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Additive and Multiplicative Inverses - Concept
Inverses, like the additive inverse or multiplicative inverses, are important for understanding how to cancel terms when solving for variables in equations and formulas. When a number is added to its additive inverse, the result zero. This is useful for getting rid of terms. When a number is multiplied to its multiplicative inverse, the result is 1. This is useful for getting rid of fractions.
Math is all about vocabulary. And there's a lot of words you gotta keep straight. Here's a couple.
Two numbers are called additive inverses if their sum is 0. Another one is two numbers are called multiplicative inverses if their products is 1, if their product is 1. Let's go through and talk more about what that means.
First thing, you gotta remember what sum means. Sum means the answer to an addition problem. If you forget, this has a little bit of a hint to it because it says add in the title.
Two numbers are additive inverses if their sum is 0. If they add up to 0. That's kind of tricky because most of the time when we're adding things, they get bigger, right, like 2 plus 3 is 5. It's getting bigger. So you have to be really clever and use what you guys know about negative numbers, because, check it out, 2 plus negative 2 gives me 0. Sometimes when you add, if you're adding a negative value, you're not increasing, you're actually decreasing.That's something that's really tricky.
So additive inverses have this property where 1 is positive and the other is negative. That's something to look for.
Let's talk about multiplicative inverses. We're talking about a product that is equal to 1. Product means the answer to a multiplication problem. And if you forgot here's a little hint for you, multiplicative.
So we need two numbers that when I multiply them the answer is 1. Again, it's kind of tricky because the multiplying we're used to is like 8 times 5. That's not 1. Three times 2. Not 1. Even I use negative numbers 2 times 4 or negative 4. I'm not getting any closer to 1.
To do multiplicative inverses you're going to have to think about fractions like 2 over 1 times its multiplicative inverse gives me the product 1. The trick is that a multiplicative inverse is like the reciprocal.
If I'm given a fraction, I want to find the reciprocal to find its multiplicative inverse.
These two concepts are going to be really,really important when you get intosolving equations. So don't forget, if you forget the vocabulary, if you forget exactly what the official definition is, there's a hint like multiplicative tells you they multiply to 1. Additive inverse tells you they're going to sum or add up to 0. Use those kind of tricks to help you in case you forge twhat the vocabulary means officially.