So this part, the integer part, is 3 and the fraction part is 17 40.

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So let me just write the fraction.

Well an improper fraction is a fraction where the numerator is larger than the denominator.

Enter the numerator of your result

Enter the denominator of your result

Maximal Main Denominator

We're going to use partial fraction expansion.

We're just multiplying two fractions where the denominator in the first one is the same as the numerator in the second one.

Let's start with the fraction 1 2.

This is just times dx.

You can imagine, the denominator tells us

Let's start with a fraction 5 12.

And what's an improper fraction?

This is the partial fraction decomposition.

We've already seen that the fraction 2 5, or fractions

This right over here is larger. So this is the larger.

And what fraction of them are pink?

This is equivalent to 9 4 times the reciprocal of this.

So let's just multiply by the reciprocal.

Let's make this the numerator.

Let's say I had the fraction 1 2.

This expression right here is a transformation of a.

And then, is equal to and then they just simplify this fraction.

But how many of these ninths do we have shaded in? Well we have one, two, three, four shaded in.

So we have to convert this to a percent, and the easiest thing to do is to first convert it into a decimal, so

Now, whenever you're dividing any fractions, you just have to remember that dividing by a fraction is the same thing as multiplying by its reciprocal.

But remember, the sections have to be equal sections.

Pride goes before destruction, and a haughty spirit before a fall.

Pride goeth before destruction, and an haughty spirit before a fall.

They're the exact same fraction, if you want to view it that way.

This right over here is smaller.

This is the exact same fraction of the entire model over here.

Let's rewrite this, so it's nice and big.

Because now we can rewrite this whole expression as the

And then we have this in the numerator.

So let's say I had the fraction 3 5.

And this fraction already is over 12 so we don't have to change it

Improper fractions have a numerator larger than the denominator.

And you might be saying, wait, wait, if I gave five out of the five equal sections shaded in, if I have 5 5 shaded in, I've got the whole thing shaded in. And you would be absolutely right. 5 5 is equal to the whole.

So 4 6 of this figure is shaded in. Let's go over here.

We were able to separate this out and do it pretty straightforward, because in this situation, the fraction part that we're subtracting from the other fraction part was smaller.

Let's see if we can learn a thing or two about partial fraction expansion, or sometimes it's called partial fraction decomposition.

He who loves disobedience loves strife. One who builds a high gate seeks destruction.

Before destruction the heart of man is proud, but before honor is humility.