Open your books to page 70 and see the blue box on the lower part.
This is about the relationship and the ways of notation of'improper fractions' and 'mixed numbers.'
<We are moving on to page 71.>
You practiced a lot about converting an improper fraction to a mixed number when you were a elementary student. Didn't you?
As you already know, writing a whole or mixed number is different from reducing. But nobody will deny it is more convenient to reduce an improper fraction to lowest terms right before he converts the fraction to a mixed number.

Actually, I have to confess that I didn't reduce improper numbers when I converted them to mixed numbers when I was young. I just thought I had to follow the order of the question. No problem says "reduce the followings to lowest terms and convert them to mixed numbers," right?
I was such a fool that I thought I was only a young boy and I had to do exactly what I was told.
Gochya! You're thinking what I'm thinking right? "Ernest was a fool~~~~." Oops! It hurts! Ha, ha!

Sto~~~p! No more pulling my leg~~~!

Now! Lets study the opposite operation. 'Writing a mixed number as an improper fraction.
Firstly, you have to multiply the denominator by the whole number, then we've got a product.
Secondly, add the numerator to the product. This sum becomes the numerator of the improper fraction that we're seeking for.
Lastly, The denominator of the improper fraction is the same as the denominator of the fractional part of the mixed number.

Here, don't duck away from what you have to do. I mean you have to study every step and get what it is.

Let's move on to page 72.

Here, we have one thing that is closely related to the fraction. That is decimal. As you already know of, all the fractions can be expressed by decimals, and vice versa.


How can we convert a decimal number to a fraction or mixed number in lowest terms?
Firstly, write all the digits of the decimal number without the decimal point. We're going to use the number as a numerator.
Secondly, once we have a numerator, we need a denominator. the denominator will be a power of 10 with as many zeros as there are places after the decimal point.
Finally, reduce if it is necessary, and if the fraction is improper, convert to a mixed number.

The most important thing when you are in the process is that you have to murmur every step with your own mouth. In this way, you can make yourself a proper teacher to teach your children in English.
It needs practice, which means you want some time to do this.

That's why I have to stop today.

Next time, I'm going to start with the 'tip' on the lower part of page 72.

Keep going!

Ernest