Problem 3 - Elementary Algebra

Question

Is every integer a rational number?

Step-by-Step Solution

Answer

Answer: Yes, all integers are rational numbers because every integer n can be expressed as the fraction n/1, where n and 1 are integers and 1 is not equal to zero.

Step 1: Define Rational Numbers and Integers

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where p and q are integers and q is not equal to zero. An integer is a whole number, which can be positive, negative, or zero.

Step 2: Consider the properties of integers

Integers are whole numbers, e.g., ..., -3, -2, -1, 0, 1, 2, 3, ... Now, we have to decide if we can express every integer as the quotient or fraction p/q.

Step 3: Rewrite an integer as a rational number

Let's take an integer n. We can rewrite it as a fraction by dividing it by 1. That is: n = n/1 Since n and 1 are integers and 1 is not equal to zero, this is a valid rational number.

Step 4: Conclusion

Since every integer n can be expressed as the fraction n/1, where n and 1 are integers and 1 is not equal to zero, every integer is a rational number.