Using the Identity and Inverse to Write Equivalent Expressions 03:44 minutes

Video Transcript

Transcript Using the Identity and Inverse to Write Equivalent Expressions

Mr. Magic has been practicing his tricks in private and is quite sure that he will be loved by the public. Today is his first show, and he’s joined by his assistant, Vanna. Little does the audience know...that Mr. Magic will be Applying the Identity and Inverse Properties in his tricks. For his first trick, Mr. Magic’s going to increase the number of rabbits. He has five to start with. Then he does his trick and poof!!! Mr. Magic’s lack of talent means that he’s been able to add zero new rabbits. The crowd boos and throws tomatoes at him.

So, what is 5 + 0? It’s 5, of course. If you add zero to any number, the number stays the same. Zero is the additive identity. The Additive Identity just means that any number will always stay the same if you add zero to it. For his next trick, Mr. Magic takes one of the tomatoes that was thrown at him. He’s going to make it into a giant tomato or so he says. At the moment, it weighs 8 ounces. He waves his wand and now it's bigger by a factor of 1! So how much does it weigh now? 8 x 1 is 8. Actually, any number multiplied by one is the same number. One is the multiplicative identity. Similar to the additive identity you just learned, the multiplicative identity states that any number will always stay the same if multiplied by 1. Mr. Magic leaves the stage, disappointed at how little the audience appreciated his amazing magic involving the additive and multiplicative identities. His assistant, Vanna, decides to continue the show, doing the opposite of Mr. Magic. She brings back the rabbits. This time she takes the 5 rabbits and makes 5 of them disappear with a wave of the wand. There aren’t any left! The crowd cheers loudly! Five minus five equals zero. -5 is the Additive Inverse of 5. The Additive Inverse of a number is the number that you must add to that number in order to get zero. If you take any positive number and add the negative of that number, you will always get zero. Similarly, if you take any negative number and add the positive of that number, the answer will always be zero. Vanna takes the same tomato that Mr. Magic worked his magic on. She tells the audience that she’s going to shrink it by a factor of eight. She waves her wand, and boom, it’s now a tiny cherry tomato. The crowd goes wild! And how much does it weigh? Eight times one eighth equals one. One eighth is the Multiplicative Inverse of 8, because the product is one. The Multiplicative Inverse of a number is the number you must multiply by to get 1. If any number 'x' is given, the Multiplicative Inverse is one over that number, because, as you can see, the product is one. Dejected, Mr. Magic plods back home if only he could think of magic tricks audiences would want to see...