Question

topic: rational and real numbers
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
match each number on the left with the correct description of the number on the right.
answer options on the right may be used more than once.
$3\frac{1}{2}$ this is an integer.
0.56 this is a rational number, but not an integer.
5 this is an irrational number.
$\sqrt{11}$
$-3\frac{1}{2}$

Explanation:

Step1: Analyze \(3\frac{1}{2}\)

\(3\frac{1}{2}=\frac{7}{2} = 3.5\), it is a fraction (rational number) but not an integer. So match with "This is a rational number, but not an integer."

Step2: Analyze \(0.56\)

\(0.56=\frac{56}{100}=\frac{14}{25}\), it is a decimal (rational number) but not an integer. So match with "This is a rational number, but not an integer."

Step3: Analyze \(5\)

\(5\) is a whole number and an integer. So match with "This is an integer."

Step4: Analyze \(\sqrt{11}\)

\(\sqrt{11}\) is a square root of a non - perfect square, so it is an irrational number. Match with "This is an irrational number."

Step5: Analyze \(-3\frac{1}{2}\)

\(-3\frac{1}{2}=-\frac{7}{2}=-3.5\), it is a fraction (rational number) but not an integer. Match with "This is a rational number, but not an integer."

Answer:

• \(3\frac{1}{2}\): This is a rational number, but not an integer.
• \(0.56\): This is a rational number, but not an integer.
• \(5\): This is an integer.
• \(\sqrt{11}\): This is an irrational number.
• \(-3\frac{1}{2}\): This is a rational number, but not an integer.