yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Meaning of the reciprocal


3m read
·Nov 10, 2024

Let's talk a little bit about reciprocals. Now, when you first learn reciprocals, some folks will immediately tell you, "Hey, just swap the numerator and the denominator."

So, for example, if I have the fraction two-thirds, the reciprocal of two-thirds, if I swap the numerator and the denominator, is three-halves. If I had the fraction five-sixths, the reciprocal of that is going to be six-fifths.

And that's all well and good, but what does this actually mean? Well, one interpretation of a reciprocal is it's the number that when you multiply it by the original number, you get one.

So, two-thirds times three-halves equals one, or five-sixths times six-fifths equals one. Another way to think about reciprocals is how many of that number, or how many of that fraction, fit into one.

So, if I were to take one and I divide it by two-thirds, one interpretation of this is saying how many two-thirds fit into one. If I take one divided by five-sixths, an interpretation of this is how many five-sixths fit into one. And we'll see that three-halves of a two-thirds fit into one, and we'll see that in a second, or that six-fifths of a five-sixths fit into one.

So, let's start with a very straightforward example. Let's say that I have the fraction one-half. So, if I have one-half, if that whole rectangle is a whole, this is one-half here.

So, if I were to ask how many one-halves fit into one, so one divided by one-half, how many one-halves fit into one? Well, I have one one-half right over here, and then I would have another one-half right over there. So, we have two one-halves, so this is equal to two.

Now, you might be saying, "Wait, two doesn't look like I just swapped the numerator and the denominator," but you have to realize that two is the same thing as two wholes. So, the reciprocal of one-half is indeed two over one, or if you take two over one, and if you have two one-halves, that is indeed going to be equal to one.

But now, let's work on two-thirds, things that are a little bit more nuanced. So, two-thirds, here I can shade that in. That's one-third, and then two-thirds. So, this right over here is two-thirds. Now, how many of these fit into one?

If we were to say what's one divided by two-thirds, well, we can clearly get a whole two-thirds into one, and then we can get another third, which is half of a two-thirds. So, we can have a whole two-thirds, and then half of a two-thirds, or one-and-a-half two-thirds.

So, we could say one divided by two-thirds is equal to one-and-a-half. Well, one-and-a-half is the exact same thing as three-halves. So, once again, you can see that three-halves times two-thirds is equal to one, or that three-halves of a two-thirds fit into one.

Let's do another example. If we were to think about three-halves, so three-halves would be, let's see, that's a half, that's two halves, and then this is three-halves right over here. So, let me mark all of that.

So, this whole thing right over here is three-halves. Now, how many three-halves fit into a whole? Well, you can see that you can't even fit a whole three-halves into a whole. You can only fit two of the three-halves.

So, one one-half and two halves of the three-halves. So, what you can see here is that this is two-thirds of the three-halves. So, if you say one divided by three-halves, how many three-halves can fit into one? Well, you can always fit two-thirds of a three-halves into one.

And this is interesting because the reciprocal of two-thirds is three-halves, and the reciprocal of three-halves is two-thirds.

More Articles

View All
Big Short Investor's Warning About Interest Rates in 2024
I think the expectation that the FED will cut rates three times from where I’m sitting is wrong. It’s just everybody’s coming to the year so bullish. If there are any disappointments, you know what’s going to hold the market up after two years of rate hik…
A Suspiciously Expensive Delivery | To Catch a Smuggler: South Pacific | National Geographic
Auckland International Airport processes 21 million passengers every year and climbing. Customs and Immigration have just been alerted to a visiting Lithuanian woman with quite a history. Officer James is keen to take on the case. It looks like she had so…
a day in the life in Tokyo with my brother vlog
Thank you Sakako for sponsoring this video. [Music] It’s me! Today, I’ve already had my breakfast and I’m currently doing my skincare. We’re going to be getting ready very very quick and then we’ll just leave the house. Today, I’m back with a vlog that …
Will COVID-19 Kill the Music Industry? | Ask Mr. Wonderful #25 Kevin O'Leary ft CEO of Rolling Stone
Hello everybody, and welcome to another episode of Ask Mr. Wonderful. Who’s my guest? This is fantastic! It’s Gus Winner, son of Young Winner, founder of Rolling Stone magazine, cultural icon, rock and roll music, fashion, politics— you name it! So much t…
Bobi Wine performs live in Central Park | National Geographic
Thank you. [Music] Thank you. Thank you. [Music] [Applause] [Music] Thank you. Foreign. [Music] [Applause] [Music] Thank you. [Music] Thank you. Foreign. [Music] [Applause] [Music] Foreign. [Music] Thank you. [Music] Thank you. [Music] Ladies and gentleme…
What's in Peanut Butter? | Ingredients With George Zaidan (Episode 7)
What’s in here? What does it do, and can I make it from scratch? Ingredients for the purposes of peanut butter: peanuts are just peanut oil and then all the stuff in here that is not peanut oil. So, things like sugars, starches, and proteins. When you bl…