Solve 5/7:(1/2-10/11)

$$\frac { 5 } { 7 } : ( \frac { 1 } { 2 } - \frac { 10 } { 11 } )$$

Evaluate

$$-\frac{110}{63}\approx -1.746031746$$

Solution Steps

Least common multiple of 2 and 11 is 22. Convert \frac{1}{2} and \frac{10}{11} to fractions with denominator 22.

$$\frac{\frac{5}{7}}{\frac{11}{22}-\frac{20}{22}}$$

Since \frac{11}{22} and \frac{20}{22} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{7}}{\frac{11-20}{22}}$$

Subtract 20 from 11 to get -9.

$$\frac{\frac{5}{7}}{-\frac{9}{22}}$$

Divide \frac{5}{7} by -\frac{9}{22} by multiplying \frac{5}{7} by the reciprocal of -\frac{9}{22}.

$$\frac{5}{7}\left(-\frac{22}{9}\right)$$

Multiply \frac{5}{7} times -\frac{22}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-22\right)}{7\times 9}$$

Do the multiplications in the fraction \frac{5\left(-22\right)}{7\times 9}.

$$\frac{-110}{63}$$

Fraction \frac{-110}{63} can be rewritten as -\frac{110}{63} by extracting the negative sign.

$$-\frac{110}{63}$$

Factor

$$-\frac{110}{63} = -1\frac{47}{63} = -1.746031746031746$$