Solve (1/3+4/8)*(1/2-9/19)

$$( \frac{ 1 }{ 3 } + \frac{ 4 }{ 8 } ) \times ( \frac{ 1 }{ 2 } - \frac{ 9 }{ 19 } )$$

Evaluate

$$\frac{5}{228}\approx 0.021929825$$

Solution Steps

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\left(\frac{1}{3}+\frac{1}{2}\right)\left(\frac{1}{2}-\frac{9}{19}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\left(\frac{2}{6}+\frac{3}{6}\right)\left(\frac{1}{2}-\frac{9}{19}\right)$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{6}\left(\frac{1}{2}-\frac{9}{19}\right)$$

Add 2 and 3 to get 5.

$$\frac{5}{6}\left(\frac{1}{2}-\frac{9}{19}\right)$$

Least common multiple of 2 and 19 is 38. Convert \frac{1}{2} and \frac{9}{19} to fractions with denominator 38.

$$\frac{5}{6}\left(\frac{19}{38}-\frac{18}{38}\right)$$

Since \frac{19}{38} and \frac{18}{38} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}\times \frac{19-18}{38}$$

Subtract 18 from 19 to get 1.

$$\frac{5}{6}\times \frac{1}{38}$$

Multiply \frac{5}{6} times \frac{1}{38} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 1}{6\times 38}$$

Do the multiplications in the fraction \frac{5\times 1}{6\times 38}.

$$\frac{5}{228}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3 \cdot 19} = 0.021929824561403508$$