Video Transcript
Unit Fractions of a Quantity
In this video, we’re going to learn
how to find unit fractions of an amount or a quantity using visual models to
help. And we’re going to explain what
this has got to do with dividing by the denominator.
Let’s start with 12 bananas and a
very hungry monkey. Now, what happens if he decides to
eat a quarter of the bananas? We know there are 12 bananas, so
this is just like asking, what is one-quarter of 12?
Now, if you remember, our video was
called unit fractions of a quantity, and one-quarter is an example of a unit
fraction. This is a fraction where we’re only
thinking of one of something. This has one as the top number or
the numerator. So all the way through this video,
we’re only going to be thinking about fractions like one-quarter, one-half,
one-fifth, one-third, and so on. And the number 12 here is the
quantity of bananas. One-quarter of 12 is a unit
fraction of a quantity. So how many bananas is this? Let’s draw a bar model to help
us.
This bar represents our 12
bananas. Now we know when a shape, a number,
or a quantity is divided into quarters, it’s split up into four equal parts. And you know a quick way to do this
is to split into half and then half again because half of a half is the same as a
quarter. Let’s divide another bar to show
quarters then, half and then half again. We’ve divided our bar into four
equal parts. Can you see which part of the
fraction tells us that we need to do this? It’s the bottom number, or the
denominator. This shows us the number of equal
parts that we need or the number we need to divide by.
So if we were being asked to find
one-half of 12, we’d need to divide by two. To find one-third of 12, we’d need
to divide by three and so on. The denominator is a clue that
tells us what we need to do here. Now, how many bananas is each of
our quarters worth? We know that half of 12 is six. And if we split each half in half,
this gives us three. And this is where our times tables
facts come in useful. We know that four times three
equals 12. And so 12 divided by our
denominator, four, equals three. And so we can say that one-quarter
of 12 bananas is three bananas. This monkey has eaten three
bananas.
Here’s another monkey. She’s full of energy. And can you see why? She’s already had her lunch. She’s eaten some bananas out of
this group. What fraction of the bananas has
she eaten? To begin with, let’s draw a ring
around the bananas that she’s eaten. This is a group of three; our
monkey has eaten three bananas. But what fraction is this out of
the whole amount? Don’t forget when we’re thinking
about fractions, we’re thinking about dividing a whole amount into parts that are
the same size or equal. Let’s split up the whole amount of
bananas so that they’re in groups of the same size.
Here’s another group of three
bananas, a third group, a fourth group, and one more. We’ve split the whole amount into
five equal groups. And we know that when we divide
something into five equal parts, each part is one-fifth. The fraction of bananas that the
monkey’s eaten is one-fifth. Let’s show this is a fraction of a
quantity. One-fifth of the whole amount of
bananas, which we haven’t counted yet but we can do so in a moment, equals three
bananas.
Let’s count in threes to find out
what our missing number is. There are three, six, nine, 12, 15
bananas in the whole amount. One-fifth of 15 is three. And remember, we can check this
because we can take the whole amount, which is 15, and divide it by the denominator
in our unit fraction. 15 divided by five equals
three. All of this tells us that the
fraction of the bananas that the monkey’s eaten is one-fifth.
Do you think you’re ready to answer
some questions now where you put into practice what you’ve learned? Let’s give it a go.
What fraction of the circles is
shaded?
In the picture, we can see a group
of circles, but only part of the whole group has been shaded. Let’s draw a box around the shaded
part. Now if our question asked us, “how
many of the circles are shaded?,” we could answer two. But we’re not asked this. We need to compare the group that
is shaded with the whole amount because we’re being asked what fraction of the
circles is shaded. In other words, if we use this bar
to represent all of the circles, we’re being asked, what fraction is this part here
worth? Remember, the important thing
whenever we talk about fractions is that we’re talking about equal parts.
Let’s split up the rest of our
group so that everything’s in equal parts. Here’s another group of two, so
that’s two equal parts, three, four, five, six, seven. We’ve divided the whole amount into
seven equal parts. We know this because each part
contains two circles. And because there are seven equal
parts, we can say each part is worth one-seventh. And because only one of our parts
is shaded, we can say one-seventh is shaded. There are two, four, six, eight,
10, 12, 14 circles altogether. And we can use this to check our
answer is correct.
To find one-seventh of 14, we can
start with 14 and divide by the denominator, which is seven. We know there are two sevens in 14,
so 14 divided by seven equals two. One-seventh of 14 circles is two
circles. And of course, this matches the two
circles that are shaded. It looks like our fraction is
correct. The fraction of the circles that’s
shaded is one-seventh.
Fill in the blank: one-quarter of
20 equals what.
In the picture, we can see a group
of 20 cakes. And to answer the problem, we need
to find a fraction of this quantity. We need to find one-quarter of
20. What do we know about the fraction
one-quarter? Well, firstly, the numerator is
one. This means it’s what we call a unit
fraction. In other words, we only need to
find one-quarter. We don’t need to find two-quarters
or three-quarters, only one. And the bottom number or the
denominator in one-quarter is a four. This tells us that we need to split
the whole amount into four equal parts. That’s what a quarter is; it’s one
out of four equal parts. So to find out what one-quarter of
20 is, we’re going to have to split up 20 into four equal parts.
Now, there are two ways we could do
this. Firstly, we could think about the
number 20 itself, and we could work out the answer to 20 divided by four. Or we could use the picture of the
cakes to help. We could divide this into four
equal groups. Let’s try both ways, and if we get
the same answer, we know we’ve got it right. Now there’s a quick way we can
split things into four. We start by finding a half, and
then if we find half again, that gives us four equal parts. We know that half of 20 is 10 and
then half of 10 is five. There are four fives in 20. 20 divided by four equals five. It looks like one-quarter of 20 is
five, but let’s just check using the picture.
First, we can split the group in
half. Now, if we split each half in half
by going down the middle, we can see we’re going to end up with some half cupcakes,
which we don’t really want. It makes it a bit more tricky to
count. So let’s just split each half in
half by drawing lines across. There we go. We’ve split the whole amount into
four equal groups, and there are one, two, three, four, five cupcakes in each
group. We were right. One-quarter of 20 equals five.
Fill in the blank: one-half of
eight equals what.
In this question, we need to find a
fraction of an amount, one-half of eight. Now we’ve got a picture to help
us. There are eight cupcakes. Now, how do we find half of an
amount? The clue is in the fraction
itself. The top number or the numerator
tells us how many parts we’re looking for. And in this case, it’s one. We’re looking for one-half. And the bottom number or the
denominator shows us how many equal parts the whole has been split into. And from what we know about
fractions already, we know this is true, don’t we? If we divide a shape or a number or
a quantity by two, we split it into two equal parts or half. So half of the whole amount, eight,
is the same as eight divided by two.
What do we get if we split eight
into two equal parts? We get four and another four. Eight divided by two equals
four. And we know this because two times
four is eight. Half of eight equals four.
What is one-fifth of five?
In this question, we need to find a
fraction of an amount. That amount is five. Let’s model it, shall we? Let’s use pufferfish. Now we can see that there are five
fish in the whole amount. But what do we do to find one-fifth
of this number? The number one, the numerator in
this fraction, tells us that it’s a unit fraction. We’re only looking for one part,
not two-fifths or three-fifths or four-fifths, only one-fifth. And the number five, that’s the
denominator, tells us how many equal parts to split the whole amount into.
To find a fifth, we divide the
whole amount into five equal parts. Each part is worth one-fifth. Now we know that five ones make
five. So if we divide five by itself, the
answer is one. We found the answer here by
dividing five into five. One-fifth of five equals one.
There were 15 birds on a tree, but
a third of them flew away. Find the number of birds that flew
away.
To begin with in this problem,
we’re told about a group of birds. There were 15 of them on a
tree. Let’s model our 15 birds using
plastic counters. Now, we’re told that some of these
birds flew away. And fortunately, we’re not told the
number of birds that flew away. This is what we need to find. Instead, we’re told the fraction of
the whole amount. This is a third. Now this is a third written in
words. But do you remember how to write it
using digits? The numerator is one. This shows us that we’re only
thinking about one-third and not two-thirds or more. And then the denominator is
three. This shows us the number of equal
parts that we need to split the whole into.
So to find one-third of 15, we can
divide 15 by the denominator, three. If we split 15 into three equal
groups, how many will there be in each group? Perhaps you can think of a times
tables fact that could help us here. We know that three times five
equals 15. 15 divided by three equals
five. And we can show this using our
counters. We’ve split the whole amount into
three equal groups, and each of the three groups, that’s each third, is worth
five. So if there were 15 birds on a
tree, but a third of them flew away, the number of bird that flew away is five.
Now what have we learned in this
video? We have learned how to find unit
fractions of amounts or quantities using models to help. We have also explained how we can
divide by the denominator.
