Solve 4*(2/9)+(-5/3):(2/9)

$$4 \cdot ( \frac { 2 } { 9 } ) + ( \frac { - 5 } { 3 } ) : ( \frac { 2 } { 9 } )$$

Evaluate

$$-\frac{119}{18}\approx -6.611111111$$

Solution Steps

Express 4\times \frac{2}{9} as a single fraction.

$$\frac{4\times 2}{9}+\frac{\frac{-5}{3}}{\frac{2}{9}}$$

Multiply 4 and 2 to get 8.

$$\frac{8}{9}+\frac{\frac{-5}{3}}{\frac{2}{9}}$$

Divide \frac{-5}{3} by \frac{2}{9} by multiplying \frac{-5}{3} by the reciprocal of \frac{2}{9}.

$$\frac{8}{9}+\frac{-5\times 9}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{8}{9}+\frac{-5\times 3}{2}$$

Multiply -5 and 3 to get -15.

$$\frac{8}{9}+\frac{-15}{2}$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\frac{8}{9}-\frac{15}{2}$$

Least common multiple of 9 and 2 is 18. Convert \frac{8}{9} and \frac{15}{2} to fractions with denominator 18.

$$\frac{16}{18}-\frac{135}{18}$$

Since \frac{16}{18} and \frac{135}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-135}{18}$$

Subtract 135 from 16 to get -119.

$$-\frac{119}{18}$$

Factor

$$-\frac{119}{18} = -6\frac{11}{18} = -6.611111111111111$$