Solve 7:(1/3+1/4-1/6)*24

$$7 : ( \frac { 1 } { 3 } + \frac { 1 } { 4 } - \frac { 1 } { 6 } ) \times 24$$

Evaluate

$$\frac{2016}{5}=403.2$$

Solution Steps

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

$$\frac{7}{\frac{4}{12}+\frac{3}{12}-\frac{1}{6}}\times 24$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{7}{\frac{4+3}{12}-\frac{1}{6}}\times 24$$

Add 4 and 3 to get 7.

$$\frac{7}{\frac{7}{12}-\frac{1}{6}}\times 24$$

Least common multiple of 12 and 6 is 12. Convert \frac{7}{12} and \frac{1}{6} to fractions with denominator 12.

$$\frac{7}{\frac{7}{12}-\frac{2}{12}}\times 24$$

Since \frac{7}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{\frac{7-2}{12}}\times 24$$

Subtract 2 from 7 to get 5.

$$\frac{7}{\frac{5}{12}}\times 24$$

Divide 7 by \frac{5}{12} by multiplying 7 by the reciprocal of \frac{5}{12}.

$$7\times \frac{12}{5}\times 24$$

Express 7\times \frac{12}{5} as a single fraction.

$$\frac{7\times 12}{5}\times 24$$

Multiply 7 and 12 to get 84.

$$\frac{84}{5}\times 24$$

Express \frac{84}{5}\times 24 as a single fraction.

$$\frac{84\times 24}{5}$$

Multiply 84 and 24 to get 2016.

$$\frac{2016}{5}$$

Factor

$$\frac{2 ^ {5} \cdot 3 ^ {2} \cdot 7}{5} = 403\frac{1}{5} = 403.2$$