Solve 2/5*(1/2+1/3)div4/9

$$\frac { 2 } { 5 } \times ( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) \div \frac { 4 } { 9 }$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{2}{5}\left(\frac{3}{6}+\frac{2}{6}\right)}{\frac{4}{9}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

$$\frac{\frac{2}{5}\times \frac{5}{6}}{\frac{4}{9}}$$

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

$$\frac{\frac{2\times 5}{5\times 6}}{\frac{4}{9}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{2}{6}}{\frac{4}{9}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{3}}{\frac{4}{9}}$$

Divide \frac{1}{3} by \frac{4}{9} by multiplying \frac{1}{3} by the reciprocal of \frac{4}{9}.

$$\frac{1}{3}\times \frac{9}{4}$$

Multiply \frac{1}{3} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 9}{3\times 4}$$

Do the multiplications in the fraction \frac{1\times 9}{3\times 4}.

$$\frac{9}{12}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$