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

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

Evaluate

$$\frac{11}{24}\approx 0.458333333$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{5}{8} and \frac{1}{4} to fractions with denominator 8.

$$\left(\frac{5}{8}-\frac{2}{8}\right)\left(\frac{8}{9}+\frac{1}{3}\right)$$

Since \frac{5}{8} and \frac{2}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-2}{8}\left(\frac{8}{9}+\frac{1}{3}\right)$$

Subtract 2 from 5 to get 3.

$$\frac{3}{8}\left(\frac{8}{9}+\frac{1}{3}\right)$$

Least common multiple of 9 and 3 is 9. Convert \frac{8}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{3}{8}\left(\frac{8}{9}+\frac{3}{9}\right)$$

Since \frac{8}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{3}{8}\times \frac{8+3}{9}$$

Add 8 and 3 to get 11.

$$\frac{3}{8}\times \frac{11}{9}$$

Multiply \frac{3}{8} times \frac{11}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 11}{8\times 9}$$

Do the multiplications in the fraction \frac{3\times 11}{8\times 9}.

$$\frac{33}{72}$$

Reduce the fraction \frac{33}{72} to lowest terms by extracting and canceling out 3.

$$\frac{11}{24}$$

Factor

$$\frac{11}{2 ^ {3} \cdot 3} = 0.4583333333333333$$