Solve (7/9-5/18)*(3/4+5/8)

$$( \frac { 7 } { 9 } - \frac { 5 } { 18 } ) \times ( \frac { 3 } { 4 } + \frac { 5 } { 8 } )$$

Evaluate

$$\frac{11}{16}=0.6875$$

Solution Steps

Least common multiple of 9 and 18 is 18. Convert \frac{7}{9} and \frac{5}{18} to fractions with denominator 18.

$$\left(\frac{14}{18}-\frac{5}{18}\right)\left(\frac{3}{4}+\frac{5}{8}\right)$$

Since \frac{14}{18} and \frac{5}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-5}{18}\left(\frac{3}{4}+\frac{5}{8}\right)$$

Subtract 5 from 14 to get 9.

$$\frac{9}{18}\left(\frac{3}{4}+\frac{5}{8}\right)$$

Reduce the fraction \frac{9}{18} to lowest terms by extracting and canceling out 9.

$$\frac{1}{2}\left(\frac{3}{4}+\frac{5}{8}\right)$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{1}{2}\left(\frac{6}{8}+\frac{5}{8}\right)$$

Since \frac{6}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\times \frac{6+5}{8}$$

Add 6 and 5 to get 11.

$$\frac{1}{2}\times \frac{11}{8}$$

Multiply \frac{1}{2} times \frac{11}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 11}{2\times 8}$$

Do the multiplications in the fraction \frac{1\times 11}{2\times 8}.

$$\frac{11}{16}$$

Factor

$$\frac{11}{2 ^ {4}} = 0.6875$$