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

$$( \frac{ 3 }{ 4 } - \frac{ 4 }{ 5 } ) \times ( \frac{ 1 }{ 3 } + \frac{ 3 }{ 5 } )=$$

Evaluate

$$-\frac{7}{150}\approx -0.046666667$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{4}{5} to fractions with denominator 20.

$$\left(\frac{15}{20}-\frac{16}{20}\right)\left(\frac{1}{3}+\frac{3}{5}\right)$$

Since \frac{15}{20} and \frac{16}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-16}{20}\left(\frac{1}{3}+\frac{3}{5}\right)$$

Subtract 16 from 15 to get -1.

$$-\frac{1}{20}\left(\frac{1}{3}+\frac{3}{5}\right)$$

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

$$-\frac{1}{20}\left(\frac{5}{15}+\frac{9}{15}\right)$$

Since \frac{5}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$-\frac{1}{20}\times \frac{5+9}{15}$$

Add 5 and 9 to get 14.

$$-\frac{1}{20}\times \frac{14}{15}$$

Multiply -\frac{1}{20} times \frac{14}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-14}{20\times 15}$$

Do the multiplications in the fraction \frac{-14}{20\times 15}.

$$\frac{-14}{300}$$

Reduce the fraction \frac{-14}{300} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{150}$$

Factor

$$-\frac{7}{150} = -0.04666666666666667$$