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For each number, put a check under each correct label.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline & Real & Rational & Irrational & Integer & Whole & Counting \\
\hline [tex]$1 / 5$[/tex] & & & & & & \\
\hline -100.5 & & & & & & \\
\hline 22 & & & & & & \\
\hline [tex]$2 \sqrt{6}$[/tex] & & & & & & \\
\hline -0.45311 & & & & & & \\
\hline -10 / 3 & & & & & & \\
\hline
\end{tabular}

Finish the sentence:

Sagot :

GinnyAnsweridn
Certainly! Let's evaluate each number and determine the correct labels based on their mathematical properties.

1. [tex]\( \frac{1}{5} \)[/tex]:
- Real: Yes, it is a real number.
- Rational: No, it cannot be expressed as an integer or simple fraction.
- Irrational: Yes, since it is not a rational number.
- Integer: No, it is not a whole number.
- Whole: No, it is not a non-negative integer.
- Counting: No, it is not a positive integer.

2. [tex]\(-100.5\)[/tex]:
- Real: Yes, it is a real number.
- Rational: No, it cannot be simply expressed as a fraction.
- Irrational: Yes, since it is not a rational number.
- Integer: No, it is not a whole number.
- Whole: No, it is not a non-negative integer.
- Counting: No, it is not a positive integer.

3. [tex]\(22\)[/tex]:
- Real: Yes, it is a real number.
- Rational: Yes, it is a rational number (can be expressed as [tex]\(\frac{22}{1}\)[/tex]).
- Irrational: No, it is a rational number.
- Integer: Yes, it is an integer.
- Whole: Yes, it is a non-negative integer.
- Counting: Yes, it is a positive integer.

4. [tex]\(2\sqrt{6}\)[/tex]:
- Real: Yes, it is a real number.
- Rational: No, it cannot be expressed as a simple fraction.
- Irrational: Yes, since it is not a rational number.
- Integer: No, it is not an integer.
- Whole: No, it is not a non-negative integer.
- Counting: No, it is not a positive integer.

5. [tex]\(-0.45311\)[/tex]:
- Real: Yes, it is a real number.
- Rational: No, it cannot be simply expressed as a fraction.
- Irrational: Yes, since it is not a rational number.
- Integer: No, it is not an integer.
- Whole: No, it is not a non-negative integer.
- Counting: No, it is not a positive integer.

6. [tex]\(-\frac{10}{3}\)[/tex]:
- Real: Yes, it is a real number.
- Rational: No, it cannot be expressed as a simple fraction.
- Irrational: Yes, since it is not a rational number.
- Integer: No, it is not an integer.
- Whole: No, it is not a non-negative integer.
- Counting: No, it is not a positive integer.

Now, let's fill in the table accordingly:

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
& Real & Rational & Irrational & Integer & Whole & Counting \\
\hline
[tex]$1 / 5$[/tex] & ✓ & & ✓ & & & \\
\hline
-100.5 & ✓ & & ✓ & & & \\
\hline
22 & ✓ & ✓ & & ✓ & ✓ & ✓ \\
\hline
[tex]$2 \sqrt{6}$[/tex] & ✓ & & ✓ & & & \\
\hline
[tex]$-0.45311$[/tex] & ✓ & & ✓ & & & \\
\hline
[tex]$-10 / 3$[/tex] & ✓ & & ✓ & & & \\
\hline
\end{tabular}
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