Solve -15/11-1/4:(5/6-3/8)

$$- 1 \frac { 5 } { 11 } - \frac { 1 } { 4 } : ( \frac { 5 } { 6 } - \frac { 3 } { 8 } )$$

Evaluate

$$-2$$

Solution Steps

Multiply 1 and 11 to get 11.

$$-\frac{11+5}{11}-\frac{\frac{1}{4}}{\frac{5}{6}-\frac{3}{8}}$$

Add 11 and 5 to get 16.

$$-\frac{16}{11}-\frac{\frac{1}{4}}{\frac{5}{6}-\frac{3}{8}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{3}{8} to fractions with denominator 24.

$$-\frac{16}{11}-\frac{\frac{1}{4}}{\frac{20}{24}-\frac{9}{24}}$$

Since \frac{20}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{16}{11}-\frac{\frac{1}{4}}{\frac{20-9}{24}}$$

Subtract 9 from 20 to get 11.

$$-\frac{16}{11}-\frac{\frac{1}{4}}{\frac{11}{24}}$$

Divide \frac{1}{4} by \frac{11}{24} by multiplying \frac{1}{4} by the reciprocal of \frac{11}{24}.

$$-\frac{16}{11}-\frac{1}{4}\times \frac{24}{11}$$

Multiply \frac{1}{4} times \frac{24}{11} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{16}{11}-\frac{1\times 24}{4\times 11}$$

Do the multiplications in the fraction \frac{1\times 24}{4\times 11}.

$$-\frac{16}{11}-\frac{24}{44}$$

Reduce the fraction \frac{24}{44} to lowest terms by extracting and canceling out 4.

$$-\frac{16}{11}-\frac{6}{11}$$

Since -\frac{16}{11} and \frac{6}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-16-6}{11}$$

Subtract 6 from -16 to get -22.

$$\frac{-22}{11}$$

Divide -22 by 11 to get -2.

$$-2$$

Factor

$$-2$$