Solve 1/2-(-3)div6/5+4/9(-3/8)-1

$$\frac{ 1 }{ 2 } -(-3) \div \frac{ 6 }{ 5 } + \frac{ 4 }{ 9 } (- \frac{ 3 }{ 8 } )-1$$

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

Divide -3 by \frac{6}{5} by multiplying -3 by the reciprocal of \frac{6}{5}.

$$\frac{1}{2}-\left(-3\times \frac{5}{6}\right)+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Express -3\times \frac{5}{6} as a single fraction.

$$\frac{1}{2}-\frac{-3\times 5}{6}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Multiply -3 and 5 to get -15.

$$\frac{1}{2}-\frac{-15}{6}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Reduce the fraction \frac{-15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}-\left(-\frac{5}{2}\right)+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

The opposite of -\frac{5}{2} is \frac{5}{2}.

$$\frac{1}{2}+\frac{5}{2}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Since \frac{1}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{1+5}{2}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Add 1 and 5 to get 6.

$$\frac{6}{2}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Divide 6 by 2 to get 3.

$$3+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Multiply \frac{4}{9} times -\frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{4\left(-3\right)}{9\times 8}-1$$

Do the multiplications in the fraction \frac{4\left(-3\right)}{9\times 8}.

$$3+\frac{-12}{72}-1$$

Reduce the fraction \frac{-12}{72} to lowest terms by extracting and canceling out 12.

$$3-\frac{1}{6}-1$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{18}{6}-\frac{1}{6}-1$$

Since \frac{18}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-1}{6}-1$$

Subtract 1 from 18 to get 17.

$$\frac{17}{6}-1$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{17}{6}-\frac{6}{6}$$

Since \frac{17}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-6}{6}$$

Subtract 6 from 17 to get 11.

$$\frac{11}{6}$$

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$