Hello. This video is an introduction to fractions.
The goals of this video are to understand the concept of a fraction,
and also to state what fraction a model represents.
All of us have an intuitive understanding of fractions.
For example, if a group of your friends go out for pizza and you plan on eating,
at some point you will take
one piece of pizza, and then you will eat it. Well this one piece of pizza that
you've taken represents a fraction
of the whole pizza. And since the pizza was divided into eight equal parts
and you have one them, this would be a model for
one-eighth of the pizza.
A fraction, or fractional number
is used to represent a part of a whole. Fractions consist of two numbers:
a numerator, which is above the fraction bar,
and the denominator, which is below the fraction bar. The denominator tells you
the number of equal parts
into which something is divided, while the numerator tells you how many of these
equal parts are being considered.
So for example, this fraction two-fifths,
notice how the circle is divided into five equal parts
with two of them being shaded. Over here we have three-eighths
where we have divided into equal parts,
again three of them shaded. I'd like to take a look at this idea a little bit more.
I'm going to visit one of these two web sites.
You might want to pause the video and jot these down. Now what this tool allows us to do,
is it allows us to choose our numerator and denominator
and then this will model the fraction over here on the right.
So for example, if I have a numerator of one, notice it's just one big piece.
But if I change it to two, three, four,
it divides that circle into that number of equal parts.
Now if I go to the numerator and increase this, it's going to
change the number of pieces that are shaded.
So there's one-fourth, two-fourths, three-fourths,
and so on. One thing I want you to notice is when I change it four-fourths,
of course that's the same as one whole. Four equal pieces considering all four of them.
And in fact I can consider more than four,
but what happens is as soon as I increase the past four,
of course it's going to be greater than one.
And I can continue this pattern
indefinitely. So for example if I have thirteen-fourths,
notice that one whole is divided into four equal parts,
if I want to consider thirteen of them, it's going to be greater than three,
in fact it'll be three and one-fourth. I would encourage you to spend some time playing around with this,
it really does help develop the idea of how fractions work.
Let's see if we can model the fractions that are presented. This first one we have
a circle divided into eight equal parts,
so our denominator of course would be eight. And the number of pieces shaded would be four.
Another idea we would consider very soon.
We can see that four-eighths is equivalent to one-half.
Number two: one circle is divided into five equal parts so our denominator is
five. And the number of shaded pieces, we have five here, and then three more,
so a total of eight-fifths. Again, you may have thought of this as one and three-fifths,
that would be a mixed number,
which we will discuss shortly as well. But for right now we'll leave it as
eight-fifths. Here's some additional information about fractions we should be aware of.
Fractions like one-third are not integers
they are rational numbers.
Rational numbers consist of all the numbers that can be represented
in the form of a over b, where b
does not equal zero. So if you can write it as a fraction
where the denominator is not equal to zero, it would be considered a rational number.
Number two: the fraction
n over n is equal to one, for any integer
n not equal to zero. Again we illustrated that earlier, but what that is saying is:
if my numerator and denominator are equal,
it's going to be equal to one. That should make sense. If I have a circle that is
divided into three equal parts,
and I consider three of them, I would have a complete circle, or one.
Number three: the fraction zero
over n is equal to zero for any integer n not equal to zero.
Again that's fairly logical if I have three pieces, but I consider zero of them,
of course that would be zero. One thing I'd like to point out here, a fraction bar
is another way to write division. So zero-thirds
represents the same thing as zero divided by three, which again of course is zero.
This idea again will come up soon.
Two more. Fractions less than one are often called
proper fractions. So for example, one-third,
two-fifths, eleven-fifteenths,
and so on. Those are all considered proper fractions,
because the numerator is less than the denominator.
Number five: fractions equal to, or greater than one are often called
improper fractions.
So if my denominator is five and I have a numerator of let's say seven, that would
be considered an improper fraction,
which would be greater than one. We should also note that if the
numerator and denominator are equal,
by eight-eighths, that is also considered an improper fraction.
I'd like to leave you with some interesting statistics involving fractions.
Almost half of the dogs in the United States sleep in a
family members bed. Americans throw away over one-fourth
of the three hundred fifty million pounds of food
they purchase each year. Number three,
the US has one-twentieth of the world's population
and produces three-tenths of the world's waste.
The United States is responsible for almost one-fourth
of the world's energy consumption. We use approximately one million gallons of oil
every two minutes.
Thank you for tuning in.