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  • - [Instructor] We are told

  • that Billy has 1/4 of a pound of trail mix.

  • He wants to share it equally

  • between himself and his brother.

  • How much trail mix would they each get?

  • So pause this video and try to figure that out.

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

  • So Billy starts with 1/4 of a pound of trail mix.

  • So how can we represent 1/4?

  • Well, if this is a whole pound,

  • let's just imagine this rectangle is a whole pound,

  • I could divide it into four equal sections.

  • So let's see, this would be roughly two equal sections,

  • and then if I were to divide each of those into two,

  • now I have four equal sections.

  • So Billy is starting with 1/4 of a pound.

  • Draw a little bit, try to make it a little bit more equal.

  • Billy is starting with 1/4 of a pound,

  • so let's say that is that 1/4 of a pound

  • that he starts with.

  • He's starting with 1/4 of a pound,

  • and he wants to share it equally

  • between himself and his brother.

  • So he wants to share it equally

  • between two people right over here.

  • So what we wanna do is essentially say,

  • let's start with our total amount of trail mix,

  • and then we're going to divide it into two equal shares.

  • So when they ask us how much trail mix would they each get,

  • we're really trying to figure out

  • what is this 1/4 divided by two?

  • So what would that be?

  • Well, what if we were to take

  • all of these four equal sections and divide them into two?

  • So I'll divide that one into two.

  • I will divide this one into two.

  • I will divide this one into two,

  • and then I would divide this one into two.

  • And now what are each of these sections?

  • Well, each of these are now 1/8.

  • That's a 1/8 right over there,

  • the whole is divided into eight equal sections.

  • And so you can see, that when you start with that 1/4,

  • and you divide it into two equal sections,

  • so one section and two equal sections right over there,

  • each of these is equal to 1/8.

  • So 1/4 divided by two is equal to 1/8.

  • Let's do another example.

  • So we are told Matt is filling containers of rice.

  • Each container holds 1/4 of a kilogram of rice.

  • And then they tell us if Matt has three kilograms of rice,

  • how many containers can he fill?

  • So like always, pause this video,

  • and see if you can figure that out.

  • All right, so let's think about what's going on.

  • We're starting with a total amount, three kilograms of rice,

  • and we're trying to divide it into equal sections.

  • In this case we're trying to divide it into equal sections

  • of 1/4 of a kilogram.

  • So we are trying to figure out

  • what three divided by 1/4 is going to be equal to.

  • Now to imagine that, let's imagine three wholes,

  • this would be three whole kilograms.

  • So that is one whole, this is two wholes,

  • trying to make them all the same, but it's hand-drawn,

  • so it's not as exact as I would like.

  • So that's three whole kilograms here.

  • And he wants to divide it into sections of 1/4.

  • So if you divide it into fourths,

  • how many fourths are you going to have?

  • Well, let's do that.

  • So let's see, if we were to divide it into halves,

  • it would look like this.

  • If you divide these three wholes into halves.

  • But then if you want to divide it into fourths,

  • it would look like this,

  • I'm trying to get it as close to equal sections.

  • They should be exactly equal sections.

  • So I am almost there.

  • So there you have it.

  • So I've just taken three wholes

  • and I've divided it into fourths.

  • So how many fourths are there?

  • Well, there are one, two, three, four, five, six,

  • seven, eight, nine, 10, 11, 12 fourths.

  • So three divided by 1/4 is equal to 12.

  • And I encourage you to really think about

  • why this is the case,

  • that if we take a whole number like three

  • and you divide it by 1/4,

  • we're getting a value larger than three.

  • And we're getting a value that is four times three.

  • Think about why that is the case.

- [Instructor] We are told

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