Math Problem Statement
Solution
Let's classify the given numbers according to the subsets in which each belongs. Here's the breakdown of the possible subsets:
- A. Real, Irrational: Numbers that are real but cannot be expressed as a fraction of two integers.
- B. Real, Rational: Numbers that are real and can be written as a ratio (fraction) of two integers.
- C. Real, Rational, Integer: Numbers that are rational and also belong to the set of integers.
- D. Real, Rational, Integer, Whole: Numbers that are integers and whole numbers (non-negative).
- E. Real, Rational, Integer, Whole, Natural: Numbers that belong to the natural numbers (positive integers) as well as whole numbers and integers.
Now, for the numbers provided:
-
:
- is an irrational number, and multiplying by 3 will keep it irrational.
- So, belongs to set A (Real, Irrational).
-
:
- This is a decimal that can be expressed as a fraction (615/1000), so it's a rational number.
- It belongs to set B (Real, Rational).
-
:
- This is an integer and a natural number.
- It belongs to set E (Real, Rational, Integer, Whole, Natural).
-
:
- is a whole number, an integer, and a rational number.
- It belongs to set D (Real, Rational, Integer, Whole).
-
:
- This is a rational number because it can be expressed as a fraction (1/5).
- It belongs to set B (Real, Rational).
-
(which is 7):
- , a natural number and an integer.
- It belongs to set E (Real, Rational, Integer, Whole, Natural).
Summary of Answers:
- : A
- : B
- : E
- : D
- : B
- : E
Let me know if you want further clarification on any of these! Here are some related questions:
- What are some examples of irrational numbers other than ?
- Why is considered a whole number but not a natural number?
- How can we express any terminating decimal as a fraction?
- What are the differences between integers, whole numbers, and natural numbers?
- Why does belong to the natural number set?
Tip: Remember, every integer is a rational number, but not every rational number is an integer!
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Math Problem Analysis
Mathematical Concepts
Number Classification
Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole Numbers
Natural Numbers
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8
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