## Guest Post: Why Study Algebra

Many students who begin learning Algebra and even the ones who have spent many years learning Algebra have a common question: Why study this? Where will this be used? Why are there letters like $x, y, z$ used instead of numbers in Math?  In this article we will try to address this question.

We all directly or indirectly use Algebra in our everyday life and most of the times unknowingly. For those who have spent some years with algebra will find $k \times xy$ too algebraic but immediately recognize  $\frac{1}{2} \times b \times h$ as the formula for the area of a triangle. Though one can see that conceptually both the expressions are identical (with one constant and two variables) and algebraic, one instantly connects with the usefulness of an expression or a formula than its abstract counterpart. » Read more

## A Mathematical Response to Senator Sotto’s Claims on PH’s Population

The Philippines is not overpopulated according to Senator Tito Sotto.  In this post, I am going to use mathematics to explain why I think otherwise. This post is an example on how to use mathematics in real life, in particular,  to support arguments. It is intended for elementary school and middle school students.

image via Wikipedia

Senator Sotto: “The Philippines is not overpopulated.”

Fact: There are 196 countries in the world and the Philippines is the 12th in terms of population. This  means that it is  on the top 7% of most populated countries. This is despite the country’s small land area compared to the most populated countries. In the table above, seven of the top 15 countries are also in the top 15 largest countries in terms of area.  As you can see, relative to other countries, the Philippines is quite overpopulated. » Read more

## The Mathematics of Leap Years Explained

Year 2016 is a leap year!.  The years 2000, 2004, 2008 and 2012 are leap years too, so you probably see the pattern that the years divisible by 4 are leap years. Now, is this always true?

The answer is NO. The years 1900, 2100, 2200, and 2300 are divisible by 4, but they are not leap years. Uhm, are all years  divisible by 100 not leap years?

The answer is still no. The years 1600, 2000 and 2400 are divisible by 100, but are leap years.

If you are a little bit confused, examine the GB Leap Year Test (wink) diagram below.

As we can see, if a year is divisible by 4 and not divisible by 100, then we are sure that it is a leap year. So, 1924, 1936, 2028 are leap years (Can you give four more examples?).

Now, if a year is divisible by 100, we are not sure if it is a leap year yet; we need to test if it is divisible by 400.  If it is divisible by 400, then, it is a leap year, otherwise, it is not. So, 1700, 1800, and 1900 are not leap years, but 1600 and 2000 are leap years.

We can summarize the discussion above as follows.

• Years that are divisible by 4 and not divisible by 100 are leap years.
• Years that are divisible by 100 but not divisible by 400 are NOT leap years.
• Years that are divisible by 400 are leap years. » Read more