### Video Transcript

Area a is two-fifths square
metres. Area b is 415 square
decimetres. Express the ratio of areas a to
b in its simplest form.

Let’s start by noticing that
the areas are given in different units. The area of a is given in
square metres. And the area of b is given in
square decimetres. We will need to convert these
into the same unit. But let’s start by looking at
area a. It will be good if we could
write the fractional value of two-fifths as a decimal. We can recall that one-fifth is
equal to 0.2. So two-fifths must be
equivalent to double that, which is 0.4. So two-fifths of a square metre
is equal to 0.4 square metres. Area b is given as 415 square
decimetres. So we will need to use a
conversion between square metres and square decimetres. And that is that one square
metre is equal to 100 square decimetres.

So let’s change our area a in
square metres into square decimetres. To do this, we take our value
of 0.4. And we multiply it by 100,
giving us 40. So now, we can say that area a
is equivalent to 40 square decimetres. The question then asks us to
express these areas as a ratio, with a first and then b. So we write our values of 40 to
415. And we don’t worry about units
in a ratio. Now, we need to see if we can
write this ratio in a simpler form. We can notice that since 40
ends in zero and 415 ends in five, then both of these numbers must be divisible
by five. So dividing both sides of our
ratio by five will give us eight to 83. Since we can’t simplify this
any further, this will be our final answer.