Solve 2/3-4/5-1/-frac{2{3}}=

$$\frac { \frac { 2 } { 3 } - \frac { 4 } { 5 } - 1 } { - \frac { 2 } { 3 } } =$$

Evaluate

$$\frac{17}{10}=1.7$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{\frac{10}{15}-\frac{12}{15}-1}{-\frac{2}{3}}$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-12}{15}-1}{-\frac{2}{3}}$$

Subtract 12 from 10 to get -2.

$$\frac{-\frac{2}{15}-1}{-\frac{2}{3}}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{-\frac{2}{15}-\frac{15}{15}}{-\frac{2}{3}}$$

Since -\frac{2}{15} and \frac{15}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-2-15}{15}}{-\frac{2}{3}}$$

Subtract 15 from -2 to get -17.

$$\frac{-\frac{17}{15}}{-\frac{2}{3}}$$

Divide -\frac{17}{15} by -\frac{2}{3} by multiplying -\frac{17}{15} by the reciprocal of -\frac{2}{3}.

$$-\frac{17}{15}\left(-\frac{3}{2}\right)$$

Multiply -\frac{17}{15} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-17\left(-3\right)}{15\times 2}$$

Do the multiplications in the fraction \frac{-17\left(-3\right)}{15\times 2}.

$$\frac{51}{30}$$

Reduce the fraction \frac{51}{30} to lowest terms by extracting and canceling out 3.

$$\frac{17}{10}$$

Factor

$$\frac{17}{2 \cdot 5} = 1\frac{7}{10} = 1.7$$