Solve 1/2+2/3+5/6/frac{7{12}}-frac{2}{5}frac{5}{6}

$$\frac{ \frac{ 1 }{ 2 } + \frac{ 2 }{ 3 } + \frac{ 5 }{ 6 } }{ \frac{ 7 }{ 12 } } - \frac{ 2 }{ 5 } \frac{ 5 }{ 6 }$$

Evaluate

$$\frac{65}{21}\approx 3.095238095$$

Solution Steps

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

$$\frac{\frac{3}{6}+\frac{4}{6}+\frac{5}{6}}{\frac{7}{12}}-\frac{2}{5}\times \frac{5}{6}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+4}{6}+\frac{5}{6}}{\frac{7}{12}}-\frac{2}{5}\times \frac{5}{6}$$

Add 3 and 4 to get 7.

$$\frac{\frac{7}{6}+\frac{5}{6}}{\frac{7}{12}}-\frac{2}{5}\times \frac{5}{6}$$

Since \frac{7}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7+5}{6}}{\frac{7}{12}}-\frac{2}{5}\times \frac{5}{6}$$

Add 7 and 5 to get 12.

$$\frac{\frac{12}{6}}{\frac{7}{12}}-\frac{2}{5}\times \frac{5}{6}$$

Divide 12 by 6 to get 2.

$$\frac{2}{\frac{7}{12}}-\frac{2}{5}\times \frac{5}{6}$$

Divide 2 by \frac{7}{12} by multiplying 2 by the reciprocal of \frac{7}{12}.

$$2\times \frac{12}{7}-\frac{2}{5}\times \frac{5}{6}$$

Express 2\times \frac{12}{7} as a single fraction.

$$\frac{2\times 12}{7}-\frac{2}{5}\times \frac{5}{6}$$

Multiply 2 and 12 to get 24.

$$\frac{24}{7}-\frac{2}{5}\times \frac{5}{6}$$

Multiply \frac{2}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{24}{7}-\frac{2\times 5}{5\times 6}$$

Cancel out 5 in both numerator and denominator.

$$\frac{24}{7}-\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{24}{7}-\frac{1}{3}$$

Least common multiple of 7 and 3 is 21. Convert \frac{24}{7} and \frac{1}{3} to fractions with denominator 21.

$$\frac{72}{21}-\frac{7}{21}$$

Since \frac{72}{21} and \frac{7}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{72-7}{21}$$

Subtract 7 from 72 to get 65.

$$\frac{65}{21}$$

Factor

$$\frac{5 \cdot 13}{3 \cdot 7} = 3\frac{2}{21} = 3.0952380952380953$$