Solve +10/11:(-1/3-1/2)div5/4=

$$+ \frac { 10 } { 11 } : ( - \frac { 1 } { 3 } - \frac { 1 } { 2 } ) \div \frac { 5 } { 4 } =$$

Evaluate

$$-\frac{48}{55}\approx -0.872727273$$

Solution Steps

Divide \frac{\frac{10}{11}}{-\frac{1}{3}-\frac{1}{2}} by \frac{5}{4} by multiplying \frac{\frac{10}{11}}{-\frac{1}{3}-\frac{1}{2}} by the reciprocal of \frac{5}{4}.

$$\frac{\frac{10}{11}\times 4}{\left(-\frac{1}{3}-\frac{1}{2}\right)\times 5}$$

Express \frac{10}{11}\times 4 as a single fraction.

$$\frac{\frac{10\times 4}{11}}{\left(-\frac{1}{3}-\frac{1}{2}\right)\times 5}$$

Multiply 10 and 4 to get 40.

$$\frac{\frac{40}{11}}{\left(-\frac{1}{3}-\frac{1}{2}\right)\times 5}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{40}{11}}{\left(-\frac{2}{6}-\frac{3}{6}\right)\times 5}$$

Since -\frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{40}{11}}{\frac{-2-3}{6}\times 5}$$

Subtract 3 from -2 to get -5.

$$\frac{\frac{40}{11}}{-\frac{5}{6}\times 5}$$

Express -\frac{5}{6}\times 5 as a single fraction.

$$\frac{\frac{40}{11}}{\frac{-5\times 5}{6}}$$

Multiply -5 and 5 to get -25.

$$\frac{\frac{40}{11}}{\frac{-25}{6}}$$

Fraction \frac{-25}{6} can be rewritten as -\frac{25}{6} by extracting the negative sign.

$$\frac{\frac{40}{11}}{-\frac{25}{6}}$$

Divide \frac{40}{11} by -\frac{25}{6} by multiplying \frac{40}{11} by the reciprocal of -\frac{25}{6}.

$$\frac{40}{11}\left(-\frac{6}{25}\right)$$

Multiply \frac{40}{11} times -\frac{6}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{40\left(-6\right)}{11\times 25}$$

Do the multiplications in the fraction \frac{40\left(-6\right)}{11\times 25}.

$$\frac{-240}{275}$$

Reduce the fraction \frac{-240}{275} to lowest terms by extracting and canceling out 5.

$$-\frac{48}{55}$$

Factor

$$-\frac{48}{55} = -0.8727272727272727$$