Find the product of any integer and -1.
A) The product is always negative.
B) The product is always positive.
C) The product depends on whether the integer is odd or even.
D) The product is always zero.
To understand the multiplication rule of -1, let's break it down step-by-step in a way that can be easily understood by someone who might not have previous experience with multiplying integers and negative numbers.
Step 1: Start with any integer.
For example, let's consider the integer 5.
Step 2: Multiply the integer by -1.
When we multiply 5 by -1, we get -5.
Step 3: Understand the pattern.
The multiplication rule of -1 states that when we multiply any integer by -1, the sign (positive or negative) of the integer changes. If the original integer is positive, the result will be negative, and if the original integer is negative, the result will be positive. In other words, the product is the opposite sign of the original integer.
Now, let's apply this understanding to the answer choices:
A) The product is always negative.
This is the correct answer. When we multiply any integer by -1, the product will always be negative. For example, -1 times 5 is -5.
B) The product is always positive.
This is not correct. As explained earlier, the product will be negative, not positive.
C) The product depends on whether the integer is odd or even.
This is not correct either. The product of an integer multiplied by -1 does not depend on whether the integer is odd or even. It solely depends on changing the sign.
D) The product is always zero.
This is also incorrect. The product will not be zero. The multiplication rule of -1 changes the sign, but it does not affect the value itself.
So, the correct answer is A) The product is always negative.
I hope this explanation helps you understand the multiplication rule of -1 and how it applies to multiplying integers with negative numbers.