Solve (2-2*(-1/3)div5/2-3/5)*(-1/3)+1

$$(2-2 \times (- \frac{ 1 }{ 3 } ) \div \frac{ 5 }{ 2 } - \frac{ 3 }{ 5 } ) \times (- \frac{ 1 }{ 3 } )+1$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

Express 2\left(-\frac{1}{3}\right) as a single fraction.

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

Multiply 2 and -1 to get -2.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

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

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

Multiply -\frac{2}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-2\times 2}{3\times 5}.

$$\left(2-\frac{-4}{15}-\frac{3}{5}\right)\left(-\frac{1}{3}\right)+1$$

Fraction \frac{-4}{15} can be rewritten as -\frac{4}{15} by extracting the negative sign.

$$\left(2-\left(-\frac{4}{15}\right)-\frac{3}{5}\right)\left(-\frac{1}{3}\right)+1$$

The opposite of -\frac{4}{15} is \frac{4}{15}.

$$\left(2+\frac{4}{15}-\frac{3}{5}\right)\left(-\frac{1}{3}\right)+1$$

Convert 2 to fraction \frac{30}{15}.

$$\left(\frac{30}{15}+\frac{4}{15}-\frac{3}{5}\right)\left(-\frac{1}{3}\right)+1$$

Since \frac{30}{15} and \frac{4}{15} have the same denominator, add them by adding their numerators.

$$\left(\frac{30+4}{15}-\frac{3}{5}\right)\left(-\frac{1}{3}\right)+1$$

Add 30 and 4 to get 34.

$$\left(\frac{34}{15}-\frac{3}{5}\right)\left(-\frac{1}{3}\right)+1$$

Least common multiple of 15 and 5 is 15. Convert \frac{34}{15} and \frac{3}{5} to fractions with denominator 15.

$$\left(\frac{34}{15}-\frac{9}{15}\right)\left(-\frac{1}{3}\right)+1$$

Since \frac{34}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{34-9}{15}\left(-\frac{1}{3}\right)+1$$

Subtract 9 from 34 to get 25.

$$\frac{25}{15}\left(-\frac{1}{3}\right)+1$$

Reduce the fraction \frac{25}{15} to lowest terms by extracting and canceling out 5.

$$\frac{5}{3}\left(-\frac{1}{3}\right)+1$$

Multiply \frac{5}{3} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-1\right)}{3\times 3}+1$$

Do the multiplications in the fraction \frac{5\left(-1\right)}{3\times 3}.

$$\frac{-5}{9}+1$$

Fraction \frac{-5}{9} can be rewritten as -\frac{5}{9} by extracting the negative sign.

$$-\frac{5}{9}+1$$

Convert 1 to fraction \frac{9}{9}.

$$-\frac{5}{9}+\frac{9}{9}$$

Since -\frac{5}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{-5+9}{9}$$

Add -5 and 9 to get 4.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$