Welcome to an example
of how to subtract two fractions with unlike denominators.
The main thing to remember when adding or subtracting fractions,
is that we must have a common denominator.
The reason we need a common denominator
is that we're subtracting or adding
parts or pieces of the same size.
Here we have two-thirds,
minus one-forth,
the first thing to recognize here,
is that we do not have
a common denominator,
and therefore we cannot subtract the fractions,
with the fractions in this form.
If we're able to determine the smallest possible common denominator,
it's called the least common denominator,
which is the least common multiple of three and four.
It's also the smallest number
divisible by both three and four.
So, by listing multiples of three and four,
we can see the least common multiple,
of three and four is twelve,
and therefore the least common denominator is twelve.
But, we don't always have to use the least common denominator,
we can use any common denominator.
So, one way to always find a common denominator,
would be to find their product of the two denominators.
Notice here,
three times four is twelve,
So, the product does give us the least common denominator,
and that's just because
three and four
don't share any common factors other than one.
In most cases it won't be the least common denominator
but who is give us a common denominator.
Lets go ahead and use
the common denominator of twelve,
So, we need to write both of these fractions as equivalent fractions
with the denominator of twelve
So, for two-thirds we multiply,
numerator and denominator by four
and for one-forth we'll multiply
numerator and denominator by three.
So, this tells us that two-thirds,
is equivalent to eight-twelves,
and one-forth is equivalent to three-twelves.
and then we have a common denominator we can subtract,
denominator stays the same,
and we subtract the numerators
eight minus three is equal to five.
So, the difference is five-twelves,
which is now simplified
because the only common factor between five and twelve is one.
But let's also look at the model shown here below.
If we define the rectangle as one whole,
this is the model for two-thirds,
and this is the model for one-fourth.
We want to remove,
one-fourth from two-thirds
or this amount from this amount.
To do this though,
we need the pieces to be the same size.
So, we cut or partition
this rectangle into twelve equal parts or pieces
we would take each third,
and divide into four
equal sized pieces.
Notice how here we did multiply,
both numerator and denominator by four.
So, we'll divide,
this one-third,
into four equal parts or pieces
as well as this one-third
and as well as this third.
Notice now we have a total of twelve parts or pieces now
with eight of them shaded,
which shows us that two-thirds is equivalent to eight-twelves
and now we want to cut or partition
this rectangle into twelve equal parts or pieces,
which means we'll take each fourth,
and divide into three
smaller parts or pieces.
So, this shows us that one-fourth is equivalent to three twelves.
and now because the pieces are the same size
we can remove or take away,
three pieces from these eight pieces,
which leaves us with five pieces
each piece the size of one-twelves
and that's reason why the difference is five-twelves.
And let's go and show the model for five-twelves.
We'll cut or partition the rectangle into twelve equal parts or pieces,
and we shade five of them
again if we have eight pieces.
we take away or remove three of them,
we left with five pieces
each piece is equal to one-twelfth,
giving us a difference of five-twelves.
I hope you found this helpful.