In Class 9 Math (Number Systems), you must evaluate statements based on the hierarchy of numbers. A frequent question is: 'Every rational number is a whole number.'
Whole Numbers: 0, 1, 2, 3...
Rational Numbers: Any number written as a fraction (p/q).
Fractions (1/2) and Negatives (-5) are Rational, but NOT Whole numbers.
Therefore, All Whole numbers are Rational, but NOT all Rational numbers are Whole.
Statement: Every rational number is a whole number. Answer: FALSE.
Let's define both sets:
Whole Numbers (W): These are complete, non-fractional numbers starting from zero.
Rational Numbers (Q): A rational number is ANY number that can be written in the form p/q, where p and q are integers and q is not zero.
Proof of Falsehood: Take the rational number 1/2 (or 0.5). Is 0.5 a whole number? No. Take the rational number -3. Is -3 a whole number? No (it's an integer). Therefore, not every rational number is a whole number.
Statement: Every whole number is a rational number. Answer: TRUE. Reason: Every whole number (like 7) can easily be written in the p/q form (as 7/1), satisfying the rule for rational numbers.
False. Rational numbers include fractions (like 1/2) and negative numbers (like -5). These are not whole numbers.
True. Every whole number can be expressed as a fraction by putting a 1 in the denominator (e.g., 8 can be written as 8/1), making it a rational number.
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