negative 4 or -4 is the answer

Final Answer: The opposite of 4 is -4, which is the number with the reversed sign. On a number line, 4 and -4 are positioned in opposite directions relative to 0. They also cancel each other out when added together, resulting in 0. ; Explanation: The opposite of a number is simply the number with a reversed sign. In other words, if a number is positive, its opposite is negative, and vice versa. For the number 4, which is positive, the opposite would be -4. To understand this better: Positive and Negative Numbers: A positive number is indicated without a sign (e.g., 4), while a negative number has a minus sign in front of it (e.g., -4). Number Line Representation: On a number line, positive numbers are to the right of 0, and negative numbers are to the left. Thus, +4 is to the right of 0 while -4 is to the left, showing that they are opposites of each other. Addition of Opposites: When you add a number and its opposite, the result is always 0. For instance, if you add 4 and -4, you get: 4 + ( − 4 ) = 0 This demonstrates that they completely cancel each other out. ; Examples & Evidence: For instance, the opposite of 3 is -3, the opposite of 10 is -10, and similarly, the opposite of -5 is 5. This pattern shows that every positive number has a corresponding negative number and vice versa. The properties of numbers in mathematics state that every real number has an opposite that can be found by reversing its sign. This concept is fundamental in understanding how numbers interact in arithmetic.

There are additive inverses (4 and –4) and multiplicative inverses (4 and 1/4). So in a sense, they are opposites since when you add the first pair you get 0, and when you multiply the second pair you get 1.

Why are these opposites though? Well, zero is a special number in addition, since anything plus zero is still the same. So that's why the multiplicative inverse of 4 is 1/4, since their product gives 1, and anything times 1 is still the same.

If you want, you can also define inverses for subtraction and division, so a number's opposite would be itself! (do you see why?)

For another way to define an inverse, we can look at a clock. Let's call "twelve o clock" the special number, because it's like "zero o clock". (If you add twelve hours to any number, you go around and end up at the same number.) If it were 7, then its inverse would be 5, because after 5 hours it would be 12. Another inverse for 7 would be 17, since it would still be on 12 after 17 hours. Also see that –7 is also an inverse of 7 in our clock numbers! (With clock numbers, how many inverses are there? What if we used clocks with 10 hours?)

So there are lots of ways to define number opposites. And opposites come up in a lot of different ways, which you'll find out if you learn about something called group theory!