# Positive negative and inverse relationship of addition

### Inverse property of addition (video) | Khan Academy

An inverse correlation, also known as negative correlation, is a First, the existence of negative correlation, or positive correlation for that. The direction of a correlation is either positive or negative. In a negative correlation, the variables move in inverse, or opposite, directions. Although true for definite positive inverse proportionality, this has the being used, for example, subtraction is inverse addition, division is inverse multiplication, Or can I continue to tell people not to call negative relationships inverse? have.

A similar inverse relationship exists between multiplication and division, but there's an important difference. The net result of multiplying and dividing a number by the same factor is to multiply the number by 1, which leaves it unchanged.

### PreMBA Analytical Methods

This inverse relationship is useful when simplifying complex algebraic expressions and solving equations. Another pair of inverse mathematical operations is raising a number to an exponent "n" and taking the nth root of the number. The square relationship is the easiest to consider. If you square 2, you get 4, and if you take the square root of 4, you get 2. This inverse relationship is also useful to remember when solving complex equations. Functions Can Be Inverse or Direct A function is a rule that produces one, and only one, result for each number you input.

The set of numbers you input is called the domain of the function, and the set of results the function produces is the range. If the function is direct, a domain sequence of positive numbers that get larger produces a range sequence of numbers that also get larger. An inverse function behaves in a different way.

When the numbers in the domain get larger, the numbers in the range get smaller. As x gets larger, f x gets closer and closer to 0. Basically, any function with the input variable in the denominator of a fraction, and only in the denominator, is an inverse function. Two Functions Can Have an Inverse Relationship to Each Other A third example of an inverse relationship in mathematics is a pair of functions that are inverse to each other. And all the additive-- I'll just write it down. I think it's kind of ridiculous that it's given such a fancy word for such a simple idea-- additive inverse property.

And it's just the idea that if you have a number and you add the additive inverse of the number, which is what most people call the negative of the number-- if you add the negative of the number to your number, you're going to get back to 0 because they have the same size, you could view it that way.

They both have a magnitude of 5, but this is going five to the right and then you're going five back to the left.

## Types of Relationships

Similarly, if you started at-- let me draw another number line right over here-- if you started at negative 3. If you're starting right over here at negative 3, so you've already moved three spaces to the left, and someone says, well what do I have to add to negative 3 to get back to 0?

- Negative relationship
- Negative Correlation
- Inverse property of addition

Well, I have to move three spaces to the right now. And three spaces to the right is in the positive direction.

So I have to add positive 3. So if I add positive 3 to negative 3, I will get 0. So in general, if I have any number-- if I have 1, and I say, what do I need to add to this to get back to 0? Well, I have to essentially go in the opposite direction. I have to go in the leftwards direction. So I'm going to subtract the same amount. Or I could say, I'm going to add the additive inverse, or I'm going to add the negative version of it. So this is going to be the same thing as adding negative 1, and that'll just get me back to 0.