Let’s go through each statement one by one and decide if it’s TRUE or FALSE.
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1. All counting numbers are integers.
Counting numbers are 1, 2, 3, 4, ... (sometimes called natural numbers). Integers include all whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ... So yes — every counting number is also an integer.
✔ TRUE
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2. The integer 8 can be expressed as a fraction.
Yes! Any integer can be written as a fraction over 1. For example: 8 = 8/1. That’s still a valid fraction.
✔ TRUE
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3. Non-repeating, non-terminating decimals are irrational.
That’s the definition of irrational numbers — they can’t be written as fractions, and their decimal goes on forever without repeating. Like π or √2.
✔ TRUE
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4. Whole numbers exclude zero.
Nope! Whole numbers start at 0: 0, 1, 2, 3, ... So this is wrong.
✘ FALSE
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5. The number 3.35 is a rational number.
Yes! It’s a terminating decimal, which means it can be written as a fraction: 3.35 = 335/100. Rational numbers include any number that can be written as a fraction.
✔ TRUE
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6. Irrational numbers are not included in the number line.
Wrong! Every real number — including irrationals like √2 or π — has a spot on the number line. They’re just harder to write exactly as decimals.
✘ FALSE
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7. The largest negative integer is –1.
Negative integers are -1, -2, -3, ... The closest to zero is -1, so yes — it’s the “largest” (meaning greatest value) among them.
✔ TRUE
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8. Zero is a positive integer.
No! Zero is neither positive nor negative. Positive integers start at 1.
✘ FALSE
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9. The union of the set of rational numbers and the set of irrational numbers is the set of real numbers.
Yes! Real numbers = rational + irrational. There’s no other kind of real number.
✔ TRUE
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10. The intersection of the set of positive integers and the set of negative integers is an empty set.
Positive integers: 1, 2, 3...
Negative integers: -1, -2, -3...
They have nothing in common → intersection is empty.
✔ TRUE
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Final Answer:
1. TRUE
2. TRUE
3. TRUE
4. FALSE
5. TRUE
6. FALSE
7. TRUE
8. FALSE
9. TRUE
10. TRUE
Parent Tip: Review the logic above to help your child master the concept of the real number math worksheet.
