Class 8 Exam > Class 8 Questions > Which of the following statements is true?a)E...
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Which of the following statements is true?
- a)Every fraction is a rational number.
- b)Every rational number is a fraction.
- c)Every integer is a rational number.
- d)Both (a) and (c).
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Which of the following statements is true?a)Every fraction is a ration...
- Rational Numbers: a rational number is defined as one that can be expressed in the form a/b, where a is an integer and b is a natural number. This means that every fraction is a rational number.
- But every rational number is not a fraction. For example, -4/9 is a rational number but not a fraction, as fractions include only whole numbers as numerators and natural numbers only as denominators.
- In addition, every integer can be expressed as a fraction (for example, as the integer divided by 1). Therefore, all three statements are true.
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Which of the following statements is true?a)Every fraction is a ration...
Understanding Rational Numbers and Fractions
To determine which statements are true, we need to clarify the definitions of rational numbers and fractions.
What is a Fraction?
- A fraction is a way of representing a part of a whole. It is expressed as a/b, where "a" is the numerator and "b" is the denominator (b ≠ 0).
- Every fraction can be expressed as a division of two integers.
What is a Rational Number?
- A rational number is any number that can be expressed as a fraction (a/b) where both "a" and "b" are integers and "b" is not zero.
- This means that all fractions are rational numbers.
Analyzing the Statements
- Statement (a): Every fraction is a rational number.
- True! Since every fraction can be expressed in the form a/b, it falls under the definition of a rational number.
- Statement (b): Every rational number is a fraction.
- False! While many rational numbers can be expressed as fractions, some rational numbers can also be whole numbers (e.g., 5 can be expressed as 5/1).
- Statement (c): Every integer is a rational number.
- True! Any integer can be expressed as a fraction by writing it over 1 (e.g., 4 can be written as 4/1).
Conclusion
- Since both statements (a) and (c) are true, the correct answer is option 'D': Both (a) and (c).
- This understanding highlights the relationship between fractions, rational numbers, and integers, providing clarity on their definitions and interconnections.
To determine which statements are true, we need to clarify the definitions of rational numbers and fractions.
What is a Fraction?
- A fraction is a way of representing a part of a whole. It is expressed as a/b, where "a" is the numerator and "b" is the denominator (b ≠ 0).
- Every fraction can be expressed as a division of two integers.
What is a Rational Number?
- A rational number is any number that can be expressed as a fraction (a/b) where both "a" and "b" are integers and "b" is not zero.
- This means that all fractions are rational numbers.
Analyzing the Statements
- Statement (a): Every fraction is a rational number.
- True! Since every fraction can be expressed in the form a/b, it falls under the definition of a rational number.
- Statement (b): Every rational number is a fraction.
- False! While many rational numbers can be expressed as fractions, some rational numbers can also be whole numbers (e.g., 5 can be expressed as 5/1).
- Statement (c): Every integer is a rational number.
- True! Any integer can be expressed as a fraction by writing it over 1 (e.g., 4 can be written as 4/1).
Conclusion
- Since both statements (a) and (c) are true, the correct answer is option 'D': Both (a) and (c).
- This understanding highlights the relationship between fractions, rational numbers, and integers, providing clarity on their definitions and interconnections.
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