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

Subtracting fractions with unlike denominators introduction


3m read
·Nov 10, 2024

  • [Instructor] Let's say we wanted to figure out what one half minus one third is equal to.

And we can visualize each of these fractions. One half could look like that where if I take a whole and if I divide it into two equal sections, one of those two equal sections would be a half and you see that shaded in green here.

And then from that, we're trying to subtract a third and we can visualize a third this way. That if this whole thing is a whole, I divide it into three equal sections and one of those three equal sections is a third.

So what we wanna do is take away this gray box from this green box and figure out how we can mathematically say what is left over. So pause this video and see if you can have a go at this.

And I'll give you a hint, it will be useful to be able to represent your halves and thirds in terms of a different denominator.

All right, now let's work through this together.

So the way that we can approach this is to get a common denominator. If I can express both fractions in terms of the same denominator, it's going to be a lot easier to subtract.

And the common denominator that's most useful is to find the least common denominator.

And the smallest number that is both a multiple of two and three is actually two times three, or six.

So what if we were to write each of these numbers in terms of sixths?

So how can we rewrite one half in terms of sixths? I always have trouble saying that.

Well, if I start with one half and if I multiply the denominator by three, that's going to get us to sixths and so I don't change the value of the fraction.

I need to multiply the numerator by three as well. As long as I multiply both the numerator and the denominator by the same thing, well, then that's still going to be equal to one half and you can visualize what that looks like.

If you take each of these two equal sections and turn them into three equal sections, well then you're gonna have a total of six equal sections or sixths.

Two times three in the denominator and the part that was shaded in in green which was just one of those sections is now three times as many sections.

So your one half is now equal to three over six.

And we can do the same thing over here. If we start with one third how do we express it in terms of sixths?

Well to go from three to six I would multiply it by two, and so I also wanna do that in the numerator so that I don't change the value of the fraction and we can visualize that.

Notice, if you take all three sections and you turn each of them into two sections you now have six equal sections.

So you are now dealing with sixths, and that one section before is now going to become two sections.

So this is now going to be equal to two sixths.

So we can actually rewrite things as this is the same thing as three sixths minus, minus two sixths.

And what do you think that is going to be?

Well if I have three of something and I subtract two of them away I'm going to be left with one of that something.

So I'm going to be left with one sixth in this case.

And we can visualize it just the way we visualized everything else.

If you take two of these gray bars or two of these sections from these three sections you're just going to be left with one of them.

This is one of the six equal sections.

More Articles

View All
Mule Mayhem | Live Free or Die
Oh, oh, damn it! Oh, God damn it! Hold, hold, hold! Damn it! Goddamn mules! Hold! No, you hold! Too much traffic, motorcycles, bicyclists—everything was too much for the mule. And once he started plunging down that hill and the jugs were hitting the bush…
How the Mojave Desert Compares to Mars | National Geographic
Exploration is a compulsory human trait. We’re the only animal on the planet driven so deeply by curiosity. From the surface of the Earth, the ocean floor, to space. Humans have an insatiable desire for adventure and exploration. These days we’ve been tu…
The Science of a Happy Mind, Part 1 | Nat Geo Live
Richard Davidson: The invitation in all of this work is that we can take more responsibility for our own brains. And shape our brains wittingly in a more intentional way by cultivating healthy habits of mind. (Audience applause) I’m a psychologist and neu…
Common denominators: 1/4 and 5/6 | Math | 4th grade | Khan Academy
You have two fractions: 1⁄4 and 56, and you want to rewrite them so they have the same denominator and have whole number numerators. What numbers could you use for the denominator? So, here’s our fractions: 1⁄4 and 56, and we want to rewrite these fracti…
An Affordable 3D-Printed Arm
I’m actually gonna use my arm so I can high-five so many people, 106. You’re gonna high-five 106 people? Yeah. Aren’t you gonna get tired? No, because my robo-arm’s going to do all the work. Alex was born without a fully formed arm, a condition that…
10 THINGS YOU SHOULD DO EVERY MORNING (STOIC MORNING ROUTINE) | STOICISM INSIGHTS
Welcome back, Stoicism Insights family, it’s great to have you here with us again. Today, we’re delving into a topic that’s close to the heart of Stoic philosophy, the art of crafting the perfect morning routine. But this isn’t just any morning routine, i…