Solve (4/5-1/6+2/3)div1/30

$$( \frac{ 4 }{ 5 } - \frac{ 1 }{ 6 } + \frac{ 2 }{ 3 } ) \div \frac{ 1 }{ 30 }$$

Evaluate

$$39$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert \frac{4}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{\frac{24}{30}-\frac{5}{30}+\frac{2}{3}}{\frac{1}{30}}$$

Since \frac{24}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{24-5}{30}+\frac{2}{3}}{\frac{1}{30}}$$

Subtract 5 from 24 to get 19.

$$\frac{\frac{19}{30}+\frac{2}{3}}{\frac{1}{30}}$$

Least common multiple of 30 and 3 is 30. Convert \frac{19}{30} and \frac{2}{3} to fractions with denominator 30.

$$\frac{\frac{19}{30}+\frac{20}{30}}{\frac{1}{30}}$$

Since \frac{19}{30} and \frac{20}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{19+20}{30}}{\frac{1}{30}}$$

Add 19 and 20 to get 39.

$$\frac{\frac{39}{30}}{\frac{1}{30}}$$

Reduce the fraction \frac{39}{30} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{13}{10}}{\frac{1}{30}}$$

Divide \frac{13}{10} by \frac{1}{30} by multiplying \frac{13}{10} by the reciprocal of \frac{1}{30}.

$$\frac{13}{10}\times 30$$

Express \frac{13}{10}\times 30 as a single fraction.

$$\frac{13\times 30}{10}$$

Multiply 13 and 30 to get 390.

$$\frac{390}{10}$$

Divide 390 by 10 to get 39.

$$39$$

Factor

$$3\times 13$$