Question

check each set that includes the number shown. \\(\frac{5}{9}\\) \
\\(\times\\) natural numbers \
\\(\times\\) whole numbers \
\\(\times\\) integers \
\\(\checkmark\\) rational numbers \
\\(\times\\) irrational numbers \
\\(\checkmark\\) real numbers \
complete \
check each set that includes the number shown. \\(-17\\) \
\\(\square\\) natural numbers \
\\(\square\\) whole numbers \
\\(\square\\) integers \
\\(\square\\) rational numbers \
\\(\square\\) irrational numbers \
\\(\square\\) real numbers \
done \\(\checkmark\\)

Explanation:

Step1: Analyze -17's number type

Natural numbers are positive integers (1, 2, 3...), so -17 is not natural. Whole numbers are non - negative integers (0, 1, 2...), so -17 is not whole. Integers include positive/negative whole numbers and 0, so -17 is an integer. Rational numbers are numbers that can be expressed as a fraction $\frac{a}{b}$ (b≠0), -17 = $\frac{- 17}{1}$, so it's rational. Irrational numbers can't be expressed as a fraction, so -17 is not irrational. Real numbers include all rational and irrational numbers, so -17 is real.

Step2: Check each set

• Natural numbers: Unchecked (×), since -17 is negative.
• Whole numbers: Unchecked (×), since -17 is negative.
• Integers: Checked (√), as -17 is an integer.
• Rational numbers: Checked (√), as -17 = $\frac{-17}{1}$.
• Irrational numbers: Unchecked (×), as -17 is rational.
• Real numbers: Checked (√), as all integers are real.

Answer:

• natural numbers: ×
• whole numbers: ×
• integers: √
• rational numbers: √
• irrational numbers: ×
• real numbers: √