Solve 5/6div1/3+3/4-1/2*frac{2}{3}

$$\frac { 5 } { 6 } \div \frac { 1 } { 3 } + \frac { 3 } { 4 } - \frac { 1 } { 2 } \times \frac { 2 } { 3 }$$

Evaluate

$$\frac{35}{12}\approx 2.916666667$$

Solution Steps

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

$$\frac{5}{6}\times 3+\frac{3}{4}-\frac{1}{2}\times \frac{2}{3}$$

Express \frac{5}{6}\times 3 as a single fraction.

$$\frac{5\times 3}{6}+\frac{3}{4}-\frac{1}{2}\times \frac{2}{3}$$

Multiply 5 and 3 to get 15.

$$\frac{15}{6}+\frac{3}{4}-\frac{1}{2}\times \frac{2}{3}$$

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

$$\frac{5}{2}+\frac{3}{4}-\frac{1}{2}\times \frac{2}{3}$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{10}{4}+\frac{3}{4}-\frac{1}{2}\times \frac{2}{3}$$

Since \frac{10}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{4}-\frac{1}{2}\times \frac{2}{3}$$

Add 10 and 3 to get 13.

$$\frac{13}{4}-\frac{1}{2}\times \frac{2}{3}$$

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

$$\frac{13}{4}-\frac{1\times 2}{2\times 3}$$

Cancel out 2 in both numerator and denominator.

$$\frac{13}{4}-\frac{1}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{13}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{39}{12}-\frac{4}{12}$$

Since \frac{39}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39-4}{12}$$

Subtract 4 from 39 to get 35.

$$\frac{35}{12}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2} \cdot 3} = 2\frac{11}{12} = 2.9166666666666665$$