Solve 11/3+1/4-4/9/frac{1{36}}

$$\frac{ 1 \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 } - \frac{ 4 }{ 9 } }{ \frac{ 1 }{ 36 } }$$

Evaluate

$$41$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{\frac{3+1}{3}+\frac{1}{4}-\frac{4}{9}}{\frac{1}{36}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{4}{3}+\frac{1}{4}-\frac{4}{9}}{\frac{1}{36}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{4}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{16}{12}+\frac{3}{12}-\frac{4}{9}}{\frac{1}{36}}$$

Since \frac{16}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{16+3}{12}-\frac{4}{9}}{\frac{1}{36}}$$

Add 16 and 3 to get 19.

$$\frac{\frac{19}{12}-\frac{4}{9}}{\frac{1}{36}}$$

Least common multiple of 12 and 9 is 36. Convert \frac{19}{12} and \frac{4}{9} to fractions with denominator 36.

$$\frac{\frac{57}{36}-\frac{16}{36}}{\frac{1}{36}}$$

Since \frac{57}{36} and \frac{16}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{57-16}{36}}{\frac{1}{36}}$$

Subtract 16 from 57 to get 41.

$$\frac{\frac{41}{36}}{\frac{1}{36}}$$

Divide \frac{41}{36} by \frac{1}{36} by multiplying \frac{41}{36} by the reciprocal of \frac{1}{36}.

$$\frac{41}{36}\times 36$$

Cancel out 36 and 36.

$$41$$

Factor

$$41$$