Welcome to an example,
on how add or subtract fractions with unlike denominators.
The main thing to remember,
is that we add or subtract fractions,
we must have a common denominator.
we need a common denominator,
so that we add or subtract,
parts or pieces of the same size.
Once we have a common denominator,
subtract two fractions,
their denominator stays the same,
and we subtract the numerators.
Looking in our example, we have five-six minus one-half,
so the first thing to recognize here,
is that we do not have a common denominator.
and therefore we cannot subtract the fractions in this form.
If we were able to determine the smallest possible common denominator,
it's called the least common denominator,
which is the least common multiple six and two,
but is also the smallest number,
divisible by both six and two.
We don't have to use the least common denominator,
in order subtract the fractions,
we can use any common denominator.
Because, six
is the least common multiple of six and two,
which is also the smallest number,
divisible by six and two,
if you wanna to subtract these fractions
using the least common denominator,
both fractions,
need a denominator of six.
lets first, find this difference using the least common denominator of six.
The first fraction already has denominator of six,
so we have five-six
and then to write the equivalent fraction to one-half
with the denominator of six
we would multiply the numerator denominator three,
because two times three is equal to six.
So, we would have five-six minus three-six,
and now that we have a common denominator,
we can find this difference,
denominator stays six
and now, we subtract the numerators,
five minus three is equal to two.
So, this is the difference but because two and six share a common factor of two,
this does simplify,
their a couple ways of showing the simplification.
One ways to divide the numerator denominator by two
two divided by two is equal to one.
and six divided by two is equal to three.
So, the difference equals one-third.
Now lets look at the model below,
If we defined the rectangle is one whole,
here's the model for five-six,
and here's a model for one-half,
we want to remove this amount from this amount,
but before we do this,
we need the pieces to be the same size.
So, looking at the model for one-half.
we cut out partition the rectangle
into six equal parts or pieces like this,
this shows one-half is equivalent to
three-six. So, now we have
five-six.
minus three-six,
and if we remove this amount from this amount,
or these three pieces from these five pieces,
we're left with a total of two pieces
which pieces is one-six
So the difference is
two-six,
which look like this,
Again, if you remove these three pieces from these five pieces
we were left with these two pieces
But we can express this fraction using lager pieces,
the rectangle is one whole,
and if it cut into three equal parts or pieces,
here and here,
we can see that two-six is equivalent to,
one-third
I do want to show this one more way
by determining,
the common denominator
that is not the
least common denominator.
One way we can always find a common denominator,
is to find their product of the two denominator.
Here notice, six times two is equal to twelve.
So,you could write both these factions,
with denominator of twelve,
and then perform the subtraction.
let's also show that,
So, beginning with again five-six
minus one-half.
If we use a common number of twelve,
we would multiply the first fraction by two over two,
and a second fraction by six over six.
Notice now, the equivalent fractions are ten-twelves.
and then minus six twelves
subtracting,
the denominator stays the same
and ten minus six equals four.
So, the differences four-twelves.
which does simplify there's a common factor of four between four and twelve.
and notice how we do get the same result.
Four divided by four is one
and twelve divided by four is equal to three,
So, we can always find a common denominator
by determining the product two denominator,
in most cases, it won't be the least common denominator.
But will still give you a common denominator,
just requires extra simplifying,
after subtracting.
I hope you found this helpful.