Question

classify the numbers as rational or irrational.
4 9 4·9 4+9
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 (multiplication, addition) on rationals give rationals.

Step2: Classify 4

4 is an integer, so $4=\frac{4}{1}$, rational.

Step3: Classify 9

9 is an integer, so $9=\frac{9}{1}$, rational.

Step4: Classify \(4\cdot9\)

\(4\cdot9 = 36\), 36 is an integer, so rational (as \(36=\frac{36}{1}\)).

Step5: Classify \(4 + 9\)

\(4+9=13\), 13 is an integer, so rational (as \(13=\frac{13}{1}\)).

Step6: Check for irrational

None of the numbers are non - repeating, non - terminating decimals or cannot be expressed as $\frac{p}{q}$. So irrational box is empty.

Answer:

rational: 4, 9, \(4\cdot9\), \(4 + 9\)
irrational: (empty)