Solve 7/12div(4/5+9/11-3/18)

$$\frac { 7 } { 12 } \div ( \frac { 4 } { 5 } + \frac { 9 } { 11 } - \frac { 3 } { 18 } )$$

Evaluate

$$\frac{385}{958}\approx 0.401878914$$

Solution Steps

Least common multiple of 5 and 11 is 55. Convert \frac{4}{5} and \frac{9}{11} to fractions with denominator 55.

$$\frac{\frac{7}{12}}{\frac{44}{55}+\frac{45}{55}-\frac{3}{18}}$$

Since \frac{44}{55} and \frac{45}{55} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{12}}{\frac{44+45}{55}-\frac{3}{18}}$$

Add 44 and 45 to get 89.

$$\frac{\frac{7}{12}}{\frac{89}{55}-\frac{3}{18}}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{7}{12}}{\frac{89}{55}-\frac{1}{6}}$$

Least common multiple of 55 and 6 is 330. Convert \frac{89}{55} and \frac{1}{6} to fractions with denominator 330.

$$\frac{\frac{7}{12}}{\frac{534}{330}-\frac{55}{330}}$$

Since \frac{534}{330} and \frac{55}{330} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{12}}{\frac{534-55}{330}}$$

Subtract 55 from 534 to get 479.

$$\frac{\frac{7}{12}}{\frac{479}{330}}$$

Divide \frac{7}{12} by \frac{479}{330} by multiplying \frac{7}{12} by the reciprocal of \frac{479}{330}.

$$\frac{7}{12}\times \frac{330}{479}$$

Multiply \frac{7}{12} times \frac{330}{479} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 330}{12\times 479}$$

Do the multiplications in the fraction \frac{7\times 330}{12\times 479}.

$$\frac{2310}{5748}$$

Reduce the fraction \frac{2310}{5748} to lowest terms by extracting and canceling out 6.

$$\frac{385}{958}$$

Factor

$$\frac{5 \cdot 7 \cdot 11}{2 \cdot 479} = 0.40187891440501045$$