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

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

Evaluate

$$-\frac{1}{30}\approx -0.033333333$$

Solution Steps

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

$$\frac{2\times 2}{3\times 5}-\frac{1}{2}\times \frac{3}{5}$$

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

$$\frac{4}{15}-\frac{1}{2}\times \frac{3}{5}$$

Multiply \frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{15}-\frac{1\times 3}{2\times 5}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 5}.

$$\frac{4}{15}-\frac{3}{10}$$

Least common multiple of 15 and 10 is 30. Convert \frac{4}{15} and \frac{3}{10} to fractions with denominator 30.

$$\frac{8}{30}-\frac{9}{30}$$

Since \frac{8}{30} and \frac{9}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-9}{30}$$

Subtract 9 from 8 to get -1.

$$-\frac{1}{30}$$

Factor

$$-\frac{1}{30} = -0.03333333333333333$$