Solve [(9/80)/(-10/210)]/(81/-42)

$$[ ( 9 / 80 ) / ( - 10 / 210 ) ] / ( 81 / - 42 )$$

Evaluate

$$\frac{49}{40}=1.225$$

Solution Steps

Divide \frac{\frac{9}{80}}{-\frac{10}{210}} by \frac{81}{-42} by multiplying \frac{\frac{9}{80}}{-\frac{10}{210}} by the reciprocal of \frac{81}{-42}.

$$\frac{\frac{9}{80}\left(-42\right)}{\left(-\frac{10}{210}\right)\times 81}$$

Express \frac{9}{80}\left(-42\right) as a single fraction.

$$\frac{\frac{9\left(-42\right)}{80}}{\left(-\frac{10}{210}\right)\times 81}$$

Multiply 9 and -42 to get -378.

$$\frac{\frac{-378}{80}}{\left(-\frac{10}{210}\right)\times 81}$$

Reduce the fraction \frac{-378}{80} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{189}{40}}{\left(-\frac{10}{210}\right)\times 81}$$

Reduce the fraction \frac{10}{210} to lowest terms by extracting and canceling out 10.

$$\frac{-\frac{189}{40}}{-\frac{1}{21}\times 81}$$

Express -\frac{1}{21}\times 81 as a single fraction.

$$\frac{-\frac{189}{40}}{\frac{-81}{21}}$$

Reduce the fraction \frac{-81}{21} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{189}{40}}{-\frac{27}{7}}$$

Divide -\frac{189}{40} by -\frac{27}{7} by multiplying -\frac{189}{40} by the reciprocal of -\frac{27}{7}.

$$-\frac{189}{40}\left(-\frac{7}{27}\right)$$

Multiply -\frac{189}{40} times -\frac{7}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-189\left(-7\right)}{40\times 27}$$

Do the multiplications in the fraction \frac{-189\left(-7\right)}{40\times 27}.

$$\frac{1323}{1080}$$

Reduce the fraction \frac{1323}{1080} to lowest terms by extracting and canceling out 27.

$$\frac{49}{40}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {3} \cdot 5} = 1\frac{9}{40} = 1.225$$