Solve (4/5-3/4)*11/9+1/3

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

Evaluate

$$\frac{7}{18}\approx 0.388888889$$

Solution Steps

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

$$\left(\frac{16}{20}-\frac{15}{20}\right)\times \frac{1\times 9+1}{9}+\frac{1}{3}$$

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

$$\frac{16-15}{20}\times \frac{1\times 9+1}{9}+\frac{1}{3}$$

Subtract 15 from 16 to get 1.

$$\frac{1}{20}\times \frac{1\times 9+1}{9}+\frac{1}{3}$$

Multiply 1 and 9 to get 9.

$$\frac{1}{20}\times \frac{9+1}{9}+\frac{1}{3}$$

Add 9 and 1 to get 10.

$$\frac{1}{20}\times \frac{10}{9}+\frac{1}{3}$$

Multiply \frac{1}{20} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 10}{20\times 9}+\frac{1}{3}$$

Do the multiplications in the fraction \frac{1\times 10}{20\times 9}.

$$\frac{10}{180}+\frac{1}{3}$$

Reduce the fraction \frac{10}{180} to lowest terms by extracting and canceling out 10.

$$\frac{1}{18}+\frac{1}{3}$$

Least common multiple of 18 and 3 is 18. Convert \frac{1}{18} and \frac{1}{3} to fractions with denominator 18.

$$\frac{1}{18}+\frac{6}{18}$$

Since \frac{1}{18} and \frac{6}{18} have the same denominator, add them by adding their numerators.

$$\frac{1+6}{18}$$

Add 1 and 6 to get 7.

$$\frac{7}{18}$$

Factor

$$\frac{7}{2 \cdot 3 ^ {2}} = 0.3888888888888889$$