Solve (9/10+3/4)*5/6-1/2

$$( \frac { 9 } { 10 } + \frac { 3 } { 4 } ) \times \frac { 5 } { 6 } - \frac { 1 } { 2 }$$

Evaluate

$$\frac{7}{8}=0.875$$

Solution Steps

Least common multiple of 10 and 4 is 20. Convert \frac{9}{10} and \frac{3}{4} to fractions with denominator 20.

$$\left(\frac{18}{20}+\frac{15}{20}\right)\times \frac{5}{6}-\frac{1}{2}$$

Since \frac{18}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{18+15}{20}\times \frac{5}{6}-\frac{1}{2}$$

Add 18 and 15 to get 33.

$$\frac{33}{20}\times \frac{5}{6}-\frac{1}{2}$$

Multiply \frac{33}{20} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 5}{20\times 6}-\frac{1}{2}$$

Do the multiplications in the fraction \frac{33\times 5}{20\times 6}.

$$\frac{165}{120}-\frac{1}{2}$$

Reduce the fraction \frac{165}{120} to lowest terms by extracting and canceling out 15.

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

Least common multiple of 8 and 2 is 8. Convert \frac{11}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{11}{8}-\frac{4}{8}$$

Since \frac{11}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-4}{8}$$

Subtract 4 from 11 to get 7.

$$\frac{7}{8}$$

Factor

$$\frac{7}{2 ^ {3}} = 0.875$$