Solve (2/3*5/6+4/9-3/4+frac{2}{9}*frac{5}{9}divfrac{2}{9})

$$( \frac { 2 } { 3 } \times \frac { 5 } { 6 } + \frac { 4 } { 9 } - \frac { 3 } { 4 } + \frac { 2 } { 9 } \times \frac { 5 } { 9 } \div \frac { 2 } { 9 } )$$

Evaluate

$$\frac{29}{36}\approx 0.805555556$$

Solution Steps

Multiply \frac{2}{3} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 5}{3\times 6}+\frac{4}{9}-\frac{3}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

Do the multiplications in the fraction \frac{2\times 5}{3\times 6}.

$$\frac{10}{18}+\frac{4}{9}-\frac{3}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

Reduce the fraction \frac{10}{18} to lowest terms by extracting and canceling out 2.

$$\frac{5}{9}+\frac{4}{9}-\frac{3}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

Since \frac{5}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{5+4}{9}-\frac{3}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

Add 5 and 4 to get 9.

$$\frac{9}{9}-\frac{3}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

Divide 9 by 9 to get 1.

$$1-\frac{3}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{4}{4}-\frac{3}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

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

$$\frac{4-3}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{4}+\frac{\frac{2}{9}\times \frac{5}{9}}{\frac{2}{9}}$$

Cancel out \frac{2}{9} and \frac{2}{9}.

$$\frac{1}{4}+\frac{5}{9}$$

Least common multiple of 4 and 9 is 36. Convert \frac{1}{4} and \frac{5}{9} to fractions with denominator 36.

$$\frac{9}{36}+\frac{20}{36}$$

Since \frac{9}{36} and \frac{20}{36} have the same denominator, add them by adding their numerators.

$$\frac{9+20}{36}$$

Add 9 and 20 to get 29.

$$\frac{29}{36}$$

Factor

$$\frac{29}{2 ^ {2} \cdot 3 ^ {2}} = 0.8055555555555556$$