Let's see if we can write 0.15 as a fraction.
So the important thing here is to look at
what place these digits are in.
So this 1 right over here, this is in the tenths place.
So you could view that as 1 × 1/10.
This 5 right over here is in the hundredths place.
So you could view that as 5 × 1/100.
So if I were to rewrite this,
I can rewrite this as the sum of –
this 1 represents 1 × 1/10,
So that would literally be 1/10 – plus –
And this 5 represents 5 × 1/100.
So it would be plus 5/100.
And if we want to add them up,
if we want to find a common denominator –
(The common denominator is 100.)
Both 10 and –
[100] is the least common multiple.
[100] is a multiple of both 10 and 100.
So we can rewrite this as something over 100 plus something over 100.
This isn't going to change. This was already 5/100.
If we multiply the denominator here by 10 –
(That's what we did. We multiplied it by 10.)
– then we're going to have to multiply this numerator by 10.
And so this is the same thing as 10/100.
And now we're ready to add.
This is the same thing as 10 + 5, is 15/100.
And you could have done that
a little bit quicker just by inspecting this.
You would say, "Look!
My smallest place right over here is in the hundredths place."
Instead of calling this 1/10, I could call this literally 10/100.
Or, I could say this whole thing is 15 100ths.
And now if I want to reduce this to lowest terms,
we can – Let's see,
Both the numerator and the denominator are divisible by 5.
So let's divide them both by 5.
And so the numerator, 15, divided by 5 is 3.
The denominator, 100, divided by 5 is 20.
And that's about as simplified as we can get.