Solve (1/3-3/4+5/6)*48

$$( \frac { 1 } { 3 } - \frac { 3 } { 4 } + \frac { 5 } { 6 } ) \times 48$$

Evaluate

$$20$$

Solution Steps

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

$$\left(\frac{4}{12}-\frac{9}{12}+\frac{5}{6}\right)\times 48$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{4-9}{12}+\frac{5}{6}\right)\times 48$$

Subtract 9 from 4 to get -5.

$$\left(-\frac{5}{12}+\frac{5}{6}\right)\times 48$$

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

$$\left(-\frac{5}{12}+\frac{10}{12}\right)\times 48$$

Since -\frac{5}{12} and \frac{10}{12} have the same denominator, add them by adding their numerators.

$$\frac{-5+10}{12}\times 48$$

Add -5 and 10 to get 5.

$$\frac{5}{12}\times 48$$

Express \frac{5}{12}\times 48 as a single fraction.

$$\frac{5\times 48}{12}$$

Multiply 5 and 48 to get 240.

$$\frac{240}{12}$$

Divide 240 by 12 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$