Solve -2/3+2.4*3.overline{8}-5/6

$$- \frac { 2 } { 3 } + 2.4 \cdot 3 . \overline { 8 } - \frac { 5 } { 6 }$$

Evaluate

$$\frac{98}{15}\approx 6.533333333$$

Solution Steps

Multiply 2.4 and 3 to get 7.2.

$$-\frac{2}{3}+7.2$$

Convert decimal number 7.2 to fraction \frac{72}{10}. Reduce the fraction \frac{72}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{3}+\frac{36}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{2}{3} and \frac{36}{5} to fractions with denominator 15.

$$-\frac{10}{15}+\frac{108}{15}$$

Since -\frac{10}{15} and \frac{108}{15} have the same denominator, add them by adding their numerators.

$$\frac{-10+108}{15}$$

Add -10 and 108 to get 98.

$$\frac{98}{15}$$

Factor

$$\frac{2 \cdot 7 ^ {2}}{3 \cdot 5} = 6\frac{8}{15} = 6.533333333333333$$