Solve (5/6+7/8-7/6)div1/24

$$( \frac { 5 } { 6 } + \frac { 7 } { 8 } - \frac { 7 } { 6 } ) \div \frac { 1 } { 24 }$$

Evaluate

$$13$$

Solution Steps

Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{7}{8} to fractions with denominator 24.

$$\frac{\frac{20}{24}+\frac{21}{24}-\frac{7}{6}}{\frac{1}{24}}$$

Since \frac{20}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20+21}{24}-\frac{7}{6}}{\frac{1}{24}}$$

Add 20 and 21 to get 41.

$$\frac{\frac{41}{24}-\frac{7}{6}}{\frac{1}{24}}$$

Least common multiple of 24 and 6 is 24. Convert \frac{41}{24} and \frac{7}{6} to fractions with denominator 24.

$$\frac{\frac{41}{24}-\frac{28}{24}}{\frac{1}{24}}$$

Since \frac{41}{24} and \frac{28}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{41-28}{24}}{\frac{1}{24}}$$

Subtract 28 from 41 to get 13.

$$\frac{\frac{13}{24}}{\frac{1}{24}}$$

Divide \frac{13}{24} by \frac{1}{24} by multiplying \frac{13}{24} by the reciprocal of \frac{1}{24}.

$$\frac{13}{24}\times 24$$

Cancel out 24 and 24.

$$13$$

Factor

$$13$$