Solve -2/3left(4/5+8/15right)=-2/3frac{4}{5}+-frac{2}{3}frac{-8}{15}

$$- \frac{ 2 }{ 3 } \left( \frac{ 4 }{ 5 } + \frac{ 8 }{ 15 } \right) = - \frac{ 2 }{ 3 } \frac{ 4 }{ 5 } +- \frac{ 2 }{ 3 } \frac{ -8 }{ 15 }$$

Verify

Solution Steps

Least common multiple of 5 and 15 is 15. Convert \frac{4}{5} and \frac{8}{15} to fractions with denominator 15.

$$-\frac{2}{3}\left(\frac{12}{15}+\frac{8}{15}\right)=-\frac{2}{3}\times \frac{4}{5}-\frac{2}{3}\times \frac{-8}{15}$$

Since \frac{12}{15} and \frac{8}{15} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}\times \frac{12+8}{15}=-\frac{2}{3}\times \frac{4}{5}-\frac{2}{3}\times \frac{-8}{15}$$

Add 12 and 8 to get 20.

$$-\frac{2}{3}\times \frac{20}{15}=-\frac{2}{3}\times \frac{4}{5}-\frac{2}{3}\times \frac{-8}{15}$$

Reduce the fraction \frac{20}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{2}{3}\times \frac{4}{3}=-\frac{2}{3}\times \frac{4}{5}-\frac{2}{3}\times \frac{-8}{15}$$

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

$$\frac{-2\times 4}{3\times 3}=-\frac{2}{3}\times \frac{4}{5}-\frac{2}{3}\times \frac{-8}{15}$$

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

$$\frac{-8}{9}=-\frac{2}{3}\times \frac{4}{5}-\frac{2}{3}\times \frac{-8}{15}$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$-\frac{8}{9}=-\frac{2}{3}\times \frac{4}{5}-\frac{2}{3}\times \frac{-8}{15}$$

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

$$-\frac{8}{9}=\frac{-2\times 4}{3\times 5}-\frac{2}{3}\times \frac{-8}{15}$$

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

$$-\frac{8}{9}=\frac{-8}{15}-\frac{2}{3}\times \frac{-8}{15}$$

Fraction \frac{-8}{15} can be rewritten as -\frac{8}{15} by extracting the negative sign.

$$-\frac{8}{9}=-\frac{8}{15}-\frac{2}{3}\times \frac{-8}{15}$$

Fraction \frac{-8}{15} can be rewritten as -\frac{8}{15} by extracting the negative sign.

$$-\frac{8}{9}=-\frac{8}{15}-\frac{2}{3}\left(-\frac{8}{15}\right)$$

Multiply -\frac{2}{3} times -\frac{8}{15} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{8}{9}=-\frac{8}{15}+\frac{-2\left(-8\right)}{3\times 15}$$

Do the multiplications in the fraction \frac{-2\left(-8\right)}{3\times 15}.

$$-\frac{8}{9}=-\frac{8}{15}+\frac{16}{45}$$

Least common multiple of 15 and 45 is 45. Convert -\frac{8}{15} and \frac{16}{45} to fractions with denominator 45.

$$-\frac{8}{9}=-\frac{24}{45}+\frac{16}{45}$$

Since -\frac{24}{45} and \frac{16}{45} have the same denominator, add them by adding their numerators.

$$-\frac{8}{9}=\frac{-24+16}{45}$$

Add -24 and 16 to get -8.

$$-\frac{8}{9}=-\frac{8}{45}$$

Least common multiple of 9 and 45 is 45. Convert -\frac{8}{9} and -\frac{8}{45} to fractions with denominator 45.

$$-\frac{40}{45}=-\frac{8}{45}$$

Compare -\frac{40}{45} and -\frac{8}{45}.

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