Solve 1/3*[-2/3*(2/5-1/3)]:(-frac{1}{15})*3+frac{1}{3}

$$\frac { 1 } { 3 } \cdot [ - \frac { 2 } { 3 } \cdot ( \frac { 2 } { 5 } - \frac { 1 } { 3 } ) ] : ( - \frac { 1 } { 15 } ) \cdot 3 + \frac { 1 } { 3 }$$

Evaluate

$$1$$

Solution Steps

Multiply \frac{1}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-2\right)}{3\times 3}.

$$\frac{\frac{-2}{9}\left(\frac{2}{5}-\frac{1}{3}\right)}{-\frac{1}{15}}\times 3+\frac{1}{3}$$

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

$$\frac{-\frac{2}{9}\left(\frac{2}{5}-\frac{1}{3}\right)}{-\frac{1}{15}}\times 3+\frac{1}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{2}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{-\frac{2}{9}\left(\frac{6}{15}-\frac{5}{15}\right)}{-\frac{1}{15}}\times 3+\frac{1}{3}$$

Since \frac{6}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{2}{9}\times \frac{6-5}{15}}{-\frac{1}{15}}\times 3+\frac{1}{3}$$

Subtract 5 from 6 to get 1.

$$\frac{-\frac{2}{9}\times \frac{1}{15}}{-\frac{1}{15}}\times 3+\frac{1}{3}$$

Multiply -\frac{2}{9} times \frac{1}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-2}{9\times 15}}{-\frac{1}{15}}\times 3+\frac{1}{3}$$

Do the multiplications in the fraction \frac{-2}{9\times 15}.

$$\frac{\frac{-2}{135}}{-\frac{1}{15}}\times 3+\frac{1}{3}$$

Fraction \frac{-2}{135} can be rewritten as -\frac{2}{135} by extracting the negative sign.

$$\frac{-\frac{2}{135}}{-\frac{1}{15}}\times 3+\frac{1}{3}$$

Divide -\frac{2}{135} by -\frac{1}{15} by multiplying -\frac{2}{135} by the reciprocal of -\frac{1}{15}.

$$-\frac{2}{135}\left(-15\right)\times 3+\frac{1}{3}$$

Express -\frac{2}{135}\left(-15\right) as a single fraction.

$$\frac{-2\left(-15\right)}{135}\times 3+\frac{1}{3}$$

Multiply -2 and -15 to get 30.

$$\frac{30}{135}\times 3+\frac{1}{3}$$

Reduce the fraction \frac{30}{135} to lowest terms by extracting and canceling out 15.

$$\frac{2}{9}\times 3+\frac{1}{3}$$

Express \frac{2}{9}\times 3 as a single fraction.

$$\frac{2\times 3}{9}+\frac{1}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{9}+\frac{1}{3}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}+\frac{1}{3}$$

Since \frac{2}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{3}$$

Add 2 and 1 to get 3.

$$\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$1$$

Factor

$$1$$