Solve [1/2+3/4(2/5)]+(-1/6)

$$[ \frac { 1 } { 2 } + \frac { 3 } { 4 } ( \frac { 2 } { 5 } ) ] + ( - \frac { 1 } { 6 } )$$

Evaluate

$$\frac{19}{30}\approx 0.633333333$$

Solution Steps

Multiply \frac{3}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{3\times 2}{4\times 5}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{3\times 2}{4\times 5}.

$$\frac{1}{2}+\frac{6}{20}-\frac{1}{6}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+\frac{3}{10}-\frac{1}{6}$$

Least common multiple of 2 and 10 is 10. Convert \frac{1}{2} and \frac{3}{10} to fractions with denominator 10.

$$\frac{5}{10}+\frac{3}{10}-\frac{1}{6}$$

Since \frac{5}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{5+3}{10}-\frac{1}{6}$$

Add 5 and 3 to get 8.

$$\frac{8}{10}-\frac{1}{6}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}-\frac{1}{6}$$

Least common multiple of 5 and 6 is 30. Convert \frac{4}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{24}{30}-\frac{5}{30}$$

Since \frac{24}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-5}{30}$$

Subtract 5 from 24 to get 19.

$$\frac{19}{30}$$

Factor

$$\frac{19}{2 \cdot 3 \cdot 5} = 0.6333333333333333$$