Solve (5/6+7/12-11/24)div1/24

$$( \frac{ 5 }{ 6 } + \frac{ 7 }{ 12 } - \frac{ 11 }{ 24 } ) \div \frac{ 1 }{ 24 }$$

Evaluate

$$23$$

Solution Steps

Least common multiple of 6 and 12 is 12. Convert \frac{5}{6} and \frac{7}{12} to fractions with denominator 12.

$$\frac{\frac{10}{12}+\frac{7}{12}-\frac{11}{24}}{\frac{1}{24}}$$

Since \frac{10}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+7}{12}-\frac{11}{24}}{\frac{1}{24}}$$

Add 10 and 7 to get 17.

$$\frac{\frac{17}{12}-\frac{11}{24}}{\frac{1}{24}}$$

Least common multiple of 12 and 24 is 24. Convert \frac{17}{12} and \frac{11}{24} to fractions with denominator 24.

$$\frac{\frac{34}{24}-\frac{11}{24}}{\frac{1}{24}}$$

Since \frac{34}{24} and \frac{11}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{34-11}{24}}{\frac{1}{24}}$$

Subtract 11 from 34 to get 23.

$$\frac{\frac{23}{24}}{\frac{1}{24}}$$

Divide \frac{23}{24} by \frac{1}{24} by multiplying \frac{23}{24} by the reciprocal of \frac{1}{24}.

$$\frac{23}{24}\times 24$$

Cancel out 24 and 24.

$$23$$

Factor

$$23$$