Solve 5/8-1/4*(8/9div2/3)

$$\frac { 5 } { 8 } - \frac { 1 } { 4 } \times ( \frac { 8 } { 9 } \div \frac { 2 } { 3 } )$$

Evaluate

$$\frac{7}{24}\approx 0.291666667$$

Solution Steps

Divide \frac{8}{9} by \frac{2}{3} by multiplying \frac{8}{9} by the reciprocal of \frac{2}{3}.

$$\frac{5}{8}-\frac{1}{4}\times \frac{8}{9}\times \frac{3}{2}$$

Multiply \frac{8}{9} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{8}-\frac{1}{4}\times \frac{8\times 3}{9\times 2}$$

Do the multiplications in the fraction \frac{8\times 3}{9\times 2}.

$$\frac{5}{8}-\frac{1}{4}\times \frac{24}{18}$$

Reduce the fraction \frac{24}{18} to lowest terms by extracting and canceling out 6.

$$\frac{5}{8}-\frac{1}{4}\times \frac{4}{3}$$

Multiply \frac{1}{4} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{8}-\frac{1\times 4}{4\times 3}$$

Cancel out 4 in both numerator and denominator.

$$\frac{5}{8}-\frac{1}{3}$$

Least common multiple of 8 and 3 is 24. Convert \frac{5}{8} and \frac{1}{3} to fractions with denominator 24.

$$\frac{15}{24}-\frac{8}{24}$$

Since \frac{15}{24} and \frac{8}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-8}{24}$$

Subtract 8 from 15 to get 7.

$$\frac{7}{24}$$

Factor

$$\frac{7}{2 ^ {3} \cdot 3} = 0.2916666666666667$$