Solve 0.2-3/frac{2{3}-3}

$$\frac { 0.2 - 3 } { \frac { 2 } { 3 } - 3 }$$

Evaluate

$$1.2$$

Solution Steps

Subtract 3 from 0.2 to get -2.8.

$$\frac{-2.8}{\frac{2}{3}-3}$$

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

$$\frac{-2.8}{\frac{2}{3}-\frac{9}{3}}$$

Since \frac{2}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2.8}{\frac{2-9}{3}}$$

Subtract 9 from 2 to get -7.

$$\frac{-2.8}{-\frac{7}{3}}$$

Divide -2.8 by -\frac{7}{3} by multiplying -2.8 by the reciprocal of -\frac{7}{3}.

$$-2.8\left(-\frac{3}{7}\right)$$

Convert decimal number -2.8 to fraction -\frac{28}{10}. Reduce the fraction -\frac{28}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{14}{5}\left(-\frac{3}{7}\right)$$

Multiply -\frac{14}{5} times -\frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-14\left(-3\right)}{5\times 7}$$

Do the multiplications in the fraction \frac{-14\left(-3\right)}{5\times 7}.

$$\frac{42}{35}$$

Reduce the fraction \frac{42}{35} to lowest terms by extracting and canceling out 7.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$