Solve left|-9/4right|divleft|-4/9right|

$$\left| \frac{ -9 }{ 4 } \right| \div \left| \frac{ -4 }{ 9 } \right|$$

Evaluate

$$\frac{81}{16}=5.0625$$

Solution Steps

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{|-\frac{9}{4}|}{|\frac{-4}{9}|}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{9}{4} is \frac{9}{4}.

$$\frac{\frac{9}{4}}{|\frac{-4}{9}|}$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{\frac{9}{4}}{|-\frac{4}{9}|}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{4}{9} is \frac{4}{9}.

$$\frac{\frac{9}{4}}{\frac{4}{9}}$$

Divide \frac{9}{4} by \frac{4}{9} by multiplying \frac{9}{4} by the reciprocal of \frac{4}{9}.

$$\frac{9}{4}\times \frac{9}{4}$$

Multiply \frac{9}{4} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 9}{4\times 4}$$

Do the multiplications in the fraction \frac{9\times 9}{4\times 4}.

$$\frac{81}{16}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {4}} = 5\frac{1}{16} = 5.0625$$