{-\frac{6+1}{6}-\frac{7}{8}}{\frac{7}{12}}+\frac{3\times 3+1}{3}$$

Add 6 and 1 to get 7.

$$\frac{-\frac{7}{6}-\frac{7}{8}}{\frac{7}{12}}+\frac{3\times 3+1}{3}$$

Least common multiple of 6 and 8 is 24. Convert -\frac{7}{6} and \frac{7}{8} to fractions with denominator 24.

$$\frac{-\frac{28}{24}-\frac{21}{24}}{\frac{7}{12}}+\frac{3\times 3+1}{3}$$

Since -\frac{28}{24} and \frac{21}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-28-21}{24}}{\frac{7}{12}}+\frac{3\times 3+1}{3}$$

Subtract 21 from -28 to get -49.

$$\frac{-\frac{49}{24}}{\frac{7}{12}}+\frac{3\times 3+1}{3}$$

Divide -\frac{49}{24} by \frac{7}{12} by multiplying -\frac{49}{24} by the reciprocal of \frac{7}{12}.

$$-\frac{49}{24}\times \frac{12}{7}+\frac{3\times 3+1}{3}$$

Multiply -\frac{49}{24} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-49\times 12}{24\times 7}+\frac{3\times 3+1}{3}$$

Do the multiplications in the fraction \frac{-49\times 12}{24\times 7}.

$$\frac{-588}{168}+\frac{3\times 3+1}{3}$$

Reduce the fraction \frac{-588}{168} to lowest terms by extracting and canceling out 84.

$$-\frac{7}{2}+\frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$-\frac{7}{2}+\frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$-\frac{7}{2}+\frac{10}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{7}{2} and \frac{10}{3} to fractions with denominator 6.

$$-\frac{21}{6}+\frac{20}{6}$$

Since -\frac{21}{6} and \frac{20}{6} have the same denominator, add them by adding their numerators.

$$\frac{-21+20}{6}$$

Add -21 and 20 to get -1.

$$-\frac{1}{6}$$

Factor

$$-\frac{1}{6} = -0.16666666666666666$$