Solve 24*(1/2+1/3-1/4)

$$24 \times ( \frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } - \frac{ 1 }{ 4 } )$$

Evaluate

$$14$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$24\left(\frac{3}{6}+\frac{2}{6}-\frac{1}{4}\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$24\left(\frac{3+2}{6}-\frac{1}{4}\right)$$

Add 3 and 2 to get 5.

$$24\left(\frac{5}{6}-\frac{1}{4}\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$24\left(\frac{10}{12}-\frac{3}{12}\right)$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$24\times \frac{10-3}{12}$$

Subtract 3 from 10 to get 7.

$$24\times \frac{7}{12}$$

Express 24\times \frac{7}{12} as a single fraction.

$$\frac{24\times 7}{12}$$

Multiply 24 and 7 to get 168.

$$\frac{168}{12}$$

Divide 168 by 12 to get 14.

$$14$$

Factor

$$2\times 7$$