What type of number can be written as a fraction [tex]$\frac{p}{q}$[/tex], where [tex]$p$[/tex] and [tex]$q$[/tex] are integers and [tex]$q$[/tex] is not equal to zero?
A. All numbers
B. A rational number
C. [tex]$\pi$[/tex]
D. An irrational number
Answer (2)
Rational numbers are defined as numbers that can be expressed in the form q p , where p and q are integers and q = 0 .
The question asks to identify the type of number that fits this definition.
By definition, a rational number is a number that can be written as a fraction q p , where p and q are integers and q is not equal to zero.
Therefore, the answer is $\boxed{\text{B}}.
Explanation
Understanding the Question We are asked to identify the type of number that can be expressed as a fraction q p , where p and q are integers, and q is not zero. This is a fundamental concept in number theory.
Definition of Rational Numbers Let's consider the definition of a rational number. A rational number is any number that can be expressed as the quotient or fraction q p of two integers, where p is the numerator and q is the denominator, and q is not equal to zero.
Analyzing the Options Now, let's examine the given options:
A. All numbers: This is incorrect because not all numbers can be expressed in this form (e.g., irrational numbers like 2 or π ).
B. A rational number: This aligns perfectly with the definition we discussed.
C. π : π is an irrational number, meaning it cannot be expressed as a fraction of two integers.
D. An irrational number: Irrational numbers, by definition, cannot be expressed in the form q p where p and q are integers and q = 0 .
Conclusion Therefore, the correct answer is B. A rational number .
Examples
Rational numbers are used extensively in everyday life. For example, when you divide a pizza into slices, the number of slices you have compared to the total number of slices represents a rational number. If you have 3 slices out of 8, that's 8 3 of the pizza. Similarly, measurements in cooking, like 2 1 cup of flour or 4 1 teaspoon of salt, are rational numbers. Understanding rational numbers helps in accurately measuring and dividing quantities in various real-world scenarios.
The type of number that can be expressed as a fraction q p , where p and q are integers and q = 0 , is known as a rational number. Therefore, the correct answer is B. A rational number .
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