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

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

Evaluate

$$\frac{11}{20}=0.55$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{1}{2} to fractions with denominator 4.

$$\left(\frac{5}{4}-\frac{2}{4}\right)\left(\frac{1}{3}+\frac{2}{5}\right)$$

Since \frac{5}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-2}{4}\left(\frac{1}{3}+\frac{2}{5}\right)$$

Subtract 2 from 5 to get 3.

$$\frac{3}{4}\left(\frac{1}{3}+\frac{2}{5}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{3}{4}\left(\frac{5}{15}+\frac{6}{15}\right)$$

Since \frac{5}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}\times \frac{5+6}{15}$$

Add 5 and 6 to get 11.

$$\frac{3}{4}\times \frac{11}{15}$$

Multiply \frac{3}{4} times \frac{11}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 11}{4\times 15}$$

Do the multiplications in the fraction \frac{3\times 11}{4\times 15}.

$$\frac{33}{60}$$

Reduce the fraction \frac{33}{60} to lowest terms by extracting and canceling out 3.

$$\frac{11}{20}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 5} = 0.55$$