Solve 2/15-[0.0(6)-31/6-(9/10-0.(3))]

$$\frac { 2 } { 15 } - [ 0.0 ( 6 ) - 3 \frac { 1 } { 6 } - ( \frac { 9 } { 10 } - 0 . ( 3 ) ) ]$$

Evaluate

$$\frac{21}{5}=4.2$$

Solution Steps

Multiply 0 and 6 to get 0.

$$\frac{2}{15}-\left(0-\frac{3\times 6+1}{6}-\left(\frac{9}{10}-0\times 3\right)\right)$$

Multiply 3 and 6 to get 18.

$$\frac{2}{15}-\left(0-\frac{18+1}{6}-\left(\frac{9}{10}-0\times 3\right)\right)$$

Add 18 and 1 to get 19.

$$\frac{2}{15}-\left(0-\frac{19}{6}-\left(\frac{9}{10}-0\times 3\right)\right)$$

Subtract \frac{19}{6} from 0 to get -\frac{19}{6}.

$$\frac{2}{15}-\left(-\frac{19}{6}-\left(\frac{9}{10}-0\times 3\right)\right)$$

Multiply 0 and 3 to get 0.

$$\frac{2}{15}-\left(-\frac{19}{6}-\left(\frac{9}{10}-0\right)\right)$$

Subtract 0 from \frac{9}{10} to get \frac{9}{10}.

$$\frac{2}{15}-\left(-\frac{19}{6}-\frac{9}{10}\right)$$

Least common multiple of 6 and 10 is 30. Convert -\frac{19}{6} and \frac{9}{10} to fractions with denominator 30.

$$\frac{2}{15}-\left(-\frac{95}{30}-\frac{27}{30}\right)$$

Since -\frac{95}{30} and \frac{27}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{15}-\frac{-95-27}{30}$$

Subtract 27 from -95 to get -122.

$$\frac{2}{15}-\frac{-122}{30}$$

Reduce the fraction \frac{-122}{30} to lowest terms by extracting and canceling out 2.

$$\frac{2}{15}-\left(-\frac{61}{15}\right)$$

The opposite of -\frac{61}{15} is \frac{61}{15}.

$$\frac{2}{15}+\frac{61}{15}$$

Since \frac{2}{15} and \frac{61}{15} have the same denominator, add them by adding their numerators.

$$\frac{2+61}{15}$$

Add 2 and 61 to get 63.

$$\frac{63}{15}$$

Reduce the fraction \frac{63}{15} to lowest terms by extracting and canceling out 3.

$$\frac{21}{5}$$

Factor

$$\frac{3 \cdot 7}{5} = 4\frac{1}{5} = 4.2$$