Martha States That –6 Is a Rational Number. Which Is a Correct Explanation for This Statement?
In mathematics, rational numbers play a significant role, representing numbers that can be expressed as a fraction of two integers. Martha’s statement, claiming that -6 is a rational number, is indeed correct. Let’s delve into the world of rational numbers and understand why this statement holds true.
To begin with, we need to understand what rational numbers are. A rational number is a number that can be written in the form of p/q, where p and q are integers and q is not equal to zero. The numerator, p, can be positive, negative, or zero, while the denominator, q, must be positive.
In the case of -6, we can express it as -6/1. Here, -6 represents the numerator, and 1 is the denominator. Both -6 and 1 are integers, satisfying the criteria for a rational number. Therefore, -6 is a rational number.
To further illustrate this, let’s consider the definition of rational numbers more broadly. Any integer can also be expressed as a fraction by setting the denominator to 1. For example, the number 3 can be written as 3/1. Similarly, -6 can be written as -6/1. Hence, -6 qualifies as a rational number as it can be expressed as a fraction of two integers.
Additionally, we can represent rational numbers on a number line. The number line encompasses all real numbers, including rational and irrational numbers. Rational numbers are located at regular intervals on the number line. So, if we were to plot -6 on a number line, we would find it at the exact position where the line intersects with the point labeled -6. This further solidifies the fact that -6 is a rational number.
1. Is every integer a rational number?
Yes, every integer is indeed a rational number. This is because an integer can be expressed as a fraction by setting the denominator to 1.
2. Can a rational number be negative?
Yes, a rational number can be negative. The sign of the rational number depends on the sign of the numerator.
3. Can a rational number have a zero denominator?
No, a rational number cannot have a zero denominator. Division by zero is undefined in mathematics.
4. What are some examples of irrational numbers?
Examples of irrational numbers include √2, π (pi), and e (Euler’s number). These numbers cannot be expressed as fractions and have non-recurring, non-terminating decimal representations.
5. Are all fractions rational numbers?
Yes, all fractions are rational numbers. A fraction is defined as a ratio of two integers, satisfying the criteria for rational numbers.
In conclusion, Martha’s statement that -6 is a rational number is accurate. Rational numbers can be expressed as a fraction of two integers, and -6 can be written as -6/1, satisfying this condition. Whether we consider the definition of rational numbers, their representation on a number line, or their ability to be expressed as fractions, -6 fulfills all the criteria for being a rational number.