An Alternative Algorithm for Subtraction

In the previous posts, I have shared to you an alternative algorithm for multiplication and division. In this post, I am going to share with you a different algorithm for performing subtraction. This algorithm does not involve “borrowing” from a higher place value but subtracts individual digits. To illustrate this algorithm, let’s consider some examples.

Example 1: 847 – 728

First, we separate the digits of the numbers as shown below.

Second, we subtract the corresponding digits.   Continue reading

Euclidean Algorithm Explained for Elementary School

In number theory, the Euclidean algorithm is a method for getting the greatest common factor (GCF) or highest common factor (HCF) of two positive integers. It is usually used for larger numbers since prime factorization can be used to get the greatest common factor of small numbers. Many students are confused with this method, but if you look at it closely, even elementary students can actually do it.

Let us start with an example. Note that in the discussion below, we will use the terms dividend and divisor. In the division a ÷ b, a is the dividend and b is the divisor.  Continue reading

The Mystery of the Four Consecutive Numbers in the Fibonacci Sequence

The Fibonacci Sequence

The Fibonacci sequence is the sequence of integers 0, 1, 1, 2, 3, 5, 8, 13, 21,…  or 1, 1, 2, 3, 5, 8, 13, 21, …  It is a sequence of numbers that starts with 0 (or 1) and  each number is the sum of the previous two. The sequence first appeared in Liber Abaci, a book written by Leonardo of Pisa, more popularly known as Fibonacci.

fibonacci sequence

The sequence appear in many branches as well as in many form. Take for instance the rectangle above. You can create  a rectangle whose sides are consecutive numbers of the Fibonacci Sequence. The Fibonacci Sequence also appears in the Pascal’s Triangle. Continue reading

What are prime gaps and who is Yitang Zhang?

You have probably read a news about one professor proving The Prime Gap conjecture. In this post, I will give you an overview of what the excitement is all about in the mathematics community.

Prof. Yitan Zhang (courtesy of UNH via Slate.com)

This post is written for the high school students and those who are interested in mathematics that are non mathematics majors.

What are Prime Numbers?

Most of us are familiar with prime numbers. A prime number is a positive integer that is divisible only by 1 and itself.  The number 5 is a prime number, while 8 is not prime because 8 is divisible by 2 and 4. If we examine the 10 positive integers, it is easy to see that only four are prime numbers: 2, 3, 5 and 7. In the figure below, shown are the prime numbers less than 100. Continue reading

4 Types of Composite Numbers You Probably Have Not Heard Of

There are numbers that are named because of their special characteristics. Prime numbers for example are unique because they only have two factors, 1 and itself.  Composite numbers, on the other hand, have more than two factors.

composite numbers
Speaking of composite numbers, there are different types of such numbers that you probably have not heard of. In this post, we familiarize ourselves with these types of numbers. Continue reading

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