Let’s go through each number one by one and classify it correctly.
We’re working with rational numbers — which means any number that can be written as a fraction (including integers, decimals that terminate or repeat, etc.).
The categories we use are:
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Integer: Whole numbers and their negatives (like -3, 0, 5)
-
Rational: Any number that can be written as a fraction of two integers (so all integers are rational too)
Note: The worksheet shows nested circles — Rational Numbers include Integers, which include Whole Numbers, etc. But for this homework, since the first example says “-17 → integer, Rational”, we’ll list both if applicable — but note: every integer is also rational, so we always write “Rational” at minimum, and add “integer” if it’s a whole number or its negative.
Also, fractions like 9/10 or 14/5 are rational but NOT integers.
Negative decimals? Still rational if they terminate or repeat — but here all given numbers are either integers or simple fractions.
Let’s solve each:
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2) 0
→ Zero is an integer (it’s a whole number).
→ All integers are rational.
✔ Answer:
integer, Rational
---
3) 2
→ Positive whole number → integer
→ Also rational
✔ Answer:
integer, Rational
---
4) -4
→ Negative whole number → integer
→ Also rational
✔ Answer:
integer, Rational
---
5) 9/10
→ This is a fraction — not a whole number → NOT an integer
→ But it’s a ratio of two integers → Rational
✔ Answer:
Rational
---
6) -20
→ Negative whole number → integer
→ Also rational
✔ Answer:
integer, Rational
---
7) 1.3
→ Decimal that terminates → can be written as 13/10 → Rational
→ Not a whole number → NOT an integer
✔ Answer:
Rational
---
8) 6
→ Positive whole number → integer
→ Also rational
✔ Answer:
integer, Rational
---
9) 15/3
→ Let’s simplify: 15 ÷ 3 = 5 → which is an integer!
→ So even though it looks like a fraction, it simplifies to an integer
→ Therefore: integer, Rational
✔ Answer:
integer, Rational
---
10) -12/6
→ Simplify: -12 ÷ 6 = -2 → which is an integer
→ So again, despite being a fraction, it equals an integer
✔ Answer:
integer, Rational
---
11) 14/5
→ 14 ÷ 5 = 2.8 → decimal that terminates → Rational
→ Not a whole number → NOT an integer
✔ Answer:
Rational
---
12) -50/9
→ -50 ÷ 9 ≈ -5.555... → repeating decimal → still Rational (since it’s a fraction of integers)
→ Not a whole number → NOT an integer
✔ Answer:
Rational
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Now let’s compile the final answers in order:
Final Answer:
2) integer, Rational
3) integer, Rational
4) integer, Rational
5) Rational
6) integer, Rational
7) Rational
8) integer, Rational
9) integer, Rational
10) integer, Rational
11) Rational
12) Rational
Parent Tip: Review the logic above to help your child master the concept of classifying numbers worksheets.
