Solve (12/3-1/3)+(11/2*11/3):frac{5}{6}=

$$( 1 \frac { 2 } { 3 } - \frac { 1 } { 3 } ) + ( 1 \frac { 1 } { 2 } \cdot 1 \frac { 1 } { 3 } ) : \frac { 5 } { 6 } =$$

Evaluate

$$\frac{56}{15}\approx 3.733333333$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Since \frac{5}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 5 to get 4.

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Multiply 1 and 3 to get 3.

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

Add 3 and 1 to get 4.

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

Multiply \frac{3}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$\frac{4}{3}+\frac{\frac{4}{2}}{\frac{5}{6}}$$

Divide 4 by 2 to get 2.

$$\frac{4}{3}+\frac{2}{\frac{5}{6}}$$

Divide 2 by \frac{5}{6} by multiplying 2 by the reciprocal of \frac{5}{6}.

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

Express 2\times \frac{6}{5} as a single fraction.

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

Multiply 2 and 6 to get 12.

$$\frac{4}{3}+\frac{12}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{12}{5} to fractions with denominator 15.

$$\frac{20}{15}+\frac{36}{15}$$

Since \frac{20}{15} and \frac{36}{15} have the same denominator, add them by adding their numerators.

$$\frac{20+36}{15}$$

Add 20 and 36 to get 56.

$$\frac{56}{15}$$

Factor

$$\frac{2 ^ {3} \cdot 7}{3 \cdot 5} = 3\frac{11}{15} = 3.7333333333333334$$