Solve (1/3+1/4-4/9)div1/36

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

Evaluate

$$5$$

Solution Steps

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

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

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

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

Add 4 and 3 to get 7.

$$\frac{\frac{7}{12}-\frac{4}{9}}{\frac{1}{36}}$$

Least common multiple of 12 and 9 is 36. Convert \frac{7}{12} and \frac{4}{9} to fractions with denominator 36.

$$\frac{\frac{21}{36}-\frac{16}{36}}{\frac{1}{36}}$$

Since \frac{21}{36} and \frac{16}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21-16}{36}}{\frac{1}{36}}$$

Subtract 16 from 21 to get 5.

$$\frac{\frac{5}{36}}{\frac{1}{36}}$$

Divide \frac{5}{36} by \frac{1}{36} by multiplying \frac{5}{36} by the reciprocal of \frac{1}{36}.

$$\frac{5}{36}\times 36$$

Cancel out 36 and 36.

$$5$$

Factor

$$5$$