Solve 1/4+{1/3div1/2*(1/5-frac{1}{10})}

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

Evaluate

$$\frac{19}{60}\approx 0.316666667$$

Solution Steps

Divide \frac{1}{3} by \frac{1}{2} by multiplying \frac{1}{3} by the reciprocal of \frac{1}{2}.

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

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{1}{4}+\frac{2}{3}\left(\frac{1}{5}-\frac{1}{10}\right)$$

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{1}{4}+\frac{2}{3}\left(\frac{2}{10}-\frac{1}{10}\right)$$

Since \frac{2}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}+\frac{2}{3}\times \frac{2-1}{10}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{4}+\frac{2}{3}\times \frac{1}{10}$$

Multiply \frac{2}{3} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}+\frac{2\times 1}{3\times 10}$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 10}.

$$\frac{1}{4}+\frac{2}{30}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}+\frac{1}{15}$$

Least common multiple of 4 and 15 is 60. Convert \frac{1}{4} and \frac{1}{15} to fractions with denominator 60.

$$\frac{15}{60}+\frac{4}{60}$$

Since \frac{15}{60} and \frac{4}{60} have the same denominator, add them by adding their numerators.

$$\frac{15+4}{60}$$

Add 15 and 4 to get 19.

$$\frac{19}{60}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 3 \cdot 5} = 0.31666666666666665$$