The Integer Property of Multiplication

When we talk about integers, we are referring to a set of numbers that includes positive and negative whole numbers, as well as zero. Integers are closed under addition and subtraction, meaning that when you add or subtract two integers, the result will always be an integer.

The Property of Closure

The property of closure also applies to multiplication. This means that when you multiply two integers, the result will always be an integer. In other words, the product of two integers is always an integer.

Multiplying the Integer 19

Let's consider the specific integer 19. When you multiply 19 by any other integer, the result will always be an integer. This is because 19 is an integer itself, and when you multiply it by another integer, you are essentially combining or grouping that integer 19 a certain number of times.

For example, if we multiply 19 by 2, we are essentially grouping 19 two times: 19 + 19 = 38. Since 19 and 2 are both integers, their product is also an integer.

Similarly, if we multiply 19 by -3, we are grouping 19 -3 times: 19 + 19 + 19 = -57. Again, both 19 and -3 are integers, so their product is an integer.

Conclusion

In conclusion, the integer 19 has the property that when it is multiplied by any other integer, the result will always be an integer. This is because integers are closed under multiplication, meaning that the product of two integers is always an integer. Therefore, the statement "19 is an integer and its product will be an integer" is true.