Edia | Free math homework in minutes - Free Printable

Let's solve each question on the worksheet step by step and explain the reasoning.

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Definitions to Remember:

- Rational Numbers: Numbers that can be expressed as a fraction $ \frac{p}{q} $, where $ p $ and $ q $ are integers and $ q \ne 0 $. This includes all integers, fractions, terminating decimals, and repeating decimals.
- Integers: Whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...).
- Whole Numbers: Non-negative integers (0, 1, 2, 3, ...). So, they include 0 and all positive integers but not negative numbers.

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Question 1:

Number: 9

- Is 9 a rational number?
✔ Yes — it can be written as $ \frac{9}{1} $, so it’s rational.
- Is 9 an integer?
✔ Yes — it’s a whole number without a fractional part.
- Is 9 a whole number?
✔ Yes — it’s a non-negative integer.

✔ Answer:
✔ Rational number
✔ Integer
✔ Whole number

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Question 2:

Number: 27

- Rational? Yes → $ \frac{27}{1} $
- Integer? Yes
- Whole number? Yes

✔ Answer:
✔ Rational number
✔ Integer
✔ Whole number

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Question 3:

Choose the integers.

Options:
- $-33$ → ✔ Integer (negative whole number)
- $-0.3810964...$ → ✘ Not an integer (decimal)
- $30$ → ✔ Integer
- $38$ → ✔ Integer
- $-\frac{5}{4}$ → ✘ Not an integer (fraction = -1.25)
- $-3$ → ✔ Integer

✔ Answer:
✔ $-33$
✔ $30$
✔ $38$
✔ $-3$

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Question 4:

Choose the integers.

Options:
- $34$ → ✔ Integer
- $4.29$ → ✘ Decimal → not integer
- $-3.30354...$ → ✘ Decimal → not integer
- $-2.319632...$ → ✘ Decimal → not integer
- $0.2$ → ✘ Decimal → not integer
- $-17$ → ✔ Integer

✔ Answer:
✔ $34$
✔ $-17$

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Question 5:

Choose the whole numbers.

Whole numbers: 0, 1, 2, 3, ...

Options:
- $-3.44$ → ✘ Negative → not whole
- $\sqrt{51}$ → ✘ $ \sqrt{51} \approx 7.14 $, not an integer → not whole
- $-3.9$ → ✘ Negative → not whole
- $4.874222...$ → ✘ Decimal → not whole
- $-\frac{13}{8}$ → ✘ Negative fraction → not whole
- $5\sqrt{2}$ → ✘ $ \sqrt{2} $ is irrational → $ 5\sqrt{2} $ is irrational → not whole

✘ None of these are whole numbers.

But wait — let's double-check:

Is any of these a whole number?

No. All are either negative, decimal, or irrational.

✔ Answer:
None of the options are whole numbers.

But since it says "choose the whole numbers" and there are no correct ones, the answer is:
✘ No selections

However, if we must select from the list, then none are whole numbers.

So, no boxes should be checked.

But let's confirm:

- $ \sqrt{51} $: $ \sqrt{49} = 7 $, $ \sqrt{64} = 8 $, so ~7.14 → not integer → not whole
- $ 5\sqrt{2} \approx 5(1.414) = 7.07 $ → not integer

So yes, none qualify.

✔ Answer:
→ No choices are whole numbers.

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Question 6:

Choose the whole numbers.

Options:
- $34$ → ✔ Whole number
- $31$ → ✔ Whole number
- $13$ → ✔ Whole number
- $-\frac{5}{8}$ → ✘ Negative fraction → not whole
- $\frac{3}{5}$ → ✘ Fraction → not whole
- $32$ → ✔ Whole number

✔ Answer:
✔ $34$
✔ $31$
✔ $13$
✔ $32$

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✔ Final Answers Summary:

#### 1. 9
- ✔ Rational number
- ✔ Integer
- ✔ Whole number

#### 2. 27
- ✔ Rational number
- ✔ Integer
- ✔ Whole number

#### 3. Choose integers:
- ✔ $-33$
- ✔ $30$
- ✔ $38$
- ✔ $-3$

#### 4. Choose integers:
- ✔ $34$
- ✔ $-17$

#### 5. Choose whole numbers:
- ✘ None of the options are whole numbers
(All are negative, decimals, or irrational)

#### 6. Choose whole numbers:
- ✔ $34$
- ✔ $31$
- ✔ $13$
- ✔ $32$

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📝 Notes:

- Whole numbers do not include negatives or fractions.
- Integers include negative numbers, zero, and positives.
- Rational numbers include all numbers that can be written as fractions (including integers and terminating/repeating decimals).

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