Solve (2/3-1/2)(1/3-1/5)=

$$( \frac{ 2 }{ 3 } - \frac{ 1 }{ 2 } )( \frac{ 1 }{ 3 } - \frac{ 1 }{ 5 } )=$$

Evaluate

$$\frac{1}{45}\approx 0.022222222$$

Solution Steps

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

$$\left(\frac{4}{6}-\frac{3}{6}\right)\left(\frac{1}{3}-\frac{1}{5}\right)$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{6}\left(\frac{1}{3}-\frac{1}{5}\right)$$

Subtract 3 from 4 to get 1.

$$\frac{1}{6}\left(\frac{1}{3}-\frac{1}{5}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{1}{6}\left(\frac{5}{15}-\frac{3}{15}\right)$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}\times \frac{5-3}{15}$$

Subtract 3 from 5 to get 2.

$$\frac{1}{6}\times \frac{2}{15}$$

Multiply \frac{1}{6} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{6\times 15}$$

Do the multiplications in the fraction \frac{1\times 2}{6\times 15}.

$$\frac{2}{90}$$

Reduce the fraction \frac{2}{90} to lowest terms by extracting and canceling out 2.

$$\frac{1}{45}$$

Factor

$$\frac{1}{3 ^ {2} \cdot 5} = 0.022222222222222223$$