Question

classify the numbers as rational or irrational.
4 -2 4 + -2 4·-2
rational irrational

Explanation:

Step1: Recall rational number definition

A rational number is a number that can be expressed as $\frac{p}{q}$ where $p, q$ are integers and $q
eq0$. Integers are rational, and operations (addition, multiplication) on rational numbers give rational numbers.

Step2: Classify 4

4 is an integer, so it's rational (since $4=\frac{4}{1}$, $p = 4$, $q = 1$ integers, $q
eq0$).

Step3: Classify -2

-2 is an integer, so it's rational (since $-2=\frac{-2}{1}$, $p=-2$, $q = 1$ integers, $q
eq0$).

Step4: Classify $4 + (-2)$

Calculate $4+(-2)=4 - 2=2$. 2 is an integer, so it's rational (as integers are rational).

Step5: Classify $4\cdot(-2)$

Calculate $4\times(-2)=-8$. -8 is an integer, so it's rational (as integers are rational).

Step6: Check for irrational

None of the numbers or results of operations are non - repeating, non - terminating decimals (which define irrational numbers). So no numbers are irrational.

Answer:

rational: 4, -2, \(4 + (-2)\), \(4\cdot(-2)\)
irrational: (no numbers)