Solve (1/3+1/9)*(5/4-3/4)

$$( \frac { 1 } { 3 } + \frac { 1 } { 9 } ) \cdot ( \frac { 5 } { 4 } - \frac { 3 } { 4 } )$$

Evaluate

$$\frac{2}{9}\approx 0.222222222$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{1}{9} to fractions with denominator 9.

$$\left(\frac{3}{9}+\frac{1}{9}\right)\left(\frac{5}{4}-\frac{3}{4}\right)$$

Since \frac{3}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{9}\left(\frac{5}{4}-\frac{3}{4}\right)$$

Add 3 and 1 to get 4.

$$\frac{4}{9}\left(\frac{5}{4}-\frac{3}{4}\right)$$

Since \frac{5}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{9}\times \frac{5-3}{4}$$

Subtract 3 from 5 to get 2.

$$\frac{4}{9}\times \frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{4}{9}\times \frac{1}{2}$$

Multiply \frac{4}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 1}{9\times 2}$$

Do the multiplications in the fraction \frac{4\times 1}{9\times 2}.

$$\frac{4}{18}$$

Reduce the fraction \frac{4}{18} to lowest terms by extracting and canceling out 2.

$$\frac{2}{9}$$

Factor

$$\frac{2}{3 ^ {2}} = 0.2222222222222222$$