Solve 1/2div(1/2-1/12)-1/12+frac{6}{5}(frac{3}{4}-frac{1}{2})

$$\frac { 1 } { 2 } \div ( \frac { 1 } { 2 } - \frac { 1 } { 12 } ) - \frac { 1 } { 12 } + \frac { 6 } { 5 } ( \frac { 3 } { 4 } - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{17}{12}\approx 1.416666667$$

Solution Steps

Least common multiple of 2 and 12 is 12. Convert \frac{1}{2} and \frac{1}{12} to fractions with denominator 12.

$$\frac{\frac{1}{2}}{\frac{6}{12}-\frac{1}{12}}-\frac{1}{12}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Since \frac{6}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{2}}{\frac{6-1}{12}}-\frac{1}{12}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{1}{2}}{\frac{5}{12}}-\frac{1}{12}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Divide \frac{1}{2} by \frac{5}{12} by multiplying \frac{1}{2} by the reciprocal of \frac{5}{12}.

$$\frac{1}{2}\times \frac{12}{5}-\frac{1}{12}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Multiply \frac{1}{2} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 12}{2\times 5}-\frac{1}{12}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Do the multiplications in the fraction \frac{1\times 12}{2\times 5}.

$$\frac{12}{10}-\frac{1}{12}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}-\frac{1}{12}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Least common multiple of 5 and 12 is 60. Convert \frac{6}{5} and \frac{1}{12} to fractions with denominator 60.

$$\frac{72}{60}-\frac{5}{60}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Since \frac{72}{60} and \frac{5}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{72-5}{60}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Subtract 5 from 72 to get 67.

$$\frac{67}{60}+\frac{6}{5}\left(\frac{3}{4}-\frac{1}{2}\right)$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{67}{60}+\frac{6}{5}\left(\frac{3}{4}-\frac{2}{4}\right)$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{67}{60}+\frac{6}{5}\times \frac{3-2}{4}$$

Subtract 2 from 3 to get 1.

$$\frac{67}{60}+\frac{6}{5}\times \frac{1}{4}$$

Multiply \frac{6}{5} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{67}{60}+\frac{6\times 1}{5\times 4}$$

Do the multiplications in the fraction \frac{6\times 1}{5\times 4}.

$$\frac{67}{60}+\frac{6}{20}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{67}{60}+\frac{3}{10}$$

Least common multiple of 60 and 10 is 60. Convert \frac{67}{60} and \frac{3}{10} to fractions with denominator 60.

$$\frac{67}{60}+\frac{18}{60}$$

Since \frac{67}{60} and \frac{18}{60} have the same denominator, add them by adding their numerators.

$$\frac{67+18}{60}$$

Add 67 and 18 to get 85.

$$\frac{85}{60}$$

Reduce the fraction \frac{85}{60} to lowest terms by extracting and canceling out 5.

$$\frac{17}{12}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$