Solve 7/12*2/7+1/3div5/6quad(frac{2}{3}+frac{1}{6}+frac{3}{8})*24

$$\frac { 7 } { 12 } \times \frac { 2 } { 7 } + \frac { 1 } { 3 } \div \frac { 5 } { 6 } \quad ( \frac { 2 } { 3 } + \frac { 1 } { 6 } + \frac { 3 } { 8 } ) \times 24$$

Evaluate

$$\frac{353}{30}\approx 11.766666667$$

Solution Steps

Multiply \frac{7}{12} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 2}{12\times 7}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Cancel out 7 in both numerator and denominator.

$$\frac{2}{12}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

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

$$\frac{1}{6}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Divide \frac{1}{3} by \frac{5}{6} by multiplying \frac{1}{3} by the reciprocal of \frac{5}{6}.

$$\frac{1}{6}+\frac{1}{3}\times \frac{6}{5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Multiply \frac{1}{3} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6}+\frac{1\times 6}{3\times 5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Do the multiplications in the fraction \frac{1\times 6}{3\times 5}.

$$\frac{1}{6}+\frac{6}{15}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

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

$$\frac{1}{6}+\frac{2}{5}\left(\frac{4}{6}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{4+1}{6}+\frac{3}{8}\right)\times 24$$

Add 4 and 1 to get 5.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{5}{6}+\frac{3}{8}\right)\times 24$$

Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{3}{8} to fractions with denominator 24.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{20}{24}+\frac{9}{24}\right)\times 24$$

Since \frac{20}{24} and \frac{9}{24} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}+\frac{2}{5}\times \frac{20+9}{24}\times 24$$

Add 20 and 9 to get 29.

$$\frac{1}{6}+\frac{2}{5}\times \frac{29}{24}\times 24$$

Multiply \frac{2}{5} times \frac{29}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6}+\frac{2\times 29}{5\times 24}\times 24$$

Do the multiplications in the fraction \frac{2\times 29}{5\times 24}.

$$\frac{1}{6}+\frac{58}{120}\times 24$$

Reduce the fraction \frac{58}{120} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}+\frac{29}{60}\times 24$$

Express \frac{29}{60}\times 24 as a single fraction.

$$\frac{1}{6}+\frac{29\times 24}{60}$$

Multiply 29 and 24 to get 696.

$$\frac{1}{6}+\frac{696}{60}$$

Reduce the fraction \frac{696}{60} to lowest terms by extracting and canceling out 12.

$$\frac{1}{6}+\frac{58}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{58}{5} to fractions with denominator 30.

$$\frac{5}{30}+\frac{348}{30}$$

Since \frac{5}{30} and \frac{348}{30} have the same denominator, add them by adding their numerators.

$$\frac{5+348}{30}$$

Add 5 and 348 to get 353.

$$\frac{353}{30}$$

Factor

$$\frac{353}{2 \cdot 3 \cdot 5} = 11\frac{23}{30} = 11.766666666666667$$