Difference Between “Inverse” and “Reciprocal”
“Inverse” vs “Reciprocal”
Math definitely pulls out the life force in me. Maybe others are experiencing that too. Since almost everyone has a fear of figures and numbers, they fear math. Only mathematicians, businessmen, and geniuses love it. They love it because they love to compute. As for mathematicians, they love to compute equations. As for businessmen, they love to compute money. As for geniuses, they just love to answer challenging math problems. As for me, I will only love math if I become a successful businessman or entrepreneur. For now, I’m not loving it. Math uses calculators for computing large sums of money, but I only use my fingers to count my pennies.
Math is incorporated in our daily lives. When we go shopping, we deal with math. How much is that and this? How much is my change? Even when we are eating, math never leaves our side. Give her a portion or two slices of cake. I want a glass of juice or a liter of Coke. We also deal with math when we are doing our jobs. When will I get my salary? How much will be deducted when I pay taxes? You see, math is like sticky gum stuck in our hair. We cannot remove the gum unless we cut it.
When we were in high school, we tackled the terms “inverse” and “reciprocal.” If you would define it according to the English context, “inverse” means “the opposite” while “reciprocal” means “shared.” However, in math, they have more complicated meanings and explanations. For those who dislike math right to the core, you won’t care as much as I do. Nevertheless, let us define the differences between “inverse” and “reciprocal” on their many contexts.
As I browsed the ‘net for the differences between inverse and reciprocal, I have come across many definitions, but they are only pointing at almost the same thing.
In a physics forum, one explained that inverse can be applied to many situations. If you are talking about inverse in the arithmetic perspective, here’s how it goes. If you add (+)2 with a ()2, the negative 2 is called the additive inverse. So, the additive inverse for a positive three is negative three and so on. On the other hand, the multiplicative inverse of a number is actually its reciprocal. For example, the multiplicative inverse (reciprocal) of 2 is ½. Why? If you multiply 2 by ½, the answer is 1. You will just invert the numerator and denominator to get the multiplicative inverse (reciprocal). A whole number always has an invisible 1 as its denominator. To have a better image of it, here’s how: 2 = 2/1, 3 = 3/1 and so on. If you would get the multiplicative inverse of ¾, the answer would be 4/3. The forum also mentioned about functions, but let’s get done with it. I don’t have the mathematical mind for it.
Another one explained “inverse” and “reciprocal” in layman’s terms. He said that “reciprocal” means “equality.” He compared the terms when someone smiles at you. So, to reciprocate a smile, means to smile back. “Inverse” means “the opposite.” So, to invert a smile means to frown. Fantastic explanation. Then the reciprocal of laughing is laughing, while its inverse is crying. The reciprocal of weak is weak. Its inverse would be strong. Okay, enough with the word playing.
And that’s how it is! The difference between “inverse” and “reciprocal” is just that. Thank you for reading.
Summary:

“Inverse” and “reciprocal” are terms often used in mathematics.

“Inverse” means “opposite.”
 “Reciprocal” means “equality,” and it is also called the multiplicative inverse.
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TL;DR for Algebraic usage:
The reciprocal is swapping numerator with the denominator. Negative reciprocal is then multiplying the reciprocal by 1. Multiplicative inverses are 2 numbers whose product is 1. Additive inverses are 2 numbers whose sum is 1.
“Additive inverse are two numbers whose sum is 1” shouldn’t that say zero? Asssuming it was a typing oversight but just to clarify.