fractions represent pieces or a part of
something in a picture we can display
this by taking a full shape like a
circle and splitting it up into equal
parts you can choose how many parts you
want to split it up into in this case
we're looking at four so if we cut the
circle into four equal pieces we'll have
four out of four or still the whole one
in the orange diagram in the corner you
can see you can then start looking at
taking pieces of the hole for example
you can take one4 away and leave
3/4 1 over 4 you take away and then 3
over 4 you leave
behind when representing a fraction you
always need two numbers you need a top
and a bottom technically the top is
called the numerator and the bottom is
called the denominator however in most
math classes if you just talk about the
top and the bottom people won't usually
correct you so here you can see an
example of 1 over two we've got a circle
cut in half and then in purple we have
10 over 15 so we have 10 purple Parts
out of 15 total pieces a fraction also
represents a division the notation for a
fraction also represents a division
because a fraction and division actually
works the same way so anytime you see
one number over top of the other you can
actually replace it with any of the
following kinds of notation you could
have 3 / 5 using the line with two dots
in the top and bottom you could have 3
ID 5 using the long division notation
you could have 3 over five but written
with just a slash and you can have the
notation we were using of three ID 5 3
over five these are all different
notations for division and you should
try to get comfortable with all of them
now whenever you have a fraction you
must have equal parts you cannot have
someone's half being bigger than the
other person's half you also don't have
to use circles as the only shape you
could use rectangles you could use
triangles you could use a square
anything will work as long as you
subdivide it into equal pieces you can
use fractions to represent of anything
what we'll see later is that fraction
notation can also be used to describe a
ratio let's take a look at this example
let's say in total we have nine pets but
those nine pets are made up of three
dogs four cats and two pigs you could
then have these three fractions three
dogs out of nine pets four over n four
cats out of nine pets or two pigs out of
nine pets you could also have a test
example where you wrote a test and you
answered 16 of the 20 questions
correctly so you're overall grade of the
test is 16 out of 20 or 16 over 20 or
you could convert this to a percent
which we'll see in a later
unit now there's a few different kinds
of fractions even though these different
definitions do exist you don't have to
let that scare you because once we start
doing the math all of these different
fractions will behave in the same way so
we do have a zero fraction a zero
fraction is the first example and that's
when the numerator or the top is zero if
the numerator is zero then the fraction
always represents zero no matter what
the denominator is unless you have zero
as both the numerator and the
denominator then that's technically
undefined and something you would cover
in a later Math
course the next one is proper fractions
so a fraction is supposed to represent
part of a whole and that's why this is
the proper fraction when the numerator
the top is smaller than the bottom the
denominator any fraction like that will
always be a proper fraction and it's
smaller than
one next is a whole fraction when the
number in the top or the numerator is
equal to the number in the bottom or the
denominator then that is a whole
fraction because whenever you divide
something by itself you get one and you
have the whole part back and lastly we
have an improper fraction sometimes the
numerator or the top is bigger than the
bottom and that fraction represents
something bigger than one so if you have
7 over 5 for example you actually have
one whole piece plus two pieces more in
the next hole with those definitions in
mind we can place each of these kinds of
fractions on the number line maybe this
illustration will help make these
definitions more clear first we have the
zero fraction so on the left of the
number line without getting into the
negatives we see the zero fraction right
at
zero next is a proper fraction anytime
you have a fraction that is part of the
whole just like the original definition
that is where you have a proper fraction
then right at the one you have the whole
fraction so if the top is equal to the
bottom then you have the whole
piece lastly improper fractions are
anywhere greater than one so anytime you
have a larger numerator than denominator
you have an improper fraction and as you
can see going from left to right a zero
fraction is less than a proper fraction
which then is less than a whole fraction
and those are all less than an improper
fraction