Solve (5/6+3/4)*36/19+(2/3-frac{1}{6})*frac{8}{3}

$$( \frac { 5 } { 6 } + \frac { 3 } { 4 } ) \cdot \frac { 36 } { 19 } + ( \frac { 2 } { 3 } - \frac { 1 } { 6 } ) \cdot \frac { 8 } { 3 }$$

Evaluate

$$\frac{13}{3}\approx 4.333333333$$

Solution Steps

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{3}{4} to fractions with denominator 12.

$$\left(\frac{10}{12}+\frac{9}{12}\right)\times \frac{36}{19}+\left(\frac{2}{3}-\frac{1}{6}\right)\times \frac{8}{3}$$

Since \frac{10}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{10+9}{12}\times \frac{36}{19}+\left(\frac{2}{3}-\frac{1}{6}\right)\times \frac{8}{3}$$

Add 10 and 9 to get 19.

$$\frac{19}{12}\times \frac{36}{19}+\left(\frac{2}{3}-\frac{1}{6}\right)\times \frac{8}{3}$$

Multiply \frac{19}{12} times \frac{36}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 36}{12\times 19}+\left(\frac{2}{3}-\frac{1}{6}\right)\times \frac{8}{3}$$

Cancel out 19 in both numerator and denominator.

$$\frac{36}{12}+\left(\frac{2}{3}-\frac{1}{6}\right)\times \frac{8}{3}$$

Divide 36 by 12 to get 3.

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

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

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

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

$$3+\frac{4-1}{6}\times \frac{8}{3}$$

Subtract 1 from 4 to get 3.

$$3+\frac{3}{6}\times \frac{8}{3}$$

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

$$3+\frac{1}{2}\times \frac{8}{3}$$

Multiply \frac{1}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{1\times 8}{2\times 3}$$

Do the multiplications in the fraction \frac{1\times 8}{2\times 3}.

$$3+\frac{8}{6}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$3+\frac{4}{3}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{9}{3}+\frac{4}{3}$$

Since \frac{9}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{9+4}{3}$$

Add 9 and 4 to get 13.

$$\frac{13}{3}$$

Factor

$$\frac{13}{3} = 4\frac{1}{3} = 4.333333333333333$$