Solve {11/16div(5/6+2/3)}-1/3

$$\{ \frac { 11 } { 16 } \div ( \frac { 5 } { 6 } + \frac { 2 } { 3 } ) \} - \frac { 1 } { 3 }$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{2}{3} to fractions with denominator 6.

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

Since \frac{5}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

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

Add 5 and 4 to get 9.

$$\frac{\frac{11}{16}}{\frac{9}{6}}-\frac{1}{3}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{11}{16}}{\frac{3}{2}}-\frac{1}{3}$$

Divide \frac{11}{16} by \frac{3}{2} by multiplying \frac{11}{16} by the reciprocal of \frac{3}{2}.

$$\frac{11}{16}\times \frac{2}{3}-\frac{1}{3}$$

Multiply \frac{11}{16} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 2}{16\times 3}-\frac{1}{3}$$

Do the multiplications in the fraction \frac{11\times 2}{16\times 3}.

$$\frac{22}{48}-\frac{1}{3}$$

Reduce the fraction \frac{22}{48} to lowest terms by extracting and canceling out 2.

$$\frac{11}{24}-\frac{1}{3}$$

Least common multiple of 24 and 3 is 24. Convert \frac{11}{24} and \frac{1}{3} to fractions with denominator 24.

$$\frac{11}{24}-\frac{8}{24}$$

Since \frac{11}{24} and \frac{8}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-8}{24}$$

Subtract 8 from 11 to get 3.

$$\frac{3}{24}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$