Question

The Closure Property implies that the product of and 15 is what type of
number? (1 point)
○ Rational
○ Zero
○ an Integer
○ Irrational

Answer 1

The Closure Property refers to the fact that when two numbers from a specific set are combined (through addition, subtraction, multiplication, or division), the result is still within that set.

In this case, the question asks about the product of an unspecified number (let's denote it as \( x \)) and 15.

1. If \( x \) is a **rational number**, then \( x \times 15 \) will also be a rational number (as the product of two rational numbers is rational).
2. If \( x \) is **zero**, then \( 0 \times 15 = 0 \), which is also a rational number and an integer.
3. If \( x \) is an **integer**, the product \( x \times 15 \) will be an integer (as the product of two integers is an integer).
4. If \( x \) is an **irrational number**, the product \( x \times 15 \) will be an irrational number (as the product of a rational number and an irrational number is irrational).

Given that 15 is an integer, the product \( x \times 15 \) will be an integer if \( x \) is an integer. However, we don’t have specific information about \( x \) in this context, so we cannot determine its specific type universally.

Based on the available answer choices, considering that the number being multiplied could be any number, the best choice is:

- **An Integer**

This is because if the number being multiplied is rational or an integer, the product will definitely be an integer. If it is zero, the product is also zero (which is an integer).