To determine what number can be added to p to yield a rational number, we must first understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction m/n, where m is an integer and n is a non-zero integer.
If p is already a rational number, then adding 0 to it will still result in a rational number because rational numbers are closed under addition. In this case, you can add 0 to p.
However, if p is an irrational number (for example, √2 or π), then the number you would need to add to p to get a rational number would be the negative of p rounded to the nearest rational number or a rational approximation of it (like 3.14… for π). In simpler terms, if you have an irrational number p, you can add a rational number such as -1 times p rounded. Another easy approach is to simply identify a rational number that, when added to p, results in a number you’re certain is rational.
In summary:
- If p is rational, add 0.
- If p is irrational, consider adding a rational number such as its negative or any convenient rational number that, when summed with p, lands you back in the realm of rationality.
Understanding these concepts is fundamental in mathematics as it deepens your comprehension of numbers and their relationships.