We are ask to multiply and write the answer in lowest terms.
To multiply a fractions
we multiply the numerators and multiply the denominators.
So looking at our notes here.
Well these are the two fractions were multiplying.
The numerator would be a time c.
And the denominator would be b times d.
However the product
does need to be in simplified form
or written in lowest terms
and we can simplify
before or after
multiplying.
So in our first example we have one fourth.
Times three fifth.
So we multiply
the numerator
would be one times three.
And the denominator would be four times five.
But before we find these products.
Let's say we have any common factors other than one
between the numerator and denominator.
Notice in this case there are no common factors other than one
between the numerator denominator.
So we can go ahead and find these products
knowing the fraction will be in lowest terms or simplified.
The numerator is one time three which equals three.
The denominator is four times five which equals 20.
And before we go to our second example though
let's discuss the meaning of this product.
So the question is what does one fourth times three fifth
equals three twentieth mean.
Well it means that three twentieth is one fourth of three fifth
or we can say three twentieth is one fourth of a copy of three fifth.
Let's go ahead and model this.
If we define the rectangle as one whole.
Here's the model for three fifth.
So if we want one fourth
of this amount.
We would cut our partition is
into four equal parts or pieces.
So let's go and cut our partition as vertically.
So we'll cut this in half.
And then in half again.
So notice how by doing this
we just cut the three fifth into one, two, three, four equal parts or pieces.
Because we want one fourth of three fifth.
We want let's say this amount here.
So this is one fourth of three fifth.
But if we compare this amount to the whole. We have a total of 20 parts or pieces
And we shaded three of them
which gives us three twentieth.
This is why one fourth times three fifth equals three twentieth.
Now let's look at our second example.
Here we have one eighth times four fifth.
So the product
would have a numerator of one times four.
And a denominator of eight times five.
Again before we find these products.
Let's see if there are any common factors
other than one
between the numerator and denominator.
Well notice how eight and four do share a common factor of four
which means this does simplify and just as we simplified fractions.
If it's helpful we can always write out the prime factorization
of the factors in the numerator and denominator.
Where four is equal to two times two.
And a would be equal to two times, two times, two.
We still have a factor of five.
In this form we can see the common factors.
Two over two equals two half or two divided by two which equals one.
So two over two simplify to one over one here.
As well as here.
So now we can multiply knowing the product
will be in lowest terms or simplified.
So we have a numerator of one.
And denominator of five times two which equals ten.
Now there are several ways to show this simplifying.
Here I show it using prime factors.
A lot of time you'll see this simplifying in this form here.
Well if we recognized as a common factor of four between four and eight.
And there's one four in four and two four's in eight.
We can simplify the four to a one.
And the eight to a two.
Notice in this form when we multiply.
The product will already be in lowest terms. One times one equals one.
And two times five equals ten.
And of course we can show the same simplifying
in this form here.
By simplifying this four to a one.
And this eight to a two.
I hope you found this helpful.