Solve (5/6-2/3):8/9

$$( \frac { 5 } { 6 } - \frac { 2 } { 3 } ) : \frac { 8 } { 9 }$$

Evaluate

$$\frac{3}{16}=0.1875$$

Solution Steps

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

$$\frac{\frac{5}{6}-\frac{4}{6}}{\frac{8}{9}}$$

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

$$\frac{\frac{5-4}{6}}{\frac{8}{9}}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{1}{6}}{\frac{8}{9}}$$

Divide \frac{1}{6} by \frac{8}{9} by multiplying \frac{1}{6} by the reciprocal of \frac{8}{9}.

$$\frac{1}{6}\times \frac{9}{8}$$

Multiply \frac{1}{6} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 9}{6\times 8}$$

Do the multiplications in the fraction \frac{1\times 9}{6\times 8}.

$$\frac{9}{48}$$

Reduce the fraction \frac{9}{48} to lowest terms by extracting and canceling out 3.

$$\frac{3}{16}$$

Factor

$$\frac{3}{2 ^ {4}} = 0.1875$$