Solve [-5/2)*(4/3)(-7/10)*(-12/5-frac{8}{3})=(-frac{7}{5})

$$[ - \frac { 5 } { 2 } ) \times ( \frac { 4 } { 3 } ) ( - \frac { 7 } { 10 } ) \times ( - \frac { 12 } { 5 } - \frac { 8 } { 3 } ) = ( - \frac { 7 } { 5 } )$$

Verify

Solution Steps

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

$$\frac{-5\times 4}{2\times 3}\left(-\frac{7}{10}\right)\left(-\frac{12}{5}-\frac{8}{3}\right)=-\frac{7}{5}$$

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

$$\frac{-20}{6}\left(-\frac{7}{10}\right)\left(-\frac{12}{5}-\frac{8}{3}\right)=-\frac{7}{5}$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{10}{3}\left(-\frac{7}{10}\right)\left(-\frac{12}{5}-\frac{8}{3}\right)=-\frac{7}{5}$$

Multiply -\frac{10}{3} times -\frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-10\left(-7\right)}{3\times 10}\left(-\frac{12}{5}-\frac{8}{3}\right)=-\frac{7}{5}$$

Do the multiplications in the fraction \frac{-10\left(-7\right)}{3\times 10}.

$$\frac{70}{30}\left(-\frac{12}{5}-\frac{8}{3}\right)=-\frac{7}{5}$$

Reduce the fraction \frac{70}{30} to lowest terms by extracting and canceling out 10.

$$\frac{7}{3}\left(-\frac{12}{5}-\frac{8}{3}\right)=-\frac{7}{5}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{12}{5} and \frac{8}{3} to fractions with denominator 15.

$$\frac{7}{3}\left(-\frac{36}{15}-\frac{40}{15}\right)=-\frac{7}{5}$$

Since -\frac{36}{15} and \frac{40}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{3}\times \frac{-36-40}{15}=-\frac{7}{5}$$

Subtract 40 from -36 to get -76.

$$\frac{7}{3}\left(-\frac{76}{15}\right)=-\frac{7}{5}$$

Multiply \frac{7}{3} times -\frac{76}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-76\right)}{3\times 15}=-\frac{7}{5}$$

Do the multiplications in the fraction \frac{7\left(-76\right)}{3\times 15}.

$$\frac{-532}{45}=-\frac{7}{5}$$

Fraction \frac{-532}{45} can be rewritten as -\frac{532}{45} by extracting the negative sign.

$$-\frac{532}{45}=-\frac{7}{5}$$

Least common multiple of 45 and 5 is 45. Convert -\frac{532}{45} and -\frac{7}{5} to fractions with denominator 45.

$$-\frac{532}{45}=-\frac{63}{45}$$

Compare -\frac{532}{45} and -\frac{63}{45}.

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