Math Problem Statement
Solution
Let's analyze and classify each number into its correct subsets based on the provided options:
Subsets Legend:
- A: Real, Irrational
- B: Real, Rational
- C: Real, Rational, Integer
- D: Real, Rational, Integer, Whole
- E: Real, Rational, Integer, Whole, Natural
Numbers to Classify:
-
-4:
- It's a real number.
- It's a rational number (since it can be expressed as -4/1).
- It's an integer.
- It's not a whole number (since whole numbers are non-negative).
- Correct classification: C.
-
6.5:
- It's a real number.
- It's a rational number (as 6.5 can be expressed as 13/2).
- It's not an integer or whole number.
- Correct classification: B.
-
√5:
- It's a real number.
- It's an irrational number (since √5 cannot be expressed as a fraction).
- Correct classification: A.
-
⅔:
- It's a real number.
- It's a rational number (⅔ is a fraction of two integers).
- It's not an integer.
- Correct classification: B.
-
1.390864... (non-repeating decimal):
- It's a real number.
- It's an irrational number (since it doesn't repeat and can't be expressed as a fraction).
- Correct classification: A.
-
−√9:
- It's a real number.
- √9 = 3, so −√9 = -3.
- It's a rational number (as -3 can be expressed as -3/1).
- It's an integer.
- Correct classification: C.
Now let's summarize the answers:
- -4 → C
- 6.5 → B
- √5 → A
- ⅔ → B
- 1.390864... → A
- −√9 → C
Would you like further details or have any questions?
Here are 5 related questions you might find interesting:
- What is the difference between rational and irrational numbers?
- Can irrational numbers ever be represented as fractions?
- What defines a whole number versus an integer?
- How are real numbers classified in mathematical sets?
- Can the square root of any number be rational?
Tip: Rational numbers are always expressible as fractions, while irrational numbers have non-terminating, non-repeating decimals.
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Math Problem Analysis
Mathematical Concepts
Number classification
Real numbers
Rational and Irrational numbers
Formulas
-
Theorems
Classification of numbers into sets
Suitable Grade Level
Grades 6-9
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