Solve (2/3-3/4)*(3/5-1/2)=

$$( \frac { 2 } { 3 } - \frac { 3 } { 4 } ) \cdot ( \frac { 3 } { 5 } - \frac { 1 } { 2 } ) =$$

Evaluate

$$-\frac{1}{120}\approx -0.008333333$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\left(\frac{8}{12}-\frac{9}{12}\right)\left(\frac{3}{5}-\frac{1}{2}\right)$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-9}{12}\left(\frac{3}{5}-\frac{1}{2}\right)$$

Subtract 9 from 8 to get -1.

$$-\frac{1}{12}\left(\frac{3}{5}-\frac{1}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$-\frac{1}{12}\left(\frac{6}{10}-\frac{5}{10}\right)$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{12}\times \frac{6-5}{10}$$

Subtract 5 from 6 to get 1.

$$-\frac{1}{12}\times \frac{1}{10}$$

Multiply -\frac{1}{12} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1}{12\times 10}$$

Do the multiplications in the fraction \frac{-1}{12\times 10}.

$$\frac{-1}{120}$$

Fraction \frac{-1}{120} can be rewritten as -\frac{1}{120} by extracting the negative sign.

$$-\frac{1}{120}$$

Factor

$$-\frac{1}{120} = -0.008333333333333333$$