Solve [(4/6+17/2):(4/3-5/12)]*(frac{1}{6}+frac{1}{15})=

$$[ ( \frac { 4 } { 6 } + \frac { 17 } { 2 } ) : ( \frac { 4 } { 3 } - \frac { 5 } { 12 } ) ] \cdot ( \frac { 1 } { 6 } + \frac { 1 } { 15 } ) =$$

Evaluate

$$\frac{7}{3}\approx 2.333333333$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{3}+\frac{17}{2}}{\frac{4}{3}-\frac{5}{12}}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{17}{2} to fractions with denominator 6.

$$\frac{\frac{4}{6}+\frac{51}{6}}{\frac{4}{3}-\frac{5}{12}}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Since \frac{4}{6} and \frac{51}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+51}{6}}{\frac{4}{3}-\frac{5}{12}}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Add 4 and 51 to get 55.

$$\frac{\frac{55}{6}}{\frac{4}{3}-\frac{5}{12}}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Least common multiple of 3 and 12 is 12. Convert \frac{4}{3} and \frac{5}{12} to fractions with denominator 12.

$$\frac{\frac{55}{6}}{\frac{16}{12}-\frac{5}{12}}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Since \frac{16}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{55}{6}}{\frac{16-5}{12}}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Subtract 5 from 16 to get 11.

$$\frac{\frac{55}{6}}{\frac{11}{12}}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Divide \frac{55}{6} by \frac{11}{12} by multiplying \frac{55}{6} by the reciprocal of \frac{11}{12}.

$$\frac{55}{6}\times \frac{12}{11}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Multiply \frac{55}{6} times \frac{12}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{55\times 12}{6\times 11}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Do the multiplications in the fraction \frac{55\times 12}{6\times 11}.

$$\frac{660}{66}\left(\frac{1}{6}+\frac{1}{15}\right)$$

Divide 660 by 66 to get 10.

$$10\left(\frac{1}{6}+\frac{1}{15}\right)$$

Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{1}{15} to fractions with denominator 30.

$$10\left(\frac{5}{30}+\frac{2}{30}\right)$$

Since \frac{5}{30} and \frac{2}{30} have the same denominator, add them by adding their numerators.

$$10\times \frac{5+2}{30}$$

Add 5 and 2 to get 7.

$$10\times \frac{7}{30}$$

Express 10\times \frac{7}{30} as a single fraction.

$$\frac{10\times 7}{30}$$

Multiply 10 and 7 to get 70.

$$\frac{70}{30}$$

Reduce the fraction \frac{70}{30} to lowest terms by extracting and canceling out 10.

$$\frac{7}{3}$$

Factor

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$