Video Transcript
Nonunit Fractions for Halves,
Thirds, and Quarters
In this video, we’re going to learn
how to write and model nonunit fractions. And we’re especially going to be
thinking about fractions that have denominators of two, three, or four.
Let’s start with a hungry
mouse. What she needs is a nice, big piece
of cheese. Now, if we look carefully at this
cheese, we can see that it’s already been cut into mouse-sized pieces already. The whole has been split into four
equal parts. We can see quarters. And depending on where you’re from,
you might call these fourths. Now, if our mouse decides to eat
one of these slices of cheese, we can say she’s eaten one-quarter. Now, so far, when we’ve been
learning about fractions, we’ve always talked about one part. This is the same as the one slice
of cheese that this mouse has eaten, one out of four equal parts.
I’m sure you know this already. Fractions that have a one as their
numerator, in other words, when we’re talking about one part, are called unit
fractions. But as you can see, our piece of
cheese is made up of more than one part. So that’s why in this video we’re
going to be thinking about fractions that have other numbers as a numerator too. These are what we call nonunit
fractions. And the only way we’re going to
find them is if we start eating this cheese up.
Oh! Here’s another hungry mouse looking
longingly at this piece of cheese. Now, what happens if this mouse
eats one of the four pieces? He’s eaten one-quarter too. It might be hard to see this
because we’re slowly getting rid of the slices of cheese, aren’t we? So let’s draw dotted lines to show
where they once were.
So if our first mouse ate
one-quarter and our second mouse ate one-quarter, we can say that they’ve both eaten
two-quarters. Watch how we write this as a
fraction, two out of a possible four equal parts. And because we’re not talking about
one-quarter anymore — we’re talking about two-quarters — this is one of those
nonunit fractions that we mentioned. These mice have eaten two-quarters
of the whole cheese.
In fact, you might know another
fraction you could describe this as. It’s the same as a half, isn’t
it? Half of the cheese has gone. Not for long, looks like we’ve got
another hungry mouth to feed. And if this mouse eats another of
our slices of cheese — remember, this is another one of the original four — then
three out of the four pieces have been eaten. Three-quarters have been eaten. And this nonunit fraction is going
to have a numerator of three. Remember that the numerator or the
top number in a fraction shows us the number of parts that we’re talking about. So it’s three parts. And then it’s going to have a
denominator of four. And remember, the denominator shows
us the number of equal parts that there are altogether, three out of a possible
four, three-quarters.
We’ve only got one slice or
one-quarter left. Now, we can’t let a good cheese go
to waste, can we? Now, the whole cheese has been
eaten, four-quarters. Now, watch what happens when we
write this as a fraction, four parts out of a total of four equal parts. Four-quarters is the same as one
whole. Can you see that both the numerator
and the denominator are the same? Whenever we see this when we’re
talking about fractions, we know we’re talking about one whole.
Let’s give you a quick example, two
halves, same number on the top and the bottom of this fraction. So we know it must be the same as
one whole. And we know this is true, don’t
we? One-half, two-halves or one
whole.
Now, we did say at the start of
this video that we were going to be working with nonunit fractions that have
denominators of two, three, and four. In other words, we’re going to be
thinking about whole amounts that have been split into two equal parts, three equal
parts, or four equal parts. And that’s why in the title of our
video it mentioned halves, thirds, and quarters.
Let’s try answering some questions
now where we have to put into practice everything we’ve learned about nonunit
fractions, in other words, those fractions where we’re talking about more than one
part.
Pick the rectangle that matches
Jacob’s description. One-third is colored blue. Two-thirds are colored yellow.
In this question, we can see four
different rectangles. And we’re told to pick the
rectangle that matches Jacob’s description. So perhaps we’d better read his
description carefully. In his description, Jacob mentions
two fractions. He tells us that one-third of the
rectangle is colored blue. And then he mentions another
fraction. Two-thirds are colored yellow. Now, what is this word “third” that
he mentions?
A third is a type of fraction. It’s when one whole has been split
into three equal parts. Now, there are two things that are
really important about that definition. Firstly, we’re looking for
something that’s been split into three parts. And then they need to be three
equal parts too. So to begin with, let’s look at our
rectangles and see which ones have been split into thirds.
If we look at our first rectangle,
we can see that it has been split into three parts, but they’re not all the same
size, are they? This part over here is a lot bigger
than the other two. These parts are not equal. So we can’t say that this
rectangle’s been split into thirds. It’s really important to understand
why this rectangle is not correct because it might be quite easy to choose it as the
correct answer. It does have one out of three parts
colored blue and two out of three parts colored yellow. But they’re not equal parts, and so
they’re not thirds. Don’t be caught out by this
rectangle.
Now, if we look at our second
rectangle, again, we can see one part blue, two parts yellow, and they are all equal
parts. But there’s a part that’s colored
white too. There are four equal parts. This rectangle doesn’t show thirds
either; it shows quarters. So this doesn’t match Jacob’s
description.
Now, if we look at our final two
rectangles, we can see that each one has been split into three parts. And each of those three parts is
equal. These have both been split into
what we call thirds. But only one of our rectangles is
correct. Jacob says that one-third is
colored blue, in other words, one out of three equal parts. Looks like the correct rectangle
might be this one, doesn’t it? This has one out of three equal
parts that’s blue.
Now, when Jacob tells us that
two-thirds are colored yellow, he’s telling us that two out of three equal parts are
colored yellow. And we can see these in the first
rectangle too. Notice that these two parts aren’t
right next to each other. When we show a fraction, it doesn’t
have to be that we color the parts side by side. As long as any two of the three
parts are shaded, then two-thirds are shaded. We knew we were looking for a
rectangle that had been divided into three equal parts, where one of those parts was
colored blue and the other two parts were colored yellow. The correct rectangle is this one
here. One-third is blue, and two-thirds
are yellow.
Pick the shape with three-quarters
shaded.
In this question, we’re thinking
about quarters. Now, we know that quarters are part
of a whole amount, when one whole has been split into four equal parts. Now, if we look at the circles that
are in this picture, we can see that each one of them has been split into four equal
parts. There’s a quick way to find
quarters. And that’s to split a circle once
down the middle to show halves and then dividing each of those halves into half with
a line across the middle, four equal parts or quarters.
Can you see that each of the
circles has got black lines to show that it’s been divided in this way? So the first thing that we can say
about our possible answers is that they all show quarters. But we’re looking for a shape that
has three-quarters that are shaded. Our first shape has one, two parts
shaded. This has two-quarters shaded, not
three-quarters. Our second shape has one, two,
three parts shaded red. Looks like these are the
three-quarters we’re looking for.
Let’s just quickly look at the
other two shapes because they’re interesting. Our third shape has one out of four
equal parts shaded. This is the one you might
recognize. It has one-quarter shaded. And our final shape has four parts
shaded. That’s four out of the possible
four. Four-quarters are shaded. And we know that four-quarters are
the same as one whole. We know that when we divide a
circle into four equal parts, they’re called quarters. And so the shape that has
three-quarters shaded is this circle here. It’s the one where three out of
four equal parts are shaded red.
What fraction is shaded?
The word fraction in this question
means part of a whole. And if we look at this triangle, we
can see that only part of the whole amount has been shaded. And we can write down this part as
a fraction. Now, what do we know about
fractions? We know we can write them by
drawing a line, a number above it, and a number below it. The bottom number in a fraction or
the denominator shows us the total number of equal parts that the whole amount has
been split into.
In this example, the whole amount
is this triangle here. And it’s been split into one, two,
three equal parts. And if you’re wondering whether
they really are equal parts, turn your head. It might help you to see that they
are. They’re all exactly the same
size. And because the whole triangle has
been split into three equal parts, we can write three as the denominator in our
fraction.
We’re talking about thirds. So now we need to ask ourselves,
how many thirds are shaded? Now, this is where the top number
or the numerator in our fraction comes in. The numerator represents the number
of selected parts, the number of parts that we’re talking about. And in this example, we’re talking
about the number of parts that are shaded. Now, when we first introduced the
fractions, we usually look at one part on its own: one-half, one-third, one-quarter,
and so on. But the numerator doesn’t have to
be one.
In this picture, we can see one,
two parts are shaded. The numerator in our fraction is
going to be two. Two out of a possible three parts
have been shaded blue. And so we can say that the fraction
of this shape that’s been shaded is two-thirds.
What fraction is shaded?
In the picture, we can see a
rectangle. It’s this long strip of a rectangle
here. And we can see that part of this
rectangle has been shaded orange, but not all of it. If all of the rectangle had been
shaded orange, we might say one rectangle is orange or one whole rectangle is
orange. But this is only part of a whole
rectangle. And we can use fractions to
represent part of a whole.
What fraction of this long
rectangle is shaded? Well, we know how to write
fractions, don’t we? We need a line, a number on the
top, and then a number on the bottom. To remember what each number
represents, the denominator or the bottom number in a fraction shows us the number
of equal parts that the whole amount has been split into. Firstly, we can look at our long
strip of a rectangle. And we can see that each of the
parts that it’s been split into they are all equal, aren’t they? And there are one, two, three, four
parts. We call these quarters. Each of these separate parts is
worth one-quarter. And because we’re talking about
quarters, we know our denominator must be four, just like all those quarters that
we’ve labeled our parts with.
So now that we know we’re talking
about quarters, let’s go back to our question. What fraction is shaded is really
asking us how many quarters are shaded. To remember what the numerator in
the fraction represents, we use it to show the number of parts that we’re talking
about. And in this question, we’re talking
about the parts that are shaded. And there are one, two, three
shaded parts. Three out of a possible four parts
are shaded, or three-quarters. The number on the bottom tells us
that we’re talking about quarters. And the number on the top tells us
how many quarters. The fraction of this rectangle
that’s shaded is three-quarters.
Scarlett has shaded parts of the
given whole. Complete the sentences. What out of four equal parts are
shaded? What quarters of the whole is
shaded?
In the picture, we can see a whole
amount, and we’re told that Scarlett has shaded some parts of it. So what do you think the whole
amount is that’s being talked about? It’s this whole rectangle here,
isn’t it? And we can see that the whole of
this long rectangle has been divided into one, two, three, four smaller
rectangles. And they’re all the same size,
aren’t they? They’re equal parts.
Now, we’ve got some sentences about
these parts that we need to complete. But before we do that, let’s take a
moment to look carefully what we’re being asked because we can make a prediction
here. Our last missing number is the top
number in a fraction. Now, we know that the top number in
a fraction is called the numerator. Do you remember what this
represents? It’s the number of parts that have
been selected.
Well, in this particular question,
we’re talking about shaded parts. So why don’t we change our
definition? The numerator is the number of
shaded parts. Now, if we come back up and look at
our first missing number, we also need to write down the number of shaded parts,
this time as a sentence. So even if we’d never seen this
diagram, we’d be able to predict one thing. Our two missing numbers are going
to be exactly the same, aren’t they?
Alright, let’s get answering this
question. So our first sentence says, what
out of four equal parts are shaded? One, two out of four equal parts
are shaded. Now, because the whole amount has
been divided into four equal parts, we know we’re talking about quarters. And that’s why the denominator or
the bottom number in this fraction is four. Did you notice when we read the
question we said “what quarters”? As we’ve said already, the missing
number then is the numerator. The number of shaded parts is
two. So we can say two-quarters of the
whole is shaded. Two out of four equal parts are
shaded. Two-quarters of the whole is
shaded.
What have we learned in this
video? We’ve learned how to write and
model nonunit fractions that have denominators of two, three, or four.
