Question

#9 4 5/6 q) rational r) irrational #8 -√140 o) rational p) irrational

Explanation:

Step1: Recall the definition of rational and irrational numbers

A rational number can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$. An irrational number cannot be written as a fraction and has a non - repeating, non - terminating decimal expansion.

Step2: Analyze $4\frac{5}{6}$

$4\frac{5}{6}=\frac{4\times6 + 5}{6}=\frac{24 + 5}{6}=\frac{29}{6}$. Since it can be written as a fraction of two integers, it is rational.

Step3: Analyze $-\sqrt{140}$

We know that $\sqrt{140}=\sqrt{4\times35}=2\sqrt{35}$. Since $\sqrt{35}$ is non - repeating and non - terminating (because 35 is not a perfect square), $-\sqrt{140}$ is an irrational number.

Answer:

#8: P) Irrational
#9: Q) Rational