Question

#4 - 4/5
g) rational
h) irrational
#5 4π
i) rational
j) irrational
#6 √16
k) rational
l) irrational
#7 4√4
m) rational
n) irrational
#8 -√140
o) rational
p) irrational
#9 6 - 4/5
q) rational
r) irrational

Explanation:

Step1: Recall the definition of rational and irrational numbers

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

Step2: Analyze each number

For $\#4:-\frac{4}{5}$

It is in the form of a fraction $\frac{a}{b}$ where $a = - 4$ and $b = 5$ are integers and $b
eq0$. So it is a rational number. Answer: G) Rational

For $\#5:4\pi$

Since $\pi$ is an irrational number (a non - repeating, non - terminating decimal) and $4\pi$ is a non - repeating, non - terminating decimal, it is an irrational number. Answer: J) Irrational

For $\#6:\sqrt{16}$

We know that $\sqrt{16}=4=\frac{4}{1}$, which is a fraction of two integers. So it is a rational number. Answer: L) Rational

For $\#7:4\sqrt{4}$

First, $\sqrt{4}=2$, then $4\sqrt{4}=4\times2 = 8=\frac{8}{1}$, which is a fraction of two integers. So it is a rational number. Answer: M) Rational

For $\#8:-\sqrt{140}$

$\sqrt{140}=\sqrt{4\times35}=2\sqrt{35}$. Since $\sqrt{35}$ is a non - repeating, non - terminating decimal, $-\sqrt{140}$ is a non - repeating, non - terminating decimal. So it is an irrational number. Answer: P) Irrational

For $\#9:6\frac{4}{5}$

$6\frac{4}{5}=\frac{6\times5 + 4}{5}=\frac{34}{5}$, which is a fraction of two integers. So it is a rational number. Answer: Q) Rational

Answer:

Step1: Recall the definition of rational and irrational numbers

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

Step2: Analyze each number

For $\#4:-\frac{4}{5}$

It is in the form of a fraction $\frac{a}{b}$ where $a = - 4$ and $b = 5$ are integers and $b
eq0$. So it is a rational number. Answer: G) Rational

For $\#5:4\pi$

Since $\pi$ is an irrational number (a non - repeating, non - terminating decimal) and $4\pi$ is a non - repeating, non - terminating decimal, it is an irrational number. Answer: J) Irrational

For $\#6:\sqrt{16}$

We know that $\sqrt{16}=4=\frac{4}{1}$, which is a fraction of two integers. So it is a rational number. Answer: L) Rational

For $\#7:4\sqrt{4}$

First, $\sqrt{4}=2$, then $4\sqrt{4}=4\times2 = 8=\frac{8}{1}$, which is a fraction of two integers. So it is a rational number. Answer: M) Rational

For $\#8:-\sqrt{140}$

$\sqrt{140}=\sqrt{4\times35}=2\sqrt{35}$. Since $\sqrt{35}$ is a non - repeating, non - terminating decimal, $-\sqrt{140}$ is a non - repeating, non - terminating decimal. So it is an irrational number. Answer: P) Irrational

For $\#9:6\frac{4}{5}$

$6\frac{4}{5}=\frac{6\times5 + 4}{5}=\frac{34}{5}$, which is a fraction of two integers. So it is a rational number. Answer: Q) Rational