Solve 2/3-1/3(2x-3/5)

$$\frac { 2 } { 3 } - \frac { 1 } { 3 } ( 2 x - \frac { 3 } { 5 } )$$

Evaluate

$$-\frac{2x}{3}+\frac{13}{15}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{3} by 2x-\frac{3}{5}.

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

Express -\frac{1}{3}\times 2 as a single fraction.

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

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

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

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

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

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

$$\frac{2}{3}-\frac{2}{3}x+\frac{3}{15}$$

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

$$\frac{2}{3}-\frac{2}{3}x+\frac{1}{5}$$

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

$$\frac{10}{15}-\frac{2}{3}x+\frac{3}{15}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{15}-\frac{2}{3}x$$

Add 10 and 3 to get 13.

$$\frac{13}{15}-\frac{2}{3}x$$

Expand

$$-\frac{2x}{3}+\frac{13}{15}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{3} by 2x-\frac{3}{5}.

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

Express -\frac{1}{3}\times 2 as a single fraction.

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

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

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

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

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

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

$$\frac{2}{3}-\frac{2}{3}x+\frac{3}{15}$$

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

$$\frac{2}{3}-\frac{2}{3}x+\frac{1}{5}$$

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

$$\frac{10}{15}-\frac{2}{3}x+\frac{3}{15}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{15}-\frac{2}{3}x$$

Add 10 and 3 to get 13.

$$\frac{13}{15}-\frac{2}{3}x$$