Solve 1/6-(10/4-2/3):112/8+frac{20}{3}

$$\frac { 1 } { 6 } - ( \frac { 10 } { 4 } - \frac { 2 } { 3 } ) : 1 \frac { 12 } { 8 } + \frac { 20 } { 3 }$$

Evaluate

$$\frac{61}{10}=6.1$$

Solution Steps

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}-\frac{\frac{5}{2}-\frac{2}{3}}{\frac{1\times 8+12}{8}}+\frac{20}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{1}{6}-\frac{\frac{15}{6}-\frac{4}{6}}{\frac{1\times 8+12}{8}}+\frac{20}{3}$$

Since \frac{15}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}-\frac{\frac{15-4}{6}}{\frac{1\times 8+12}{8}}+\frac{20}{3}$$

Subtract 4 from 15 to get 11.

$$\frac{1}{6}-\frac{\frac{11}{6}}{\frac{1\times 8+12}{8}}+\frac{20}{3}$$

Multiply 1 and 8 to get 8.

$$\frac{1}{6}-\frac{\frac{11}{6}}{\frac{8+12}{8}}+\frac{20}{3}$$

Add 8 and 12 to get 20.

$$\frac{1}{6}-\frac{\frac{11}{6}}{\frac{20}{8}}+\frac{20}{3}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{6}-\frac{\frac{11}{6}}{\frac{5}{2}}+\frac{20}{3}$$

Divide \frac{11}{6} by \frac{5}{2} by multiplying \frac{11}{6} by the reciprocal of \frac{5}{2}.

$$\frac{1}{6}-\frac{11}{6}\times \frac{2}{5}+\frac{20}{3}$$

Multiply \frac{11}{6} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6}-\frac{11\times 2}{6\times 5}+\frac{20}{3}$$

Do the multiplications in the fraction \frac{11\times 2}{6\times 5}.

$$\frac{1}{6}-\frac{22}{30}+\frac{20}{3}$$

Reduce the fraction \frac{22}{30} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}-\frac{11}{15}+\frac{20}{3}$$

Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{11}{15} to fractions with denominator 30.

$$\frac{5}{30}-\frac{22}{30}+\frac{20}{3}$$

Since \frac{5}{30} and \frac{22}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-22}{30}+\frac{20}{3}$$

Subtract 22 from 5 to get -17.

$$-\frac{17}{30}+\frac{20}{3}$$

Least common multiple of 30 and 3 is 30. Convert -\frac{17}{30} and \frac{20}{3} to fractions with denominator 30.

$$-\frac{17}{30}+\frac{200}{30}$$

Since -\frac{17}{30} and \frac{200}{30} have the same denominator, add them by adding their numerators.

$$\frac{-17+200}{30}$$

Add -17 and 200 to get 183.

$$\frac{183}{30}$$

Reduce the fraction \frac{183}{30} to lowest terms by extracting and canceling out 3.

$$\frac{61}{10}$$

Factor

$$\frac{61}{2 \cdot 5} = 6\frac{1}{10} = 6.1$$