Solve 4/5*(1/3-2/3)=4/5*frac{1}{3}-frac{4}{5}*frac{2}{3}

$$\frac { 4 } { 5 } \times ( \frac { 1 } { 3 } - \frac { 2 } { 3 } ) = \frac { 4 } { 5 } \times \frac { 1 } { 3 } - \frac { 4 } { 5 } \times \frac { 2 } { 3 }$$

Verify

Solution Steps

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

$$\frac{4}{5}\times \frac{1-2}{3}=\frac{4}{5}\times \frac{1}{3}-\frac{4}{5}\times \frac{2}{3}$$

Subtract 2 from 1 to get -1.

$$\frac{4}{5}\left(-\frac{1}{3}\right)=\frac{4}{5}\times \frac{1}{3}-\frac{4}{5}\times \frac{2}{3}$$

Multiply \frac{4}{5} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-1\right)}{5\times 3}=\frac{4}{5}\times \frac{1}{3}-\frac{4}{5}\times \frac{2}{3}$$

Do the multiplications in the fraction \frac{4\left(-1\right)}{5\times 3}.

$$\frac{-4}{15}=\frac{4}{5}\times \frac{1}{3}-\frac{4}{5}\times \frac{2}{3}$$

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

$$-\frac{4}{15}=\frac{4}{5}\times \frac{1}{3}-\frac{4}{5}\times \frac{2}{3}$$

Multiply \frac{4}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{4}{15}=\frac{4\times 1}{5\times 3}-\frac{4}{5}\times \frac{2}{3}$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 3}.

$$-\frac{4}{15}=\frac{4}{15}-\frac{4}{5}\times \frac{2}{3}$$

Multiply \frac{4}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{4}{15}=\frac{4}{15}-\frac{4\times 2}{5\times 3}$$

Do the multiplications in the fraction \frac{4\times 2}{5\times 3}.

$$-\frac{4}{15}=\frac{4}{15}-\frac{8}{15}$$

Since \frac{4}{15} and \frac{8}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{4}{15}=\frac{4-8}{15}$$

Subtract 8 from 4 to get -4.

$$-\frac{4}{15}=-\frac{4}{15}$$

Compare -\frac{4}{15} and -\frac{4}{15}.

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