Solve 27/9div(31/2+41/6)

$$2 \frac { 7 } { 9 } \div ( 3 \frac { 1 } { 2 } + 4 \frac { 1 } { 6 } )$$

Evaluate

$$\frac{25}{69}\approx 0.362318841$$

Solution Steps

Multiply 2 and 9 to get 18.

$$\frac{\frac{18+7}{9}}{\frac{3\times 2+1}{2}+\frac{4\times 6+1}{6}}$$

Add 18 and 7 to get 25.

$$\frac{\frac{25}{9}}{\frac{3\times 2+1}{2}+\frac{4\times 6+1}{6}}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{25}{9}}{\frac{6+1}{2}+\frac{4\times 6+1}{6}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{25}{9}}{\frac{7}{2}+\frac{4\times 6+1}{6}}$$

Multiply 4 and 6 to get 24.

$$\frac{\frac{25}{9}}{\frac{7}{2}+\frac{24+1}{6}}$$

Add 24 and 1 to get 25.

$$\frac{\frac{25}{9}}{\frac{7}{2}+\frac{25}{6}}$$

Least common multiple of 2 and 6 is 6. Convert \frac{7}{2} and \frac{25}{6} to fractions with denominator 6.

$$\frac{\frac{25}{9}}{\frac{21}{6}+\frac{25}{6}}$$

Since \frac{21}{6} and \frac{25}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25}{9}}{\frac{21+25}{6}}$$

Add 21 and 25 to get 46.

$$\frac{\frac{25}{9}}{\frac{46}{6}}$$

Reduce the fraction \frac{46}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{25}{9}}{\frac{23}{3}}$$

Divide \frac{25}{9} by \frac{23}{3} by multiplying \frac{25}{9} by the reciprocal of \frac{23}{3}.

$$\frac{25}{9}\times \frac{3}{23}$$

Multiply \frac{25}{9} times \frac{3}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 3}{9\times 23}$$

Do the multiplications in the fraction \frac{25\times 3}{9\times 23}.

$$\frac{75}{207}$$

Reduce the fraction \frac{75}{207} to lowest terms by extracting and canceling out 3.

$$\frac{25}{69}$$

Factor

$$\frac{5 ^ {2}}{3 \cdot 23} = 0.36231884057971014$$